# Question 56270

Aug 2, 2017

$\text{temperature} = 2497$ $\text{^"o""C}$

#### Explanation:

We're asked to find the final temperature of the gas, given its initial pressure, final pressure, and initial temperature.

We can use Gay-Lussac's law for this problem, which is

$\underline{\frac{{P}_{1}}{{T}_{1}} = \frac{{P}_{2}}{{T}_{2}}} \textcolor{w h i t e}{a a}$ (constant volume and quantity)

where

• ${P}_{1}$ is the initial pressure

• ${P}_{2}$ is the final pressure (what we're trying to find)

• ${T}_{1}$ is the initial absolute temperature (in Kelvin)

• ${T}_{2}$ is the final absolute temperature (in Kelvin)

We have:

• ${P}_{1} = 575$ $\text{torr}$

• ${P}_{2} = 5750$ $\text{torr}$

• ${T}_{1} = 4$ $\text{^"o""C}$ + 273 = ul(277color(white)(l)"K"

• T_2 = ?

Let's rearrange the above equation to solve for the final temperature, ${T}_{2}$:

${T}_{2} = \frac{{T}_{1} {P}_{2}}{{P}_{1}}$

Plugging in known values:

T_2 = ((277color(white)(l)"K")(5750cancel("torr")))/(575cancel("torr")) = color(red)(ul(2770color(white)(l)"K"

Which, in $\text{^"o""C}$, is

T_2 = color(red)(2770color(white)(l)"K") - 273 = color(blue)(ulbar(|stackrel(" ")(" "2497color(white)(l)""^"o""C"" ")|)#