{"id":66537,"date":"2026-10-07T08:29:54","date_gmt":"2026-10-07T05:29:54","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66537"},"modified":"2026-10-13T12:15:52","modified_gmt":"2026-10-13T09:15:52","slug":"van-der-waals-equation-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/van-der-waals-equation-calculator\/","title":{"rendered":"Van der Waals Equation Calculator"},"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\">Estimate Real-Gas Pressure from the Van der Waals Equation<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66537\" data-favorite-title=\"Van der Waals Equation\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/van-der-waals-equation-calculator\/\" data-favorite-excerpt=\"Calculate the real-gas pressure from the Van der Waals equation. Enter the amount of gas, volume, temperature and the constants a and b to get the pressure, compressibility factor Z and the deviation from the ideal-gas law.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-wind-2\">\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\/van-der-waals-equation-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66537\" data-post=\"66537\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Amount of Gas (n)<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"amount_of_gas_n\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"mol\" selected>mol<\/option><option value=\"mmol\">mmol<\/option><option value=\"kmol\">kmol<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-1\">Number of moles of the gas<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Volume (V)<\/label><div class=\"term\">V<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"volume_v\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"L\" selected>L<\/option><option value=\"mL\">mL<\/option><option value=\"m3\">m\u00b3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Volume of the container holding the gas<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Temperature (T)<\/label><div class=\"term\">T<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"temperature_t\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 300\" min=\"0\" value=\"300\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"K\" selected>K<\/option><option value=\"C\">\u00b0C<\/option><option value=\"F\">\u00b0F<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Absolute temperature of the gas<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-7\">Attraction Constant (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"attraction_constant_a\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1.3708\" min=\"0\" value=\"1.3708\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"barL2\" selected>L\u00b2\u00b7bar\/mol\u00b2<\/option><option value=\"atmL2\">L\u00b2\u00b7atm\/mol\u00b2<\/option><option value=\"Pam6\">Pa\u00b7m\u2076\/mol\u00b2<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Van der Waals a \u2014 1.3708 L\u00b2\u00b7bar\/mol\u00b2 is nitrogen (N\u2082)<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-9\">Co-Volume Constant (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"covolume_constant_b\" id=\"field-9\" aria-describedby=\"calc-info-9\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.0387\" min=\"0\" value=\"0.0387\"\/><div class=\"grid grid-cols-1\"><select id=\"field-10\" name=\"unit\" aria-label=\"Unit\"><option value=\"Lmol\" selected>L\/mol<\/option><option value=\"cm3mol\">cm\u00b3\/mol<\/option><option value=\"m3mol\">m\u00b3\/mol<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-9\">Van der Waals b \u2014 0.0387 L\/mol is nitrogen (N\u2082)<\/small><\/div><div class=\"field is-single\" id=\"input-6\"><label for=\"field-11\">Pressure Unit for Results<\/label><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"pressure_unit_for_results\"><option value=\"atm\" selected>atm<\/option><option value=\"bar\">bar<\/option><option value=\"kPa\">kPa<\/option><option value=\"MPa\">MPa<\/option><option value=\"psi\">psi<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66537\">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> Pressure Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Real-Gas Pressure<\/span><span class=\"result-term\">P<\/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>Compressibility Factor Z<\/span><span class=\"result-term\">Z<\/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 class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Deviation