# What is the temperature of 0.80 mol of a gas stored in a 275 mL cylinder at 175 kPa?

Jun 1, 2017

$7.24$ $\text{K}$

#### Explanation:

First, let's express pressure $P$ in $\text{Pa}$ and volume $V$ in ${\text{m}}^{3}$:

$R i g h t a r r o w P = 175$ $\text{kPa}$

$R i g h t a r r o w P = 1.75 \times {10}^{5}$ $\text{Pa}$

$\text{and}$

$R i g h t a r r o w V = 275$ $\text{ml}$

$R i g h t a r r o w V = 2.75 \times {10}^{- 4}$ ${\text{m}}^{3}$

Then, let's solve the ideal gas law $P V = n R T$ for temperature $T$:

$R i g h t a r r o w P V = n R T$

$R i g h t a r r o w T = \frac{P V}{n R}$

Substituting the appropriate values into the equation:

$R i g h t a r r o w T = \frac{1.75 \times {10}^{5} \times 2.75 \times {10}^{- 4}}{0.80 \times 8.314}$ $\text{K}$

$R i g h t a r r o w T = \frac{48.125}{6.6512}$ $\text{K}$

$\therefore T \approx 7.24$ $\text{K}$

Therefore, the temperature is around $7.24$ $\text{K}$.