Multiple Choice
Which of the following gas laws can be combined to derive the ideal gas law equation?
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7. Gases
The Ideal Gas Law
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According to the ideal gas law, how does the pressure of a gas in a closed container change as the volume of the container decreases, assuming temperature and amount of gas remain constant?
A
Pressure remains constant as volume decreases.
B
Pressure and volume are unrelated.
C
Pressure decreases as volume decreases.
D
Pressure increases as volume decreases.
Verified step by step guidance1
Recall the ideal gas law equation: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the amount of gas (in moles), \(R\) is the ideal gas constant, and \(T\) is temperature.
Since the problem states that the temperature (\(T\)) and amount of gas (\(n\)) remain constant, and \(R\) is always constant, the product \(n \times R \times T\) is a constant value.
This means the equation simplifies to \(P \times V = \text{constant}\), which shows an inverse relationship between pressure and volume.
Therefore, if the volume \(V\) decreases, the pressure \(P\) must increase to keep the product \(P \times V\) constant.
This relationship is known as Boyle's Law, which states that pressure and volume of a gas are inversely proportional when temperature and amount of gas are held constant.
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