Problem 56353. Convert Volume Mixing Ratio to Density

Created by Meg Noah

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The partial pressure of a constituent gas species of the atmosphere can be expressed in parts per million by volume.  For example, the amount of carbon dioxide in the atmosphere is about 400 ppm.  </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a script that takes as input parameters the air parcel characteristics at some altitude above ground:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Observed Temperature of Air in K</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Observed Pressure of Air in mb</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The (string) name of the gas consituent</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The parts per million (by volume) of the gas consituent</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>and outputs:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The density of the gas consituent (in mg/m^3)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If the input gas name is 'DRY_AIR' and the partial pressure in PPMV is 1e6 (all the particles), the output will be the mass density of the air (roughly, since there are slight changes for humidity).  For other molecules, such as CO2 (carbon dioxide) or O3 (ozone), the value is the mass density of those consituents of the atmosphere. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>To make the conversion, first find the molecular density (molecules/cm3) of air (mix of all gases N2, O2, etc.) for the given temperature and pressure.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The molecular density (also known as the number density) of air can be found from the Temperature and Pressure using the ideal gas law.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>N_{air}=\\frac{P}{RT}=N_0\\frac{P}{P_0}\\frac{T_0}{T}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>using Loschmidt’s number STP:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>N_0 = 2.6867811\\times10^{19} (\\text{molecules/cm}^{3}\\text{ at STP (NIST)}) </w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>And STP Temperature and Pressure:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>T_0 = 273.15 \\text{K}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>P_0 = 1013.25 \\text{ mb}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Convert the molecular density to the mass density by multiplying</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\rho_{air}=\\frac{M_{gas}}{N_A}\\frac{PPMV}{1\\times10^6}N_{air}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>using Avagadro's number:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>N_A = 6.022140857\\times10^{23} (\\text{molecules/mole (NIST)})</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>and </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>M_{gas}</w:t></w:r></w:customXml><w:r><w:t>=the molar mass (g/mole) of the molecule.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The molar mass of ozone ('O3') is 47.9982.  The molar mass of carbon dioxide ('CO2') is 44.010.  The function template has a lookup table of common atmosphere gas constituents.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 950.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 475.375px; transform-origin: 407px 475.375px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; "><span style="">The partial pressure of a constituent gas species of the atmosphere can be expressed in parts per million by volume.  For example, the amount of carbon dioxide in the atmosphere is about 400 ppm.  </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.5px 8px; transform-origin: 330.5px 8px; unicode-bidi: normal; "><span style="">Write a script that takes as input parameters the air parcel characteristics at some altitude above ground:</span></span></div><ul style="block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; "><li style="background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; "><span style="">Observed Temperature of Air in K</span></span></li><li style="background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 99px 8px; transform-origin: 99px 8px; unicode-bidi: normal; "><span style="">Observed Pressure of Air in mb</span></span></li><li style="background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 124.5px 8px; transform-origin: 124.5px 8px; unicode-bidi: normal; "><span style="">The (string) name of the gas consituent</span></span></li><li style="background-position-x: 0px; background-position-y: 50%; block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 171.5px 8px; transform-origin: 171.5px 8px; unicode-bidi: normal; "><span style="">The parts per million (by volume) of the gas consituent</span></span></li></ul><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; "><span style="">and outputs:</span></span></div><ul style="block-size: 20.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2167px; transform-origin: 391px 10.2167px; margin-top: 10px; margin-bottom: 20px; "><li style="background-position-x: 0px; background-position-y: 50%; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="background-position-x: 0%; background-position-y: 0%; block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; "><span style="">The density of the gas consituent (in mg/m^3)</span></span></li></ul><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; "><span style="">If the input gas name is 'DRY_AIR' and the partial pressure in PPMV is 1e6 (all the particles), the output will be the mass density of the air (roughly, since there are slight changes for humidity).  For other molecules, such as CO2 (carbon dioxide) or O3 (ozone), the value is the mass density of those consituents of the atmosphere. </span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.5px 8px; transform-origin: 382.5px 8px; unicode-bidi: normal; "><span style="">To make the conversion, first find the molecular density (molecules/cm3) of air (mix of all gases N2, O2, etc.) for the given temperature and pressure.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; "><span style="">The molecular density (also known as the number density) of air can be found from the Temperature and Pressure using the ideal gas law.</span></span></div><div style="block-size: 41px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.5px; text-align: left; transform-origin: 384px 20.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" style="width: 129.5px; height: 41px;" width="129.5" height="41"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.5px 8px; transform-origin: 99.5px 8px; unicode-bidi: normal; "><span style="">using Loschmidt’s number STP:</span></span></div><ul style="block-size: 21.7167px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.8583px; transform-origin: 391px 10.8583px; margin-top: 10px; margin-bottom: 20px; "><li style="background-position-x: 0px; background-position-y: 50%; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.8583px; text-align: left; transform-origin: 363px 10.8583px; white-space: pre-wrap; margin-left: 56px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 328.5px; height: 21px;" width="328.5" height="21"></span></li></ul><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 116.5px 8px; transform-origin: 116.5px 8px; unicode-bidi: normal; "><span style="">And STP Temperature and Pressure:</span></span></div><ul style="block-size: 43.4333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 21.7167px; transform-origin: 391px 21.7167px; margin-top: 10px; margin-bottom: 20px; "><li style="background-position-x: 0px; background-position-y: 50%; block-size: 21.7167px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.8583px; text-align: left; transform-origin: 363px 10.8583px; white-space: pre-wrap; margin-left: 56px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 87px; height: 20px;" width="87" height="20"></span></li><li style="background-position-x: 0px; background-position-y: 50%; block-size: 21.7167px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.8583px; text-align: left; transform-origin: 363px 10.8583px; white-space: pre-wrap; margin-left: 56px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 103.5px; height: 20px;" width="103.5" height="20"></span></li></ul><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.5px 8px; transform-origin: 201.5px 8px; unicode-bidi: normal; "><span style="">Convert the molecular density to the mass density by multiplying</span></span></div><div style="block-size: 40px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20px; text-align: left; transform-origin: 384px 20px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" style="width: 138.5px; height: 40px;" width="138.5" height="40"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; "><span style="">using Avagadro's number:</span></span></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 312px; height: 21px;" width="312" height="21"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; "><span style="">and </span></span></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 29px; height: 20px;" width="29" height="20"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132px 8px; transform-origin: 132px 8px; unicode-bidi: normal; "><span style="">=the molar mass (g/mole) of the molecule.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; "><span style="">The molar mass of ozone ('O3') is 47.9982.  The molar mass of carbon dioxide ('CO2') is 44.010.  The function template has a lookup table of common atmosphere gas constituents.</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; "></span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; "><span style=""></span></span></div></div></div>