from Ideal-Gas Pressure<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"%\"><\/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-4\"><span class=\"field-title\"><span>Molar Volume<\/span><span class=\"result-term\">V\/n<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"L\/mol\"><\/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 is-column\" id=\"output-5\"><span class=\"field-title\"><span>Calculation Details<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66537\" aria-live=\"polite\" 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text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/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=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md 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>Van der Waals Equation 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\\[ \\left(P + a\\frac{n^2}{V^2}\\right)(V - nb) = nRT \\quad\\Longleftrightarrow\\quad P = \\frac{nRT}{V - nb} - a\\left(\\frac{n}{V}\\right)^2 \\\\\\ Z = \\frac{PV}{nRT} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(P\\) \u2014 pressure of the real gas<\/li>\n<li>\\(n\\) \u2014 amount of gas (mol)<\/li>\n<li>\\(V\\) \u2014 volume of the container (L)<\/li>\n<li>\\(T\\) \u2014 absolute temperature (K)<\/li>\n<li>\\(R\\) \u2014 gas constant, \\(0.082057\\ \\text{L\u00b7atm\/(mol\u00b7K)}\\)<\/li>\n<li>\\(a\\) \u2014 attraction constant, correcting for intermolecular attractions<\/li>\n<li>\\(b\\) \u2014 co-volume constant, correcting for the finite size of molecules<\/li>\n<li>\\(Z\\) \u2014 compressibility factor (\\(Z = 1\\) for an ideal gas)<\/li>\n<\/ul>\n<p>The equation modifies the ideal gas law with two correction terms: the \\(a\\) term lowers the pressure because molecules attract each other, and the \\(b\\) term raises it because the molecules themselves take up space that is not available for movement.<\/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>Van der Waals Equation \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> 1 mol of nitrogen (N\u2082) in a 10 L container at 300 K. For nitrogen, \\(a = 1.3708\\ \\text{L\u00b2\u00b7bar\/mol\u00b2}\\) and \\(b = 0.0387\\ \\text{L\/mol}\\). Converting \\(a\\) to L\u00b2\u00b7atm\/mol\u00b2 gives \\(a = 1.3708 \\times 0.986923 = 1.3529\\ \\text{L\u00b2\u00b7atm\/mol\u00b2}\\).<\/p>\n<p>\\[ P = \\frac{1 \\times 0.082057 \\times 300}{10 - 1 \\times 0.0387} - 1.3529 \\times \\left(\\frac{1}{10}\\right)^2 = \\frac{24.6171}{9.9613} - 0.01353 \\\\[\/p]<\/p>\n<p>\\[ P = 2.4713 - 0.0135 = 2.4578\\ \\text{atm} \\\\[\/p]<\/p>\n<p><strong>Result:<\/strong> the real-gas pressure is <strong>P = 2.4578 atm<\/strong> (about 2.4900 bar or 248.98 kPa). The ideal gas law would give 2.4617 atm, so the real pressure is 0.16% lower. The compressibility factor is Z = 0.9984 and the molar volume is 10 L\/mol.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Amount of Gas (n)<\/strong> and choose the unit (mol, mmol or kmol).<\/li>\n<li>Enter the <strong>Volume (V)<\/strong> of the container and select L, mL or m\u00b3.<\/li>\n<li>Enter the <strong>Temperature (T)<\/strong>; you can type it in K, \u00b0C or \u00b0F and the calculator converts it to kelvin.<\/li>\n<li>Enter the <strong>Attraction Constant (a)<\/strong> for your gas. The default 1.3708 L\u00b2\u00b7bar\/mol\u00b2 is nitrogen; the unit can be L\u00b2\u00b7bar\/mol\u00b2, L\u00b2\u00b7atm\/mol\u00b2 or Pa\u00b7m\u2076\/mol\u00b2.<\/li>\n<li>Enter the <strong>Co-Volume Constant (b)<\/strong> in L\/mol, cm\u00b3\/mol or m\u00b3\/mol. For nitrogen it is 0.0387 L\/mol.<\/li>\n<li>Pick the <strong>Pressure Unit for Results<\/strong> \u2014 atm, bar, kPa, MPa or psi \u2014 and read the pressure, the compressibility factor Z, the percentage deviation from the ideal-gas pressure, the molar volume and a step-by-step calculation trace.<\/li>\n<\/ol>\n<h2>What Is the Van der Waals Equation?<\/h2>\n<p>The ideal gas law, \\(PV = nRT\\), assumes that gas molecules are point particles that do not interact. Real molecules, however, occupy a finite volume and attract one another. In 1873 Johannes Diderik van der Waals proposed a modified equation of state that accounts for both effects, an achievement recognized with the 1910 Nobel Prize in Physics. The equation was the first to describe why gases condense into liquids and remains the classic textbook model for real-gas behaviour.