1.50 L with 3.00 moles of gas at 25 °C. With pressure and temperature held constant, what will be the volume (in L) of the balloon if 0.40 moles of gas are released?
1.50 L with 3.00 moles of gas at 25 °C. With pressure and temperature held constant, what will be the volume (in L) of the balloon if 0.40 moles of gas are released?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Question 14 of 39**
A balloon is filled to a volume of 1.50 L with 3.00 moles of gas at 25 °C. With pressure and temperature held constant, what will be the volume (in L) of the balloon if 0.40 moles of gas are released?
---
**Problem Explanation:**
This problem involves understanding how the volume of a gas changes with the amount of substance present, while temperature and pressure remain constant. Using Avogadro's Law, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of moles, we can solve this problem.
**Solution Approach:**
- **Initial condition:** 1.50 L with 3.00 moles of gas
- **Change in moles:** 0.40 moles are released
- **New number of moles:** 3.00 moles - 0.40 moles = 2.60 moles
To find the new volume \( V_2 \), we set up the relation based on Avogadro’s Law:
\[
\frac{V_1}{n_1} = \frac{V_2}{n_2}
\]
Where:
- \( V_1 = 1.50 \, \text{L} \)
- \( n_1 = 3.00 \, \text{moles} \)
- \( n_2 = 2.60 \, \text{moles} \)
Solving for \( V_2 \):
\[
V_2 = V_1 \times \frac{n_2}{n_1} = 1.50 \times \frac{2.60}{3.00}
\]
---
**Calculation:**
Substituting in the numbers:
\[
V_2 = 1.50 \times 0.867 = 1.30 \, \text{L}
\]
Therefore, the new volume of the balloon is 1.30 L.
---
**Instructions for Further Exploration:**
You can use the numerical keypad provided below to calculate different scenarios or check other calculations by entering different values for volume and moles.
- Number buttons from 0-9
- A decimal point button
- A clear button
- A button for scientific notation (x10)
Tap below for additional educational resources and references related to gas](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fceafadd1-9c75-4be0-aae5-882235578510%2F86a95d75-5401-4596-976e-aefed11078ef%2F18yb3aa_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 14 of 39**
A balloon is filled to a volume of 1.50 L with 3.00 moles of gas at 25 °C. With pressure and temperature held constant, what will be the volume (in L) of the balloon if 0.40 moles of gas are released?
---
**Problem Explanation:**
This problem involves understanding how the volume of a gas changes with the amount of substance present, while temperature and pressure remain constant. Using Avogadro's Law, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of moles, we can solve this problem.
**Solution Approach:**
- **Initial condition:** 1.50 L with 3.00 moles of gas
- **Change in moles:** 0.40 moles are released
- **New number of moles:** 3.00 moles - 0.40 moles = 2.60 moles
To find the new volume \( V_2 \), we set up the relation based on Avogadro’s Law:
\[
\frac{V_1}{n_1} = \frac{V_2}{n_2}
\]
Where:
- \( V_1 = 1.50 \, \text{L} \)
- \( n_1 = 3.00 \, \text{moles} \)
- \( n_2 = 2.60 \, \text{moles} \)
Solving for \( V_2 \):
\[
V_2 = V_1 \times \frac{n_2}{n_1} = 1.50 \times \frac{2.60}{3.00}
\]
---
**Calculation:**
Substituting in the numbers:
\[
V_2 = 1.50 \times 0.867 = 1.30 \, \text{L}
\]
Therefore, the new volume of the balloon is 1.30 L.
---
**Instructions for Further Exploration:**
You can use the numerical keypad provided below to calculate different scenarios or check other calculations by entering different values for volume and moles.
- Number buttons from 0-9
- A decimal point button
- A clear button
- A button for scientific notation (x10)
Tap below for additional educational resources and references related to gas
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