Question

Question #c925d

Answer 1

`"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.