Question
The molar volume of a gas increases by a factor of 2. Which parameter change could have caused the shift in molar volume?(1 point)
Responses
the temperature increasing by a factor of 2
the temperature increasing by a factor of 2
the pressure decreasing by a factor of 0.25
the pressure decreasing by a factor of 0.25
the temperature decreasing by a factor of 0.25
the temperature decreasing by a factor of 0.25
the pressure increasing by a factor of 2
Responses
the temperature increasing by a factor of 2
the temperature increasing by a factor of 2
the pressure decreasing by a factor of 0.25
the pressure decreasing by a factor of 0.25
the temperature decreasing by a factor of 0.25
the temperature decreasing by a factor of 0.25
the pressure increasing by a factor of 2
Answers
GPT-4o mini
To understand the change in molar volume of a gas, we can refer to the Ideal Gas Law, which is represented as:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume (or molar volume)
- \( n \) = number of moles (constant in this scenario)
- \( R \) = ideal gas constant
- \( T \) = temperature
Given that the molar volume increases by a factor of 2, let's analyze the options:
1. **The temperature increasing by a factor of 2**: If the temperature increases while pressure remains constant, volume would increase, but not necessarily by a factor of 2.
2. **The pressure decreasing by a factor of 0.25**: Lowering the pressure (by a factor of 0.25) would cause the volume to increase significantly. Mathematically, if pressure is decreased, the volume is expected to increase, possibly approaching a doubling effect, given a constant temperature.
3. **The temperature decreasing by a factor of 0.25**: Decreasing the temperature while keeping pressure constant would lead to a decrease in volume, not an increase.
4. **The pressure increasing by a factor of 2**: Increasing the pressure would decrease the volume, contrary to the observed increase in molar volume.
Given these considerations, the change that could have caused the shift in molar volume is:
**The pressure decreasing by a factor of 0.25.**
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume (or molar volume)
- \( n \) = number of moles (constant in this scenario)
- \( R \) = ideal gas constant
- \( T \) = temperature
Given that the molar volume increases by a factor of 2, let's analyze the options:
1. **The temperature increasing by a factor of 2**: If the temperature increases while pressure remains constant, volume would increase, but not necessarily by a factor of 2.
2. **The pressure decreasing by a factor of 0.25**: Lowering the pressure (by a factor of 0.25) would cause the volume to increase significantly. Mathematically, if pressure is decreased, the volume is expected to increase, possibly approaching a doubling effect, given a constant temperature.
3. **The temperature decreasing by a factor of 0.25**: Decreasing the temperature while keeping pressure constant would lead to a decrease in volume, not an increase.
4. **The pressure increasing by a factor of 2**: Increasing the pressure would decrease the volume, contrary to the observed increase in molar volume.
Given these considerations, the change that could have caused the shift in molar volume is:
**The pressure decreasing by a factor of 0.25.**