Using the ideal gas law to calculate the molar mass

Using the ideal gas law to calculate the molar mass

Using the ideal gas law to calculate the molar mass

08/26/16

“How can we use the ideal gas law to calculate the molar mass of an object?”

During a student’s course in Chemistry, they will probably realize that the ideal gas equation is one of the most useful equations in the entire subject. However, is it possible to use this equation to do more, such as calculate the density of a gas? Well, let’s use our mathematical skills to find out. We know of course that the ideal gas equation is PV=nRT, with P being the Pressure in atm, V being the volume of the gas, n being the number of moles, and T being the temperature. Now, there seems to be no appearance of density anywhere in this equation, but let’s take a closer look at the value n. Since n is the number of moles in an object, we can use the molar mass equation to derive that n = mass/(M), with M being the molar mass. However, we still do not have density in our equation, but could we go any further? Well, it turns out that density is mass per volume, so mass can be represented as density times volume (rho*v). By substituting these value back into the ideal gas law, we can obtain PV=(rho*V/M)*RT, and after doing a bit of rearranging we will be obtain rho = M*P/(R*T).

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