Question

The volume of a gas held at constant temperature varies indirectly as the pressure of the gas. If the volume of a gas is 1200 cubic centimeters when the pressure is 400 millimeters of mercury, what is the volume, v, when the pressure is 500 millimeters of mercury?

Answer 1

Answer:

Volume of the gas at 500 mm Hg pressure is 960 $cm^{3}$

Explanation:

Let's assume the gas behaves ideally.

According to combined gas law for an ideal gas-

                  $\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}$

Where $P_{1}$ and  $P_{2}$ are initial and final pressure of the gas respectively.  $V_{1}$ and  $V_{2}$ are initial and final volume of the gas respectively.  $T_{1}$ and  $T_{2}$ are initial and final temperature of the gas in kelvin respectively.

Here $T_{1}$ = $T_{2}$, $V_{1}$ = 1200 $cm^{3}$, $P_{1}$ = 400 mm Hg, $P_{2}$ = 500 mm Hg

So, $V_{2}=\frac{P_{1}V_{1}T_{2}}{T_{1}P_{2}}$

Hence $V_{2}=\frac{400\times 1200}{500}[tex]cm^{3}$=960 $cm^{3}$[/tex]

Hence volume of the gas at 500 mm Hg pressure is 960 $cm^{3}$