Hydrogen chloride gas (HCl) diffuses 1.8 times faster than an unknown gas. Determine the molar mass of the unknown gas. Show your work or explain your answer, giving specific values used to determine the answer.

PV=nRT

Explanation:

The molar mass of a gas can be derived from the ideal gas law, PV=nRT, by using the definition of molar mass to replace n, the number of moles.

Molar mass is defined as the mass of a substance occupied by exactly 6.022⋅1023 of that respective gas' atoms (or molecules). Since we know that 6.022⋅1023 represents Avogadro's number, and is the equivalent of 1 mole, we can describe molar mass as being equal to

M=mn, where

m - the gas' mass in grams;

n - the number of moles of gas;

We can therefore write that n=mM, which can be used in the ideal gas law equation to get the value of the gas' molar mass

PV=mM⋅RT⇒M=mRTPV, so

M=m⋅RTPV

Here's an example of how this would look in a problem:

An unknown gas has a mass of 153 g and occupies 15.0 L at a temperature of 300.0 K and a pressure of 2.00 atm. What is its molar mass