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 when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.

Answer 1

Step 1:

In this question, we are given the following:

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 when the pressure is 450 millimeters of mercury​ (mm Hg), find the volume when the pressure is 200 mm Hg.

Step 2:

This is an application of Boyle's law which states that:

Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.

`\begin{gathered} Mathematically,\text{ we have that:} \\ V\text{ }\propto\text{ }(1)/(P) \\ Then,\text{ we have that:} \\ V\text{ =}(k)/(P)\text{ \lparen where k is a constant \rparen} \end{gathered}`
`when\text{ V = 800 cubic centimetres , then P = 450 mm Hg}`
`\begin{gathered} 800\text{ =}(k)/(450) \\ cross-multiply,\text{ we have that:} \\ \text{k = 800 x 450 = 360,000} \end{gathered}`

`\begin{gathered} Then,\text{ the equation connecting V and P =} \\ \text{ V }=(360,000)/(P) \end{gathered}`

Next:

`when\text{ P = 200 mm Hg, we have that:}`
`\begin{gathered} V\text{ = }(360,000)/(200) \\ \text{V = 1800 cubic centimetres } \end{gathered}`

CONCLUSION:

The volume when the pressure is 200 mm Hg is:

`V\text{ = 1800 cubic centimetres}`