# What is the approximate temperature of a 0.50 mol sample of gas at 750 mm Hg and a volume of 12 L?

Jun 6, 2016

$T \cong 290 \cdot K$

#### Explanation:

We use the Ideal Gas Equation:

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

$T = \frac{\frac{750 \cdot m m \cdot H g}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1} \times 12 \cdot L}{0.50 \cdot m o l \times 0.0821 \cdot L \cdot a t m \cdot {K}^{-} 1 \cdot m o {l}^{-} 1}$

The key to understanding these problems is correct interpretation of the pressure reading. It is a fact that $1$ $a t m$ will support a column of mercury $760 \cdot m m$ high. So even though we report the $\text{length}$ of the column, this actually relates to the $\text{pressure}$, and I used the conversion,

$P = \frac{750 \cdot m m \cdot H g}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1}$ $\cong$ $1 \cdot a t m$.

Pressure measurement by means of a mercury column was very common back in the day. These days, laboratories tend to want want to get rid of mercury columns because it is an absolute horror to clean up mercury spills. As a student, I found mercury absolutely fascinating, so I contributed to the problem.