Question

A gas at a constant pressure has a temp of 25 degrees Celsius and a volume of 50.0 L. What will the volume be if the temp is increased to 45 degrees Celsius?

Answer 1

Step 1 - Understanding the relation between temperature and volume for a gas

There are three important variables that can modify the state of a gas: pressure, temperature and volume. They're all related by the ideal gas equation.

When pressure is kept constant, we can simplify this relation: temperature and volume become proportional, i.e., the greater the temperature, the greater the volume. This can be stated mathematically as:

`(V_1)/(T_1)=(V_2)/(T_2)`

Step 2 - Substituting the values to solve the problem

From the exercise, we know that:

`\begin{gathered} V_1=50\text{ L} \\ \\ T_1=25\degree C\text{ (298 K)} \\ \\ T_2=45\degree C(318\text{ K)} \\ \\ V_2=\text{ ?} \end{gathered}`

Note that we have converted all temperatures to Kelvin. That's because the proportionality between volume and temperature only work in K, the absolute temperature.

Substituting the values on the equation:

`(50)/(298)=(V_2)/(318)\rightarrow V_2=(318*50)/(298)=53.33\text{ L}`

The final volume will be thus 53.33 L.