Ideal Gases: General Gas Law, Amount and Volume Relationship
Question
Your instructor blows up a balloon so that it is filled with 0.55 moles of helium at 21.5°C and 1.00 atm pressure. The instructor adds an additional 0.50 moles of helium.
If the pressure in the balloon remains the same, do you expect the volume to increase or decrease? Explain your reasoning in clear and complete sentences.
Show/Hide Answer
Volume is predicted to increase.
A greater amount (n) of gas molecules will take up more volume (V) when pressure (P) and temperature (T) are constant. Since amount is proportional to volume (n α V) and the volume of the balloon can change, we predict that when amount (n) of gas molecules increase, volume (V) will increase.
Refer to Section 2.3 Relating Pressure, Volume, Amount, and Temperature – The Ideal Gas Law (1).
Strategy Map
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Check out the strategy map.
Show/Hide Strategy Map
| Strategy Map Steps |
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| 1. Identify the information given in the question and what conditions are changing. |
| 2. Identify what conditions are staying the same. |
3. Recall how the changing variables are related.
Show/Hide HintThe ideal gas constant (R) does not change, so consider the impact of increasing the moles of gas: [latex]\begin{gathered} \mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}} \end{gathered}[/latex] |
4. Simplify the general gas law to focus on your changing conditions.
Show/Hide Hint[latex]\begin{gathered} \frac{\mathrm{P}_\mathrm{i} \mathrm{V}_\mathrm{i}} {\mathrm{n}_\mathrm{i} \mathrm{T}_\mathrm{i}}=\frac{\mathrm{P}_\mathrm{f} \mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f} \mathrm{T}_\mathrm{f}} \\ \end{gathered}[/latex] Cancel terms that remain constant and determine how the change in moles impacts the volume. |
Solution
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Check out this solution.
Show/Hide Solution
Constant T and P; n is increased
[latex]\begin{gathered} \frac{\mathrm{P}_\mathrm{i} \mathrm{V}_\mathrm{i}} {\mathrm{n}_\mathrm{i} \mathrm{T}_\mathrm{i}}=\frac{\mathrm{P}_\mathrm{f} \mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f} \mathrm{T}_\mathrm{f}} \\ \end{gathered}[/latex]
[latex]\begin{gathered} \frac{\mathrm{V}_\mathrm{i}}{\mathrm{n}_\mathrm{i}}=\frac{\mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f}}(\text {constant }\mathrm{T}, \mathrm{P}) \end{gathered}[/latex]
nf > ni, therefore Vf > Vi
Answer: Volume is predicted to increase.
Explain your reasoning: A greater amount (n) of gas molecules will take up more volume (V) when pressure (P) and temperature (T) are constant. Since amount is proportional to volume (n α V) and the volume of the balloon can change, we predict that when the amount (n) of gas molecules increase, volume (V) will increase.
Guided Solution
Do you want more help?
The guided solution below will give you the reasoning for each step to get your answer, with reminders and hints.
Show/Hide Guided Solution
| Guided Solution Ideas |
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This question is a qualitative problem where we use the ideal gas law to predict how the balloon volume will be impacted by increasing the moles of gas at constant pressure.
Show/Hide Resource
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| Figure out what the question is asking for:
“Your instructor blows up a balloon so that it is filled with 0.55 moles of helium at 21.5°C and 1.00 atm pressure. The instructor adds an additional 0.50 moles of helium. If the pressure in the balloon remains the same, do you expect the volume to increase or decrease? Explain your reasoning in clear and complete statements.” The question asks you to predict what will happen to volume when moles are increased. Show/Hide Think About This!The question tells us that the pressure and temperature remain constant. |
Gas molecules collide with the container walls, exerting an internal pressure. When more molecules of gas are added, we will have more collisions.
Show/Hide Watch Out!If we were working with a fixed volume container, pressure would rise when moles are increased. |
Since this is a changing conditions problem, we use the general form of the ideal gas law.
Show/Hide Don’t Forget![latex]\begin{gathered} \frac{\mathrm{P}_\mathrm{i} \mathrm{V}_\mathrm{i}}{\mathrm{n}_\mathrm{i} \mathrm{T}_\mathrm{i}}=\frac{\mathrm{P}_\mathrm{f} \mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f} \mathrm{T}_\mathrm{f}} \end{gathered}[/latex] Show/Hide Think About This!What conditions are constant? What conditions are changing? Once you recognize these, you can cancel values that stay constant during this problem. In this case, the pressure and temperature remain constant; this means we can remove them since they are the same on both sides. Constant: T and P n is increased [latex]\begin{gathered} \frac{\mathrm{P}_\mathrm{i} \mathrm{V}_\mathrm{i}} {\mathrm{n}_\mathrm{i} \mathrm{T}_\mathrm{i}}=\frac{\mathrm{P}_\mathrm{f} \mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f} \mathrm{T}_\mathrm{f}} \\ \end{gathered}[/latex] constant T and P, Pi = Pi, and Ti = Tf [latex]\begin{gathered} \frac{\mathrm{V}_\mathrm{i}}{\mathrm{n}_\mathrm{i}}=\frac{\mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f}}(\text {constant }\mathrm{T}, \mathrm{P}) \end{gathered}[/latex] |
How are the changing variables related?
