To determine which parameter change could cause the molar volume of a gas to increase by a factor of 2, we can refer to the ideal gas law, which is expressed as:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume (which includes molar volume when divided by moles)
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature
Analysis of Each Option
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The pressure increasing by a factor of 2:
- If pressure increases while other factors remain constant, volume would decrease. This option would not increase the molar volume.
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The temperature increasing by a factor of 2:
- If temperature increases while pressure remains constant, the volume would increase, but not necessarily by a factor of 2. This alone may not guarantee a doubling of volume.
-
The pressure decreasing by a factor of 0.25:
- A decrease in pressure would lead to an increase in volume. Specifically, if pressure decreases to 25% of its original value (a factor of 0.25), the volume would technically increase by a factor of 4, assuming temperature is constant. This change definitely supports an increase in molar volume, potentially greater than a factor of 2.
-
The temperature decreasing by a factor of 0.25:
- Lowering the temperature would generally decrease the volume, assuming pressure is constant. This option would not cause an increase in molar volume.
Conclusion
The change that could cause the molar volume to increase by a factor of 2 is:
the pressure decreasing by a factor of 0.25.