# The temperature of a fixed mass of gas in a rigid container is raised from 28.00 degrees Celsius to 88.00 degrees Celsius. The initial pressure was 1000 mmHg. What is the new pressure, after heating?

Feb 11, 2017

The final pressure is $\text{1200 mmHg}$.

#### Explanation:

This is an example of Gay Lussac's temperature-pressure gas law , which states that the pressure of a gas held at constant volume, is directly proportional to the temperature in Kelvins.

The equation for this law is:

"P_1/T_1=P_2/T_2, where $P$ is pressure and $T$ is temperature in Kelvins.

Write down what you know:

${P}_{1} = \text{1000 mmHg}$
${T}_{1} = \text{28.00"^@"C" + 273.15="301.15 K}$
${T}_{2} = \text{88.00"^@"C" + 273.15="361.15 K}$

Write what you don't know: ${P}_{2}$

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

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

P_2=(1000"mmHg"xx361.15color(red)(cancel(color(black)("K"))))/(301.15color(red)(cancel(color(black)("K"))))="1200 mmHg"

Note: Because $\text{1000 mmHg}$ has one significant figure, the answer should have one significant figure, which would be $\text{1000 mmHg}$. However, that would make it difficult to understand the direct relationship between temperature and pressure, so I wrote the answer with two significant figures.