Question #c925d

1 Answer
May 21, 2017

Answer:

#"100 kPa"#

Explanation:

The idea here is that the volume of a gas is Inversely proportional to its pressure when the number of moles of gas and the temperature of the gas are kept constant #-># think Boyle's Law here.

This basically means that when the volume of a gas decreases, its pressure increases by the same factor.

#"volume" darr implies "pressure" uarr#

Mathematically, this is expressed using the following equation

#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 volume is decreasing

#"50 cm"^3 " " darr " " "20 cm"^3#

so you should expect the pressure of the gas, which would be #P_2#, to increase as a result

#"0.49346 atm" " "uarr " " P_2#

Rearrange the equation to solve for #P_2#

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

Plug in your values to find

#P_2 = (50color(red)(cancel(color(black)("cm"^3))))/(20color(red)(cancel(color(black)("cm"^3)))) * "0.49346 atm"#

#P_2 = "1.23365 atm"#

Finally, to convert this to kPa, use the fact that

#"1 atm = 101.325 kPa"#

You will end up with

#1.23365 color(red)(cancel(color(black)("atm"))) * "101.325 kPa"/(1color(red)(cancel(color(black)("atm")))) = "125 kPa" = color(darkgreen)(ul(color(black)("100 kPa")))#

The answer must be rounded to one significant figure, the number of sig figs you have for the two volumes.