Helium is used to inflate party balloons. The volume of a balloon is 2.0 L at 27 °C. gas What is the volume of the balloon at 57 °C? O a) 4.2 L O b) 0.95 L O c) 1.8 L d) 2.2 L
Helium is used to inflate party balloons. The volume of a balloon is 2.0 L at 27 °C. gas What is the volume of the balloon at 57 °C? O a) 4.2 L O b) 0.95 L O c) 1.8 L d) 2.2 L
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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![**Transcription for Educational Website**
---
**Problem Statement:**
Helium gas is used to inflate party balloons. The volume of a balloon is 2.0 liters at 27°C. What is the volume of the balloon at 57°C?
**Answer Choices:**
- a) 4.2 L
- b) 0.95 L
- c) 1.8 L
- d) 2.2 L
---
**Explanation:**
To solve this problem, you can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin, provided the pressure is constant.
The formula is:
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]
Where:
- \( V_1 \) is the initial volume (2.0 L)
- \( T_1 \) is the initial temperature (27°C)
- \( V_2 \) is the final volume (unknown)
- \( T_2 \) is the final temperature (57°C)
First, convert the temperatures from Celsius to Kelvin by adding 273.15.
- \( T_1 = 27 + 273.15 = 300.15 \) K
- \( T_2 = 57 + 273.15 = 330.15 \) K
Substitute the values into the formula:
\[
\frac{2.0 \, \text{L}}{300.15 \, \text{K}} = \frac{V_2}{330.15 \, \text{K}}
\]
Solving for \( V_2 \):
\[
V_2 = \left( \frac{2.0 \times 330.15}{300.15} \right) = 2.2 \, \text{L}
\]
Thus, the correct answer is d) 2.2 L.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F735b0976-906f-40ec-a76b-1f1d9f7b453e%2F6e193d37-ff2d-4c06-a8a6-285ec10ea7fb%2Fucnva2a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
---
**Problem Statement:**
Helium gas is used to inflate party balloons. The volume of a balloon is 2.0 liters at 27°C. What is the volume of the balloon at 57°C?
**Answer Choices:**
- a) 4.2 L
- b) 0.95 L
- c) 1.8 L
- d) 2.2 L
---
**Explanation:**
To solve this problem, you can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin, provided the pressure is constant.
The formula is:
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]
Where:
- \( V_1 \) is the initial volume (2.0 L)
- \( T_1 \) is the initial temperature (27°C)
- \( V_2 \) is the final volume (unknown)
- \( T_2 \) is the final temperature (57°C)
First, convert the temperatures from Celsius to Kelvin by adding 273.15.
- \( T_1 = 27 + 273.15 = 300.15 \) K
- \( T_2 = 57 + 273.15 = 330.15 \) K
Substitute the values into the formula:
\[
\frac{2.0 \, \text{L}}{300.15 \, \text{K}} = \frac{V_2}{330.15 \, \text{K}}
\]
Solving for \( V_2 \):
\[
V_2 = \left( \frac{2.0 \times 330.15}{300.15} \right) = 2.2 \, \text{L}
\]
Thus, the correct answer is d) 2.2 L.
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