객관식
Which equation best describes the relationship between pressure, volume, temperature, and amount of a gas contained within a piston-cylinder assembly under ideal conditions?
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7. Gases
The Ideal Gas Law
객관식
A sample of gas expands from 1.0 m^3 to 4.0 m^3 at constant temperature and pressure. According to the ideal gas law, what happens to the number of moles of gas in the system?
A
The number of moles doubles.
B
The number of moles decreases by a factor of 4.
C
The number of moles increases by a factor of 4.
D
The number of moles remains constant.
검증된 단계별 안내1
Recall the ideal gas law: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is temperature.
Note that the problem states the temperature (\(T\)) and pressure (\(P\)) are constant during the expansion.
Since \(P\), \(R\), and \(T\) are constants, the equation simplifies to \(P \times V = n \times \text{constant}\), meaning \(V\) is directly proportional to \(n\) if \(P\) and \(T\) are constant.
However, in this problem, the gas expands from 1.0 m\(^3\) to 4.0 m\(^3\) at constant \(P\) and \(T\), so the volume increases by a factor of 4.
Because \(P\) and \(T\) are constant, the number of moles \(n\) must remain constant to satisfy the ideal gas law; the increase in volume does not imply a change in \(n\).
