Question

fill in the blank question
if the pressure of a sample of gas decreases to one-half of its original value at a constant temperature, the volume of the gas ____ to ____ times its original value.

Explanation:

Step1: State Boyle's Law

For a gas at constant temperature, $P_1V_1 = P_2V_2$, where $P_1,V_1$ are initial pressure/volume, $P_2,V_2$ are final pressure/volume.

Step2: Substitute given pressure change

Let $P_2 = \frac{1}{2}P_1$. Substitute into the law:
$P_1V_1 = \frac{1}{2}P_1V_2$

Step3: Solve for final volume

Divide both sides by $P_1$:
$V_1 = \frac{1}{2}V_2$
Rearrange to find $V_2 = 2V_1$

Answer:

increases; 2