Chemistry - Gas Stoichiometry

Question

At STP a sample of gas with a mass of 20.5 grams occupies 6.20 L. What is the molar mass of this gas?

Answer 1

To solve this problem we must use the equation PV=nRT which is derived from the ideal gas law. In this equation, P is pressure, V is volume, n is moles of the gas, R is the gas constant, and T is temperature.

We can use the information given in the question to solve the moles of the gas (n), then determine the molar mass using moles (calculated) and grams (given in the question) of the gas.

STP stands for standard temperature and pressure. This is a temperature of 0 degrees Celsius (273 Kelvin) and 1 atm of pressure. The ideal gas constant is 0.082 (L*atm)/(mol*K)

To set up the equation to solve for n directly, we can divide both sides by (RT) to get:

n= (PV)/(RT)

Now, we can solve for n:

n= (PV)/(RT) = ((1atm)(6.20L)) / ((0.082(L*atm)/(mol*K))(273K)) = (6.20)/(22.39) = 0.277 moles gas

Now, using the moles and grams of the gas, we can determine the molar mass as follows:

molar mass= (g)/(mol) = 20.5g/0.277mol = 74.0 g/mol