First the units of pressure and volume need to be the same.

**Pressure**

#"1 atm=760.0 mmHg"#

**Convert mmHg to atm.**

#2219color(red)(cancelcolor(black)("mmHg"))xx(1"atm")/(760.0color(red)(cancelcolor(black)("mmHg")))="2.920 atm"#

**Volume**

#"1 L=1000 mL"#

**Convert #"L"# to #"mL"#.**

#2.30color(red)(cancel(color(black)("L")))xx(1000"mL")/(1color(red)(cancel(color(black)("L"))))="2300 mL"=2.30xx10^3"mL"#

The number of mL above is given to three significant figures using scientific notation. I will use #"2300 mL"# for convenience only.

This question is concerns **Boyle's Law** , which states that the volume #(V)# of a gas held at constant amount and temperature, is inversely proportional to the pressure #(P)#. This means that if the pressure goes up, the volume goes down, and vice-versa. The equation to use is:

#P_1V_1=P_2V_2#

**Write what you know:**

#P_1="4.53 atm"#

#V_1=2.30xx10^3"mL"#

#P_2="2.920 atm"#

**Write what you don't know:** #V_2#.

**Solution**

Rearrange the equation to isolate #V_2#. Substitute the known quantities into the equation and solve.

#V_2=(P_1V_1)/(P_2)#

#V_2=(4.53color(red)(cancel(color(black)("atm")))xx2300"mL")/(2.920color(red)(cancel(color(black)("atm"))))="3570 mL"# rounded to three significant figures