{"id":59551,"date":"2016-04-01T13:07:57","date_gmt":"2016-04-01T11:07:57","guid":{"rendered":"http:\/\/wpcalc.com\/?p=59551"},"modified":"2026-09-28T14:34:15","modified_gmt":"2026-09-28T11:34:15","slug":"molecular-mass-using-gmv-law","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/molecular-mass-using-gmv-law\/","title":{"rendered":"Molecular Mass Calculator (GMV Law)"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Molecular Mass (GMV Law) Calculator<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"59551\" data-favorite-title=\"Molecular Mass (GMV Law)\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/molecular-mass-using-gmv-law\/\" data-favorite-excerpt=\"Estimate a gas\u2019s molar mass from its density relative to hydrogen. Enter the Density of Gas and Density of Hydrogen in g\/L to calculate vapour density and molecular mass.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-chemistry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/chemistry\/molecular-mass-using-gmv-law\/\" method=\"POST\" class=\"calculator\" id=\"calculator-59551\" data-post=\"59551\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Density of Gas<\/label><input type=\"number\" name=\"density_of_gas\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" placeholder=\"e.g. 2.5\" step=\"any\" value=\"2.5\"\/><div class=\"unit\" id=\"calc-unit-1\">g\/L<\/div><small id=\"calc-info-1\">Mass per unit volume of the gas<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Density of Hydrogen<\/label><input type=\"number\" name=\"density_of_hydrogen\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" placeholder=\"e.g. 0.08988\" step=\"any\" value=\"0.08988\"\/><div class=\"unit\" id=\"calc-unit-2\">g\/L<\/div><small id=\"calc-info-2\">Standard density of hydrogen gas at STP<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"59551\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Vapour Density<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Molecular Mass<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" 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aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused 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border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Molecular Mass (GMV Law) Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ D_{\\mathrm{H_2}}=\\frac{\\rho_{\\mathrm{gas}}}{\\rho_{\\mathrm{H_2}}} \\]\n\\[ M_{\\mathrm{gas}}\\approx D_{\\mathrm{H_2}}\\times 2\\ \\mathrm{g\/mol} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(D_{\\mathrm{H_2}}\\) \u2014 vapour density relative to hydrogen (no units).<\/li>\n<li>\\(\\rho_{\\mathrm{gas}}\\) \u2014 density of the gas (g\/L).<\/li>\n<li>\\(\\rho_{\\mathrm{H_2}}\\) \u2014 density of hydrogen gas, \\(\\mathrm{H_2}\\), under the same conditions (g\/L).<\/li>\n<li>\\(M_{\\mathrm{gas}}\\) \u2014 estimated molar mass of the gas (g\/mol).<\/li>\n<\/ul>\n<p>The density ratio compares equal volumes of the two gases at the same temperature and pressure. The factor of \\(2\\ \\mathrm{g\/mol}\\) approximates the molar mass of hydrogen gas, so the result is an estimate rather than an exact molar mass.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Molecular Mass (GMV Law) \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> A gas has a density of 2.5 g\/L. Use the default hydrogen density of 0.08988 g\/L.<\/p>\n<p>\\[ D_{\\mathrm{H_2}}=\\frac{2.5\\ \\mathrm{g\/L}}{0.08988\\ \\mathrm{g\/L}}\\approx 27.8149 \\]<\/p>\n<p>\\[ M_{\\mathrm{gas}}\\approx\\frac{2.5}{0.08988}\\times 2\\ \\mathrm{g\/mol}\\approx 55.6297\\ \\mathrm{g\/mol} \\]<\/p>\n<p><strong>Result:<\/strong> Vapour density is 27.8149, and estimated molecular mass is 55.6297 g\/mol.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the sample\u2019s density in <strong>Density of Gas<\/strong>, in g\/L. The default is 2.5 g\/L.<\/li>\n<li>Enter the density of hydrogen gas in <strong>Density of Hydrogen<\/strong>, also in g\/L. The default is 0.08988 g\/L, a commonly used approximate value at standard temperature and pressure (STP).<\/li>\n<li>Read <strong>Vapour Density<\/strong> as a unitless ratio: it tells you how many times as dense the sample is as hydrogen under matching conditions.<\/li>\n<li>Read <strong>Molecular Mass<\/strong> as the estimated molar mass in g\/mol. Both inputs must be greater than zero; otherwise, the calculator reports \u201cInvalid input.\u201d<\/li>\n<\/ol>\n<h2>What vapour density tells you about molecular mass<\/h2>\n<p>Here, vapour density means density <em>relative to hydrogen<\/em>, not the gas\u2019s density in g\/L. A vapour density of 27.8149 means the gas is about 27.8149 times as dense as hydrogen when equal volumes are compared at the same temperature and pressure. Because both densities use g\/L, their units cancel in the ratio.<\/p>\n<p>The connection to molar mass comes from the gram-molecular volume principle: at the same temperature and pressure, equal volumes of ideal gases contain equal numbers of molecules. A denser gas therefore has more mass per molecule, in the same proportion as its density relative to hydrogen. Multiplying that ratio by hydrogen\u2019s approximate molar mass of 2 g\/mol gives the estimated molar mass of the sample. Hydrogen in this comparison is molecular hydrogen, \\(\\mathrm{H_2}\\), not a single hydrogen atom.<\/p>\n<p>The calculator labels the answer \u201cMolecular Mass\u201d and expresses it in g\/mol; more precisely, g\/mol is a unit of <em>molar mass<\/em>. The relative molecular mass of a molecule is unitless and is approximately the same numerical value. The result can help you assess a proposed chemical formula, but one density measurement cannot establish a gas\u2019s identity: different substances can have similar molar masses.<\/p>\n<h2>Assumptions and practical limits<\/h2>\n<ul>\n<li><strong>Match the conditions.<\/strong> Gas density changes with temperature and pressure. Use a hydrogen density measured or specified at the same temperature and pressure as the sample. Do not combine a sample measured under room conditions with the default STP hydrogen density without adjusting the conditions.<\/li>\n<li><strong>Keep the units consistent.<\/strong> Both density entries must use g\/L. If your measurements use other units, convert both before entering them.<\/li>\n<li><strong>Treat the answer as approximate.<\/strong> The calculation uses 2 g\/mol for hydrogen rather than its more precise molar mass of about 2.016 g\/mol. Real-gas behavior and measurement uncertainty can also affect the density ratio.<\/li>\n<li><strong>Consider the sample.<\/strong> A mixture gives an effective average molar mass, not the molar mass of each component. Impurities, moisture, and incomplete vaporization can make a measured gas density misleading.<\/li>\n<\/ul>\n<p>If your gas and hydrogen densities refer to different conditions, use the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/combined-gas-law\/\">Combined Gas Law calculator<\/a> to examine temperature, pressure, and volume changes. For a calculation based on measured pressure, volume, temperature, and amount of gas, see the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/ideal-gas-law\/\">Ideal Gas Law calculator<\/a>. Once you have a possible chemical formula, the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/atomic-mass\/\">Atomic Mass calculator<\/a> can help you compare it with the estimated molar mass.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Estimate a gas\u2019s molar mass from its density relative to hydrogen. Enter the Density of Gas and Density of Hydrogen in g\/L to calculate vapour density and molecular mass.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[54],"tags":[56],"class_list":["post-59551","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-stoichiometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=59551"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59551\/revisions"}],"predecessor-version":[{"id":65410,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59551\/revisions\/65410"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=59551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=59551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=59551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}