Question

according to gas law, which of the following is/are correct?
a temperature and pressure are kept constant,
then the volume of the gas is inversely
proportional to the number of molecules of gas

if the temperature and volume remain constant,
then the pressure of the gas changes is
inversely proportional to the number of
molecules of gas present

if the number of gas molecules and the
temperature remain constant, then the pressure
is inversely proportional to the volume

all of the above

Explanation:

Step1: Analyze option a

According to Avogadro's law, \(V = kn\) (where \(V\) is volume, \(n\) is the number of moles/molecules, \(k\) is a constant) when temperature (\(T\)) and pressure (\(P\)) are constant. So volume is directly proportional to the number of molecules, not inversely. So option a is incorrect.

Step2: Analyze option b

According to the ideal gas law \(PV=nRT\). When \(T\) and \(V\) are constant, \(P = kn\) (where \(k=\frac{RT}{V}\)). So pressure is directly proportional to the number of molecules, not inversely. So option b is incorrect.

Step3: Analyze option c

According to Boyle's law, \(P=\frac{k}{V}\) (where \(k = nRT\) and \(n\) and \(T\) are constant). So pressure is inversely proportional to volume. Option c is correct.

Answer:

C. If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume