Question

the volume of a gas v held at a constant temperature in a closed container varies inversely with its pressure p. if the volume of a gas is 800 cubic centimeters (cm³) when the pressure is 250 millimeters of mercury (mm hg), find the volume when the pressure is 400 mm hg. when the pressure is 400 mm hg, the volume is

Explanation:

Step1: Establish inverse - variation formula

Since $V$ varies inversely with $P$, we have $V_1P_1 = V_2P_2$.

Step2: Substitute known values

We know that $V_1 = 800\ cm^3$, $P_1 = 250\ mmHg$, and $P_2=400\ mmHg$. Substituting into the formula $V_1P_1 = V_2P_2$, we get $800\times250=V_2\times400$.

Step3: Solve for $V_2$

First, calculate $800\times250 = 200000$. Then, $V_2=\frac{200000}{400}$. So, $V_2 = 500\ cm^3$.

Answer:

$500\ cm^3$