Use the equation for the combined gas law:
#(P_1V_1)/T_1=(P_2V_2)/T_2#,
where:
#P_1# and #P_2# are the initial and final pressure, respectively, #V_1# and #V_2# are the initial and final volume, and #T_1# and #T_2# are the initial and final temperature in Kelvins.
Current STP is #0^@"C"# or #"273.15 K"#, and #"100 kPa"# or #"1 bar"#.
Organize the data:
Known
#P_1="600.0 mmHg"#
#V_1="240 mL"#
#T_1="25.0"^@"C + 273.15 = 298.2 K"# #larr# Temp must be in Kelvins.
#P_2=100 color(red)cancel(color(black)("kPa"))xx(750"mmHg")/(1color(red)cancel(color(black)("kPa")))="75000 mmHg"# #larr# Converting standard pressure to #"mmHg"#.
#T_2="273.15 K"#
Unknown
#V_2#
Solution
Rearrange the equation to isolate #V_2#. Plug in the known values and solve.
#V_2=(P_1V_1T_2)/(T_1P_2)#
#V_2=((600.0color(red)cancel(color(black)("mmHg")))xx(240"mL")xx(273.15color(red)cancel(color(black)("K"))))/((298.2color(red)cancel(color(black)("K")))xx(75000color(red)cancel(color(black)("mmHg"))))="1.8 mL"# (rounded to two significant figures)
Note:
If your teacher is still using #"1 atm"# for pressure at STP, then #P_2="760 mmHg"#, and #V_2="170 mL"#.