# Question c925d

May 21, 2017

$\text{100 kPa}$

#### 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 $\to$ think Boyle's Law here.

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

$\text{volume" darr implies "pressure} \uparrow$

Mathematically, this is expressed using the following equation

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{P}_{1} {V}_{1} = {P}_{2} {V}_{2}}}}$

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

${\text{50 cm"^3 " " darr " " "20 cm}}^{3}$

so you should expect the pressure of the gas, which would be ${P}_{2}$, to increase as a result

$\text{0.49346 atm" " "uarr " } {P}_{2}$

Rearrange the equation to solve for ${P}_{2}$

${P}_{1} {V}_{1} = {P}_{2} {V}_{2} \implies {P}_{2} = {V}_{1} / {V}_{2} \cdot {P}_{1}$

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"#

${P}_{2} = \text{1.23365 atm}$

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

$\text{1 atm = 101.325 kPa}$

You will end up with

$1.23365 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atm"))) * "101.325 kPa"/(1color(red)(cancel(color(black)("atm")))) = "125 kPa" = color(darkgreen)(ul(color(black)("100 kPa}}}}$

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