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?

1 Answer
Feb 11, 2017

Answer:

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.