Special Applications of the Ideal Gas Law

Using the Ideal Gas Law to Calculate Molar Mass

The ideal gas law can be used to calculate molar mass of a gas. This only requires that you do a little bit of math and thinking to make the appropriate substitutions. Start by thinking about the definition or formula for calculating molar mass. You already know that molar mass is defined as the mass in grams of one mole of a substance. Now, write this as an equation: $LaTeX: MM=\frac{m}{n}$

How does this relate to the ideal gas law?

We can see that moles is already a part of this equation. So, solving for moles will allow us to determine the molar mass of a gas if the mass of the sample is given.

Using the Ideal Gas Law to Calculate Density

The ideal gas law can also be used to calculate density of a gas. Let's begin as we did above, by recalling the definition or formula, in this case for density. $LaTeX: d=\frac{m}{v}$

Gas densities depend on molecular mass, so let's see if we can write a formula for calculating the density of a gas. Let's write down the ideal gas law and the formula for molar mass. $LaTeX: PV=NRT \hspace{.5in} MM=\frac{m}{n}$

Don't go past the following explanation thinking that you will just save time and skip ahead to the formula below. You will often be required to derive your own formula using simple equations such as these. It is important that you practice making such substitutions.

$Write a new formula for calculating the density of a gas. Start with what you are trying to solve for, density. Now, look for ways to make substitutions for m and V. d=m/ V The molar mass formula will allow you to solve for m. MM=m/n becomes (MM)n=m n The ideal gas law will allow you to solve for PV = nRT becomes V. = nRT/Р Now, substitute these into the density equation above. d= m/V becomes d = (MM)n /nRT/P Now, simplify this equation. Since there is a fraction in the denominator, multiply by the reciprocal to simplify. d=(MM)n (P/nRT) Cancel out any common terms.s d= MMPn(P/nRT) becomes d=MMP/RT$

The equation derived above can also be used to calculate molar mass, given density. Rearrange the equation to solve for molar mass.

Answer: $LaTeX: MM=\frac{Rtd}{P}$

Remember to work on the module practice problems as you complete each section of content.

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