Show/Hide Don’t Forget!When pressure and temperature are constant, amount (n) is directly proportional to volume (V). |
| Complete Solution |
|---|
| Since this is a changing conditions ideal gas problem, we can start with the general form of the ideal gas law:
[latex]\mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}}[/latex] [latex]\begin{gathered} \frac{\mathrm{P}_\mathrm{i} \mathrm{V}_\mathrm{i}} {\mathrm{n}_\mathrm{i} \mathrm{T}_\mathrm{i}}=\frac{\mathrm{P}_\mathrm{f} \mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f} \mathrm{T}_\mathrm{f}} \\\end{gathered}[/latex] |
| We recognize that T and P are constant, so their terms cancel each other out in our relationship since their value stays the same:
Pi = Pf, Ti = Tf [latex]\begin{gathered} \frac{\mathrm{V}_\mathrm{i}}{\mathrm{n}_\mathrm{i}}=\frac{\mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f}}(\text{constant }\mathrm{T}, \mathrm{P}) \end{gathered}[/latex] |
| Now, we need to think about the conditions that are changed:
“Your instructor blows up a balloon so that it is filled with 0.55 moles of helium at 21.5°C and 1.00 atm pressure. The instructor adds an additional 0.50 moles of helium. If the pressure in the balloon remains the same, do you expect the volume to increase or decrease?” The moles of helium increases, so nf > ni. [latex]\begin{gathered} \frac{\mathrm{V}_\mathrm{i}}{\mathrm{n}_\mathrm{i}}=\frac{\mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f}}(\text{constant }\mathrm{T}, \mathrm{P}) \end{gathered}[/latex] In order for the relationship to be valid, Vf must be greater than Vi |
| For an ideal gas, moles are proportional to volume at constant temperature and pressure. |
| Answer: Volume is predicted to increase.
Explain your reasoning: A greater amount (n) of gas molecules will take up more volume (V) when pressure (P) and temperature (T) are constant. A balloon has a variable volume, and we know that the pressure and temperature do not change. When more moles (n) of the ideal gas are added, the increased amount of gas increases collisions with the balloon walls, so to keep the pressure constant, it must expand. Since amount is proportional to volume (n α V) and the volume of the balloon can change, we predict that when the amount (n) of gas molecules increases, volume (V) will increase in order to keep the pressure constant. |
| If you would like more support to work through this problem, please check out the Qualitative Ideal Gas Problem – Guided Solution video below (3):
Direct URL link (pasted directly in editor, DID use the add media button )
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Check Your Work
Make sure you are using the correct form of the ideal gas law for changing conditions. This question is a qualitative thinking question where we are asked to explain our answer by relating it to our theory. You can use the provided data to check your prediction by solving for Vf in terms of Vi, but you also need to explain your reasoning in sentences.
Show/Hide Don’t Forget!
If you wish to use the question data to check your prediction, make sure you remember to use the final moles after the added helium.
[latex]\begin{aligned} \frac{\mathrm{V}_\mathrm{i}}{\mathrm{n}_\mathrm{i}}&=\frac{\mathrm{V}_\mathrm{f}}{\mathrm{n}_\mathrm{f}}(\text {constant }\mathrm{T}, \mathrm{P})\\ \mathrm{V}_\mathrm{f}&=\frac{\mathrm{V}_\mathrm{i}\mathrm{n}_\mathrm{f}}{\mathrm{n}_\mathrm{i}} \end{aligned}[/latex]
[latex]\begin{aligned} \mathrm{n}_\mathrm{i}&= 0.55\mathrm{~mol}\\ \mathrm{n}_\mathrm{f}&= 0.55\mathrm{~mol}+ 0.50\mathrm{~mol}= 1.05\mathrm{~mol} \end{aligned}[/latex]
[latex]\begin{aligned} \mathrm{V}_\mathrm{f}&=\frac{\left(\mathrm{V}_\mathrm{i}\right)(1.05 \mathrm{~mol})}{(0.55 \mathrm{~mol})}\\ \mathrm{V}_\mathrm{f}&=1.91\left(\mathrm{V}_\mathrm{i}\right), \text { therefore }\mathrm{V}_\mathrm{f}>\mathrm{V}_\mathrm{i} \end{aligned}[/latex]
Does your answer make chemical sense?
Show/Hide Answer
The moles of the ideal gas increased, and we were told the pressure remained constant. When more moles are added, there are more molecules colliding with the walls, which would result in an increased pressure if the container had a fixed volume. A balloon has a variable volume, so as more moles are added, the volume expands in order to keep the pressure constant.
PASS Attribution
- Question 2.E.25 is from 2.E: Gases (Exercises) in LibreTexts TRU: Fundamentals and Principles of Chemistry (CHEM 1510 and CHEM 1520) (2) and is adapted and used under a CC BY-NC-SA 4.0 license.
References
1. OpenStax. 2.3: Relating Pressure, Volume, Amount, and Temperature – The Ideal Gas Law. In TRU: Fundamentals and Principles of Chemistry (CHEM 1510 and CHEM 1520); LibreTexts, 2022. https://chem.libretexts.org/Courses/Thompson_Rivers_University/TRU%3A_Fundamentals_and_Principles_of_Chemistry_(CHEM_1510_and_CHEM_1520)/02%3A_Gases/2.03%3A_Relating_Pressure_Volume_Amount_and_Temperature_-_The_Ideal_Gas_Law.
2. OpenStax. 2.E: Gases (Exercises). In TRU: Fundamentals and Principles of Chemistry (CHEM 1510 and CHEM 1520); LibreText 2025. https://chem.libretexts.org/Courses/Thompson_Rivers_University/TRU%3A_Fundamentals_and_Principles_of_Chemistry_(CHEM_1510_and_CHEM_1520)/02%3A_Gases/2.E%3A_Gases_(Exercises)
3. TRUChemOnline. Qualitative Ideal Gas Problem – Guided Solution. YouTube, June 6, 2022. https://youtu.be/v1JkBVZ2_0I?si=PKZLcxo6ud2ox97d (accessed July 11, 2025).
