Using #"O"_2# gas as an example, the initial volume, #V_1#, is 0.17 L, and the final volume, #V_2#, is 0.02 L.
STP for the gas laws is 273.15 K and 1.00 atm. The molar volume of a gas at STP is 22.414 L/mol.
In order to determine the initial volume at STP, we need to know which gas is involved so we can determine its molar mass. I am going to use #"O"_2# gas as an example. The molar mass of #"O"_2# gas is 2 x 15.999 g/mol = 31.998 g/mol. (2 atoms O x atomic mass of O in g/mol) You will also need to use the number of moles of the gas, and the molar volume in order to convert moles to liters.
To calculate the final volume, the combined gas law will be used. The combined gas law is:
#P_1V_1"/"T_1#= #P_2V_2"/"T_2#
INITIAL VOLUME AT STP:
Step 1. To find the initial volume at STP, convert the given mass and molar mass of oxygen into moles.
#"120 g O"_2# x #"1 mol"/"31.998 g"# = #"3.7502 mol O"_2# (I am leaving some guard digits to reduce rounding errors.)
Step 2. Convert moles of #"O"_2# to liters using the molar volume of a gas at STP. This will give you the initial volume in liters,
Initial volume = #"3.7502 mol O"_2# x #"1 L"/"22.414 mol"# = #"0.167315 L O"_2# = #"0.17 L O"_2"# (Rounded to 2 significant figures due to 120 g.)
FINAL VOLUME AT 50 ATM AND 1973 K:
Known/Given:
#P_1# = 1.00 atm
#V_1#= initial velocity = 0.17 L
#T_1# = 273.15 K
#P_2# = 50 atm
#"T_1# = 1700 C + 273 =1973 K
Unknown:
#V_2# = final velocity
Equation:
#P_1V_1"/"T_1#= #P_2V_2"/"T_2#
Solution:
#V_2# = #"P"_1"V"_1"T"_2"/P"_2"T"_1"# = #"(1.00 atm)(0.17 L)(1973 K)"/"(50 atm)(273 K)"# = #"0.0246 L"# = #"0.02 L"# (Rounded to 1 significant figure due to 50 atm.)
