# A sample of 3.0 grams of an ideal gas at 127°C and 1.0 atmosphere pressure has a volume of 1.5 liters. What is the molar mass of the gas?

## The ideal gas constant R, is 0.08 (Latm)/(moleK)?

Jan 22, 2017

$\text{Molar mass}$ $\cong$ $66 \cdot g \cdot m o {l}^{-} 1$

#### Explanation:

We can use the Ideal Gas equation to give us the molar quantity.

$n = \frac{P V}{R T}$,

i.e. $\text{Mass"/"Molar mass"="Amount of substance in moles} = \frac{P V}{R T}$.

And thus $\text{Molar mass}$ $=$ $\frac{\text{Mass of gas}}{P V} \times R T =$

$\frac{3.0 \cdot g \times 0.0821 \cdot \cancel{L} \cdot a t m \cdot \cancel{{K}^{-} 1} \cdot m o {l}^{-} 1 \times 400 \cancel{K}}{1 \cdot \cancel{a t m} \times 1.5 \cdot \cancel{L}}$

=??g*mol^-1.

This is dimensionally consistent, in that all the units EXCEPT $g \cdot m o {l}^{-} 1$ cancel out.