The partial pressure of a constituent gas species of the atmosphere can be expressed in parts per million by volume.  For example, the amount of carbon dioxide in the atmosphere is about 400 ppm.  
Write a script that takes as input parameters the air parcel characteristics at some altitude above ground:
Observed Temperature of Air in K
Observed Pressure of Air in mb
The (string) name of the gas consituent
The parts per million (by volume) of the gas consituent
and outputs:
The density of the gas consituent (in mg/m^3)
If the input gas name is 'DRY_AIR' and the partial pressure in PPMV is 1e6 (all the particles), the output will be the mass density of the air (roughly, since there are slight changes for humidity).  For other molecules, such as CO2 (carbon dioxide) or O3 (ozone), the value is the mass density of those consituents of the atmosphere. 
To make the conversion, first find the molecular density (molecules/cm3) of air (mix of all gases N2, O2, etc.) for the given temperature and pressure.
The molecular density (also known as the number density) of air can be found from the Temperature and Pressure using the ideal gas law.

using Loschmidt’s number STP:

And STP Temperature and Pressure:

Convert the molecular density to the mass density by multiplying

using Avagadro's number:

and 
=the molar mass (g/mole) of the molecule.
The molar mass of ozone ('O3') is 47.9982.  The molar mass of carbon dioxide ('CO2') is 44.010.  The function template has a lookup table of common atmosphere gas constituents.

Solve

Solution Stats

197 Solutions
50 Solvers

Last Solution submitted on May 29, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Vlad Tkachuk on 9 Mar 2023

The point of this problem is to find out that the last formula, given in the problem statement, cannot be copied to the program as is.

Solution Comments

Show comments

Problem Recent Solvers50

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 56353. Convert Volume Mixing Ratio to Density

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers50

Suggested Problems

More from this Author10

Problem Tags

Community Treasure Hunt

Problem 56353. Convert Volume Mixing Ratio to Density

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers50

Suggested Problems

More from this Author10

Problem Tags

Community Treasure Hunt

Players