Question

as the pressure of a gas decreases to half its original value, what happens to the volume of the gas if temperature is held constant? (1 point)
the volume decreases to one - fourth of its original value.
the volume increases to four times its original value.
the volume increases to twice its original value.
the volume decreases to half of its original value.

Explanation:

Step1: Recall Boyle's Law

Boyle's law states that $P_1V_1 = P_2V_2$ for a given mass of gas at constant temperature, where $P_1$ and $V_1$ are the initial pressure and volume, and $P_2$ and $V_2$ are the final pressure and volume.

Step2: Set up the relationship

Let the initial pressure be $P_1$ and volume be $V_1$, and the final pressure $P_2=\frac{1}{2}P_1$. Substitute into Boyle's law: $P_1V_1=\frac{1}{2}P_1V_2$.

Step3: Solve for $V_2$

Divide both sides of the equation $P_1V_1=\frac{1}{2}P_1V_2$ by $\frac{1}{2}P_1$. We get $V_2 = 2V_1$.

Answer:

The volume increases to twice its original value.