Question

16 grams of helium gas (He) applies 380 mmHg pressure at a temperature of 0 °C. Assume ideal gas behavior. The ideal gas constant is 62.36 (L· mmHg)/(K·mol), and the molar mass of helium is 4 g/mol. (Hint: Remember that temperature needs to be in Kelvins.)How much volume does the gas occupy?

Answer 1

Answer

D. 179.2 L

Explanation

Given parameters:

Molar mass of He, M = 4 g/mol

Reacting mass of He, m = 16 grams

Pressure, P = 380 mmHg

Temperature, T = 0 °C = 0 + 273 K = 273 K

Ideal gas constant, R = 62.36 (L· mmHg)/(K·mol)

What to find:

The volume, V that the gas occupies.

Step-by-step solution:

The ideal gas equation formula is PV = nRT

But n = reacting mass/molar mass. i.e m/M

Therefore, the ideal gas equation becomes:

$PV=\frac{m}{M}RT$

Substitute the values of P, R, T, and M into the equation to get V:

$\begin{gathered} 380\times V=\frac{16}{4}\times62.36\times273 \\ 380V=4\times62.36\times273 \\ 380V=68097.12 \\ \text{Divide both sides by 380} \\ \frac{380V}{380}=\frac{68097.12}{380} \\ V=179.2\text{ L} \end{gathered}$

Hence, the gas occupies 179.2 L.