A chemical reaction produced a 0.311 g sample of gas which occupied 225 mL at 55 C exerting a...

Question:

A chemical reaction produced a {eq}0.311\ g {/eq} sample of gas which occupied {eq}225\ mL {/eq} at {eq}55 ^\circ C {/eq} exerting a pressure of {eq}886\ mm -Hg {/eq}. What is the molar mass of the gas?

Molar Mass:

Molar mass is a very useful quantity in Chemistry. It is the ratio of the total mass of a substance per mole. This quantity can be used in order to determine the number of moles of a substance given its measured mass.

Answer and Explanation:

Determine the molar mass of the given gas by dividing the acquired mass by the number of moles of gas there is using the ideal gas equation, {eq}\displaystyle n = \frac{PV}{RT} {/eq}, where {eq}\displaystyle P {/eq} is the pressure, {eq}\displaystyle V {/eq} is the volume, {eq}\displaystyle R {/eq} is the gas constant, {eq}\displaystyle T {/eq} is the temperature. We proceed with the soltuion.

{eq}\begin{align} \displaystyle \frac{m}{n} &= \frac{m}{ \frac{PV}{RT}}\\ &= \frac{3.11\ g}{\frac{886\ mmHg\cdot 0.225\ L}{62.363\ \rm{L\ mmHg/mol\ K}\cdot (55+273\ K)}}\\ &\approx 319\ \rm{g/mol} \end{align} {/eq}