Question #d42dd

1 Answer
Jun 29, 2017

Answer:

#"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.