Multiple Choice
Four containers each hold 1.0 mol of an ideal gas at different conditions. Which container has the gas stored at the highest temperature?A) 2.0 L at 1.0 atmB) 4.0 L at 1.0 atmC) 2.0 L at 2.0 atmD) 1.0 L at 1.0 atm
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7. Gases
The Ideal Gas Law Applications
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When the pressure in a beaker containing an ideal gas is lowered at constant temperature, what happens to the volume of the gas according to the ideal gas law?
A
The volume first increases, then decreases.
B
The volume remains unchanged.
C
The volume increases.
D
The volume decreases.
Verified step by step guidance1
Recall the ideal gas law, which is given by the equation \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles of gas, \(R\) is the ideal gas constant, and \(T\) is temperature.
Since the problem states that the temperature (\(T\)) is constant and the amount of gas (\(n\)) does not change, the product \(n \times R \times T\) is a constant value.
Rearrange the ideal gas law to express volume as a function of pressure: \(V = \frac{n \times R \times T}{P}\).
From this equation, observe that volume \(V\) is inversely proportional to pressure \(P\) when temperature and amount of gas are constant. This means if pressure decreases, volume must increase to keep the equation balanced.
Therefore, when the pressure in the beaker is lowered at constant temperature, the volume of the gas increases according to the ideal gas law.
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