Question

A sample of gas in a rigid container is stored at 3.0 atm pressure and 25 degrees Celsius. The temperature is raised to 60 degrees Celsius. What is the pressure now inside the container?
Select one:
a. 2.68 atm
b. 7.2 atm
c. 3.35 atm
d. 1.25 atm

Sorry to ask for help. I'm confused how to solve for pressure using gas laws. I would appreciate the mathematical explanation of the problem. Thank you in advance!

Answer 1

*I give medals!*

Answer 2

You're essentially comparing two systems, any changes from one to another can be taken into account using the ideal gas law, \(\sf PV=nRT\).

To system 1, we rearrange the equation to have all the variables on one side:

\(\sf P_1V_1=n_1RT_1\rightarrow \dfrac{P_1V_1}{n_1RT_1}=C\) where C is a constant.

Now we can say that \(\sf System_1=System_2\)

\(\sf \dfrac{P_1V_1}{n_1RT_1}=\dfrac{P_2V_2}{n_2RT_2}\)

You can use this as an easy way to solve any of these questions. So for your question:

"A sample of gas in a rigid container is stored at 3.0 atm pressure and 25 degrees Celsius. The temperature is raised to 60 degrees Celsius. What is the pressure now inside the container?"

We are told a set of conditions (system 1), and how a variable might change when we change the conditions (system 2).

\(\sf P_1=3~atm,~T_1=273^oC+25^oC=298~K\)

Temperature needs to be in the absolute scale (Kelvin).

\(\sf P_2=?,~T_2=273^oC+60^oC=333~K\)


\(\sf \dfrac{(3~atm)V_1}{n_1R(298~K)}=\dfrac{\color{red}{P_2}V_2}{n_2R(333~K)}\)

Since \(\sf n\), \(\sf V\) and R are constant (were not told they changed), we ignored them from the equation.

\(\sf \dfrac{(3~atm)}{(298~K)}=\dfrac{\color{red}{P_2}}{(333~K)}\)

We now solve for \(\sf P_2\):

\(\sf (333~K)*\dfrac{(3~atm)}{(298~K)}=\dfrac{\color{red}{P_2}}{\cancel{(333~K)}}*\cancel{(333~K)}\)


\(\sf \color{red}{P_2}=(333~\cancel K)*\dfrac{(3~atm)}{(298~\cancel K)}=3.35~atm\)


Now we assess that the answer made sense.

We now that increasing the temperature increases the kinetic energy (motion) of particles in a system. Pressure is the force of particles colliding with a surface (typically it's enclosed in a container, and so this material would be the walls) and so if the molecules are moving more (or faster) there should be more force felt by the surface, which is equivalent to saying that the pressure increased.

Answer 3

Thank you so much @aaronq It makes SO much more sense when explained this way. I really appreciate all your help.

The equations you included only added to the effect, and really illustrated how you found the solution. :)

Answer 4

No problem, I'm glad it made things clearer !