# Question f9aed

Apr 17, 2017

The final pressure $\left({P}_{2}\right)$ is $\text{475 torr}$.

#### Explanation:

This is an example of Gay-Lussac's law , which states that the pressure of a given amount of a gas is directly proportional to its temperature in Kelvins, if held at constant volume. This means that if the pressure increases, so does the temperature, and vice-versa. The equation to use is:

${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}$

where $P$ is pressure, and $T$ is temperature in Kelvins.

The Celsius temperatures must be converted to Kelvins by adding $273.15$.

Organize the information

Given
${P}_{1} = \text{435 torr}$
${T}_{1} = {23}^{\circ} \text{C"+273.15="296 K}$
${T}_{2} = {50}^{\circ} \text{C"+273.15="323 K}$

Unknown: ${P}_{2}$

Solution
Rearrange the equation to isolate ${P}_{2}$. Substitute the given values into the equation and solve.

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

P_2=(435color(white)(.)"torr"xx323color(red)cancel(color(black)("K")))/(296color(red)cancel(color(black)("K")))="475 torr"# (rounded to three significant figures)