# Question a317c

Sep 6, 2017

$\text{1.4 atm}$

#### Explanation:

The idea here is that when the volume of the gas and the number of moles of gas present in your sample remain constant, increasing the temperature of the gas will cause its pressure to increase as well $\to$ think Gay Lussac's Law here. Mathematically, this can be written like this

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}}}}$

Here

• ${P}_{1}$, ${T}_{1}$ are the pressure and absolute temperature of the gas at an initial state
• ${P}_{2}$ and ${T}_{2}$ are the pressure and absolute temperature of the gas at final state

In your case, the temperature of the gas is increasing, so you should expect to find

${P}_{2} > \text{0.96 atm}$

Rearrange the equation to solve for ${P}_{2}$

${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2} \implies {P}_{2} = {T}_{2} / {T}_{1} \cdot {P}_{1}$

Plug in your values to find

P_2 = (684 color(red)(cancel(color(black)("K"))))/(478color(red)(cancel(color(black)("K")))) * "0.96 atm" = color(darkgreen)(ul(color(black)("1.4 atm")))#

The answer is rounded to two sig figs, the number of sig figs you have for the initial pressure of the gas.