Question
Unless otherwise instructed, you may use the periodic table in the Chemistry: Problems and Solutions book for this question. You also may use the formulas on pages 238–243.
A student increases the temperature of a 556 cm3 balloon from 278 K to 308 K.
Assuming constant pressure, what should the new volume of the balloon be?
Responses
320 cm3
320 cm 3
501 cm3
501 cm 3
616 cm3
616 cm 3
1232 cm3
A student increases the temperature of a 556 cm3 balloon from 278 K to 308 K.
Assuming constant pressure, what should the new volume of the balloon be?
Responses
320 cm3
320 cm 3
501 cm3
501 cm 3
616 cm3
616 cm 3
1232 cm3
Answers
GPT-4o mini
To find the new volume of the balloon when the temperature is increased at constant pressure, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure is constant. The formula can be expressed as:
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]
Where:
- \( V_1 \) is the initial volume
- \( T_1 \) is the initial temperature
- \( V_2 \) is the final volume
- \( T_2 \) is the final temperature
Given:
- \( V_1 = 556 \, \text{cm}^3 \)
- \( T_1 = 278 \, \text{K} \)
- \( T_2 = 308 \, \text{K} \)
We need to find \( V_2 \).
Rearranging the formula to solve for \( V_2 \):
\[
V_2 = V_1 \times \frac{T_2}{T_1}
\]
Now, substituting the known values:
\[
V_2 = 556 \, \text{cm}^3 \times \frac{308 \, \text{K}}{278 \, \text{K}}
\]
Calculating \( \frac{308}{278} \):
\[
\frac{308}{278} \approx 1.108
\]
Now calculate \( V_2 \):
\[
V_2 \approx 556 \, \text{cm}^3 \times 1.108 \approx 617.64 \, \text{cm}^3
\]
Rounding it off, \( V_2 \) is approximately 618 cm³.
Since this value does not perfectly match any of the provided responses, the closest option among the choices would be **616 cm³**.
Therefore, the new volume of the balloon should be **616 cm³**.
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]
Where:
- \( V_1 \) is the initial volume
- \( T_1 \) is the initial temperature
- \( V_2 \) is the final volume
- \( T_2 \) is the final temperature
Given:
- \( V_1 = 556 \, \text{cm}^3 \)
- \( T_1 = 278 \, \text{K} \)
- \( T_2 = 308 \, \text{K} \)
We need to find \( V_2 \).
Rearranging the formula to solve for \( V_2 \):
\[
V_2 = V_1 \times \frac{T_2}{T_1}
\]
Now, substituting the known values:
\[
V_2 = 556 \, \text{cm}^3 \times \frac{308 \, \text{K}}{278 \, \text{K}}
\]
Calculating \( \frac{308}{278} \):
\[
\frac{308}{278} \approx 1.108
\]
Now calculate \( V_2 \):
\[
V_2 \approx 556 \, \text{cm}^3 \times 1.108 \approx 617.64 \, \text{cm}^3
\]
Rounding it off, \( V_2 \) is approximately 618 cm³.
Since this value does not perfectly match any of the provided responses, the closest option among the choices would be **616 cm³**.
Therefore, the new volume of the balloon should be **616 cm³**.