Question

Question #d42dd

Answer 1

`"2 L"`

Explanation:

The thing to remember here is that every time the temperature of a gas and the number of moles of gas are kept constant, the pressure and the volume of the gas have an inverse relationship described by Boyle's Law.

`color(blue)(ul(color(black)(P_1V_1 = P_2V_2)))`

Here

• `P_1` and `V_1` represent the pressure and volume of the gas at an initial state
• `P_2` and `V_2` represent the pressure and volume of the gas at a final state

In your case, the pressure of the gas is increasing

`"118 kPa " -> " 214 kPa"`

so you should expect the volume of the gas to decrease

`"4 L " > color(white)(.)V_2`

Rearrange the equation to solve for `V_2`

`P_1V_1 = P_2V_2 implies V_2 = P_1/P_2 * V_1`

Plug in your values to find

`V_2 = (118 color(red)(cancel(color(black)("kPa"))))/(214color(red)(cancel(color(black)("kPa")))) * "4 L" = color(darkgreen)(ul(color(black)("2 L")))`

The answer must be rounded to one significant figure, the number of sig figs you have for the initial volume of the gas.