Ideal gas law Chemistry

Question

1) NH3 gas is pumped into the reservoir of a refrigeration unit at a pressure of 4.76 atm. The capacity of the reservoir is 17.1 L. The temperature is 2.24◦C. What is the mass of the gas?

2) How much helium gas would it take to fill a gas balloon with a volume of 1900 cm3 when the temperature is 50.0◦C and the atmospheric pressure is 737 mm Hg?

Answer 1

Hey Shaun. Thanks for your question.

For both of these questions, you'll want to use the equation PV = nRT, the ideal gas equation, where P is pressure (in atm), V is volume (in liters), n is the number of moles of a gas, R is the ideal gas constant, and T is the temperature (in Kelvin).

1) PV = nRT

4.76 atm * 17.1 L = n * 0.0821 * (273.15 + 2.24),

so n = (4.76 * 17.1) / (0.0821 * 275.39) = 3.6 mol of NH3. BUT the question asks for the mass, so we must convert that number of moles to mass. The molar mass of NH3 is 17.031 g.

3.6 * 17.031 = 61.3 g of NH3

2) PV = nRT

Here, we need to convert volume from cubic cm to liters, which is a simple conversion. 1L = 1,000 cubic cm, so 1900 cubic cm = 1.9L. We also need to convert mmHg to atm. 760mmHg = 1 atm so 737mmHg = 0.97 atm From there, same procedure as before.

0.97 atm * 1.9 L = n * 0.0821 * (273.15 + 50)

n = (0.97 * 1.9) / (0.0821 * 323.15)

n = 0.069 mol of He

Molar mass of He₂ (helium is a diatomic gas) = 8.006 g

0.069 * 8.006 = 0.56 g of He₂.

Hope this helps!