# Question 46508

Aug 3, 2017

$\text{pressure} = 554$ $\text{torr}$

#### Explanation:

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

To do this, we can use the Gay-Lussac's law equation:

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

where

• ${P}_{1}$ is the original pressure (what we're trying to find)

• ${T}_{1}$ is the original absolute temperature, which must be in Kelvin:

$150$ $\text{^"o""C}$ + 273 = ul(423color(white)(l)"K"

• ${P}_{2}$ is the final pressure ($456$ torr")

• ${T}_{2}$ is the final temperature, which is

$75.0$ $\text{^"o""C}$ + 273 = ul(348color(white)(l)"K"

Let's rearrange the equation to solve for the unknown, ${P}_{1}$:

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

Plugging in known values, we have

P_1 = ((423cancel("K"))(456color(white)(l)"torr"))/(348cancel("K")) = color(red)(ulbar(|stackrel(" ")(" "554color(white)(l)"torr"" ")|)#