when the pressure of a gas decreases, which quantity will increase, assuming all other variables are held…

Explanation:

Step1: Recall ideal - gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the amount of gas (moles), $R$ is the ideal - gas constant, and $T$ is temperature.

Step2: Analyze the situation

Given that $n$, $R$, and $T$ are constant. We can rewrite the ideal - gas law as $P=\frac{nRT}{V}$ (Boyle's law situation when $n$ and $T$ are constant). Since $nRT$ is a constant value in this case, pressure $P$ and volume $V$ are inversely proportional.

Step3: Determine the answer

When $P$ decreases, according to the inverse - proportional relationship $P\propto\frac{1}{V}$, the volume $V$ must increase.

Answer:

C. $V$