# Determine which law is appropriate for solving the following problem. What temperature will 215 mL of a gas at 20 C and 1 atm pressure attain when it is subject to 15 atm of pressure?

Jun 4, 2017

${300}^{\circ}$ $\text{C}$

#### Explanation:

We must use the "combined gas law" $\frac{{P}_{1} {V}_{1}}{{T}_{1}} = \frac{{P}_{2} {V}_{2}}{{T}_{2}}$.

In this case, the volume is kept constant, so ${P}_{1} = {P}_{2}$.

We can therefore cancel the terms from the equation:

$R i g h t a r r o w \frac{{V}_{1}}{{T}_{1}} = \frac{{V}_{2}}{{T}_{2}}$

$R i g h t a r r o w \frac{1 \text{ atm")(20^(@) " C") = frac(15 " atm}}{{T}_{2}}$

Let's divide both sides of the equation by $15$ $\text{atm}$:

$R i g h t a r r o w \frac{1}{{300}^{\circ} \text{ C}} = \frac{1}{{T}_{2}}$

$R i g h t a r r o w {\left(\frac{1}{{300}^{\circ} \text{ C}}\right)}^{- 1} = {\left(\frac{1}{{T}_{2}}\right)}^{- 1}$

$R i g h t a r r o w {300}^{\circ}$ $\text{C} = {T}_{2}$

$\therefore {T}_{2} = {300}^{\circ}$ $\text{C}$

Therefore, the gas will attain a temperature of ${300}^{\circ}$ $\text{C}$ when it is subject to $15$ $\text{atm}$ of pressure.