# Calculate the molar mass of a gas, if 4.40 g occupies at 3.50 L at 560 mm-Hg and 41 degrees Celsius.

## Question:

Calculate the molar mass of a gas, if {eq}4.40\ g {/eq} occupies at {eq}3.50\ L {/eq} at {eq}560\ mm-Hg {/eq} and {eq}41 ^\circ {/eq} Celsius.

## Molar Mass:

The molar mass is simply the quantity that gives the mass per mole of a substance. We can acquire the molar mass by dividing the mass of a substance by the number of moles it contains. The number of moles can be acquired through a variety of methods, which includes the application of the ideal gas equation.

Determine the molar mass of the given gas by dividing the given mass, {eq}\displaystyle m = 4.40\ g {/eq}, of the gas by the number of moles, {eq}\displaystyle n {/eq}. We determine the number of moles using the ideal gas equation, {eq}\displaystyle n = \frac{PV}{RT} {/eq}, where {eq}\displaystyle P = 560\ mmHg {/eq}, {eq}\displaystyle V = 3.50\ L {/eq}, {eq}\displaystyle T = 41+273\ K = 314\ K {/eq}, and {eq}\displaystyle R = 62.364\ \rm{L\ mmHg/mol\ K} {/eq}. We first find {eq}\displaystyle n {/eq}.

{eq}\begin{align} \displaystyle n &= \frac{PV}{RT}\\ &= \frac{560\ mmHg\times 3.50\ L}{62.364\ \rm{L\ mmHg/mol\ K}\times 314\ K}\\ &= 0.010\ mol \end{align} {/eq}

Then, we acquire the molar mass.

{eq}\begin{align} \displaystyle \frac{4.40\ g}{0.010\ mol} = 440\ \rm{g/mol} \end{align} {/eq}