<\/p>\n<p>The correction \\(a(n\/V)^2\\) represents the internal pressure: molecules about to hit the wall are pulled back by their neighbours, so the observed pressure is lower than the ideal value. The constant \\(a\\) grows with the strength of intermolecular attractions and is largest for polar, easily condensable gases such as water and ammonia. The term \\(nb\\) subtracts the volume occupied by the molecules themselves, effectively shrinking the free space in which they can move; \\(b\\) is roughly four times the actual molecular volume per mole.<\/p>\n<p>Which correction dominates depends on the conditions. At moderate densities the attractions usually win and the real pressure is <em>lower<\/em> than the ideal-gas prediction. At very high densities the excluded volume takes over and the real pressure becomes <em>higher<\/em>. The compressibility factor \\(Z = PV\/nRT\\) summarizes this: \\(Z  1\\) means the finite molecular volume dominates, and \\(Z = 1\\) corresponds to ideal behaviour.<\/p>\n<h2>Constants for Common Gases<\/h2>\n<table>\n<thead>\n<tr>\n<th>Gas<\/th>\n<th>a (L\u00b2\u00b7bar\/mol\u00b2)<\/th>\n<th>b (L\/mol)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Helium (He)<\/td>\n<td>0.0346<\/td>\n<td>0.0238<\/td>\n<\/tr>\n<tr>\n<td>Nitrogen (N\u2082)<\/td>\n<td>1.3708<\/td>\n<td>0.0387<\/td>\n<\/tr>\n<tr>\n<td>Oxygen (O\u2082)<\/td>\n<td>1.382<\/td>\n<td>0.0319<\/td>\n<\/tr>\n<tr>\n<td>Methane (CH\u2084)<\/td>\n<td>2.300<\/td>\n<td>0.0430<\/td>\n<\/tr>\n<tr>\n<td>Carbon dioxide (CO\u2082)<\/td>\n<td>3.657<\/td>\n<td>0.0429<\/td>\n<\/tr>\n<tr>\n<td>Ammonia (NH\u2083)<\/td>\n<td>4.225<\/td>\n<td>0.0371<\/td>\n<\/tr>\n<tr>\n<td>Water (H\u2082O)<\/td>\n<td>5.537<\/td>\n<td>0.0305<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note that the table uses bar-based constants; switch the unit selector for <strong>a<\/strong> to L\u00b2\u00b7bar\/mol\u00b2 when using these values.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Constants are not truly constant.<\/strong> The tabulated \\(a\\) and \\(b\\) are fitted to experimental data and are most reliable at moderate pressures (roughly up to a few hundred bar). At extreme densities the equation becomes qualitative rather than quantitative.<\/li>\n<li><strong>Unreliable near condensation.<\/strong> Close to the critical point or in the two-phase region the equation can even predict a negative pressure or multiple volumes for one pressure. The calculator flags these cases with an error message instead of a number.<\/li>\n<li><strong>Best for small, non-polar molecules.<\/strong> Noble gases, nitrogen and oxygen are described well; strongly associating gases such as water vapour deviate more, especially near saturation.<\/li>\n<li><strong>The volume must exceed the co-volume.<\/strong> The term \\(V - nb\\) requires \\(V &gt; nb\\); otherwise the model has no solution, which the calculator reports explicitly.<\/li>\n<li><strong>When a = b = 0<\/strong> the equation reduces exactly to the ideal gas law, which is a quick way to sanity-check your inputs.<\/li>\n<\/ul>\n<p>If you are studying other gas-phase phenomena, you may also find the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/van-t-hoff-equation-calculator\/\">Van 't Hoff Equation Calculator<\/a> for temperature dependence of equilibrium constants, the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/grahams-law-calculator\/\">Graham's Law Calculator<\/a> for diffusion rates, or the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/clausius-clapeyron-calculator\/\">Clausius\u2013Clapeyron Calculator<\/a> for vapour pressure useful.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the real-gas pressure from the Van der Waals equation. Enter the amount of gas, volume, temperature and the constants a and b to get the pressure, compressibility factor Z and the deviation from the ideal-gas law.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[54],"tags":[55],"class_list":["post-66537","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-gases"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66537","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\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66537"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66537\/revisions"}],"predecessor-version":[{"id":67112,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66537\/revisions\/67112"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}