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 900 cubic centimeters (cm³) when the pressure is 300 millimeters of mercury (mm hg), find the volume when the pressure is 500 mm hg. when the pressure is 500 mm hg, the volume is dropdown options: mm hg per cm³, cm³ per mm hg, mm hg, cm³.

Explanation:

Step1: Establish inverse - variation formula

Since $V$ varies inversely with $P$, we have $V=\frac{k}{P}$, where $k$ is a constant. When $V = 900$ $cm^{3}$ and $P=300$ $mmHg$, we can find $k$. Substitute into the formula: $900=\frac{k}{300}$. Then $k = 900\times300=270000$.

Step2: Find new volume

Now we know $k = 270000$ and $P = 500$ $mmHg$. Substitute into $V=\frac{k}{P}$, so $V=\frac{270000}{500}=540$ $cm^{3}$.

Answer:

$540$ $cm^{3}$