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:
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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.
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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.
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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.
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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.