Question 4e962

Nov 17, 2015

$\text{1.4 L}$

Explanation:

Every time pressure, temperature, and volume are all changing for an ideal gas, you can use the combined gas law to help you find parameter required for the problem.

In this case, pressure and temperature are given, and you must determine the new volume of the gas sample.

The combined gas law equation looks like this

$\textcolor{b l u e}{\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2} \text{ }$, where

${P}_{1}$, ${V}_{1}$, ${T}_{1}$ - the pressure, volume, and temperature of the gas at an initial state
${P}_{2}$, ${V}_{2}$, ${T}_{2}$ - the pressure, volume, and temperature of the gas at a final state

Notice that this equation works when the number of moles of gas remains constant for the two states of the gas sample. Also, it is very important to remember that the temperature of the gas must be expressed in Kelvin!

So, rearrange this equation to solve for ${V}_{2}$

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

Plug in your values to get

V_2 = (0.870color(red)(cancel(color(black)("atm"))))/(1.7color(red)(cancel(color(black)("atm")))) * ( (273.15 + 60)color(red)(cancel(color(black)("K"))))/((273.15 + 104)color(red)(cancel(color(black)("K")))) * "3.0 L"#

${V}_{2} = \text{1.356 L}$

You should round this off to one sig fig, the number of sig figs you have for the final temperature of the gas, but I will leave the answer rounded to two sig figs

${V}_{2} = \textcolor{g r e e n}{\text{1.4 L}}$