Question

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?

Answer 1

The final pressure is `"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="1000 mmHg"`
`T_1="28.00"^@"C" + 273.15="301.15 K"`
`T_2="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=(P_1T_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 `"1000 mmHg"` has one significant figure, the answer should have one significant figure, which would be `"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.