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?

Md Ariful Islam

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Md Ariful Islam

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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 .

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