We'll be using the equation for the ideal gas law for each gas:
#PV=nRT#,
where:
#P# is pressure, #V# is volume, #n# is moles, #R# is the gas constant, and #T# is the temperature in Kelvins.
Known/Given
#M_"N2"="20.014 g/mol"#
#M_"Ar"="39.948 g/mol"#
#M_"O2"="31.998 g/mol"#
#V="14.0 L"#
#T="27"^@"C+273.15"="300 K"# #larr# Kelvins are used with gases.
Unknown
#n#
#P#
The gas constant, #R# is not given in this question, since the answers are given as #P_"Total"R#, where #P_"Total"# is the total pressure. The pressure of each individual gas is the partial pressure #(P_n)# of each gas multiplied by #R#; #(P_iR)#.
Solution
To determine moles, we will divide the given mass of each gas by its molar mass.
#n=("given mass")/("molar mass")#
To determine partial pressure in #P_iR#
#P_i=(nRT)/V#
Nitrogen gas
#n_"N2"=(5.60color(red)cancel(color(black)("g"))" N"_2)/(28.014color(red)cancel(color(black)("g"))/"mol")="0.1999 mol N"_2"#
#P_"N2"=(nRT)/V=("0.19999 mol R 300 K")/("14.0 L")="4 R"#
Argon gas
#n_"Ar"=(40.0color(red)cancel(color(black)("g")) " Ar")/(39.948color(red)cancel(color(black)("g"))/"mol Ar")="1.001 mol Ar"#
#P_"Ar"=(nRT)/V=("1.001 mol R 300 K")/("14.0 L")="22 R"#
Oxygen gas
#n_"O2"=(6.40color(red)cancel(color(black)("g"))"O"_2)/(31.998color(red)cancel(color(black)("g"))/"mol")="0.2000 mol O"_2"#
#P_"O2"=(nRT)/V#
#P_"O2"=("0.2000 mol R 300 K")/("14.0 L")="4 R"#
The total pressure #(P_"t")# is the sum of the partial pressures:
#P_"t"=P_"N2" + P_"Ar" + P_"O2"#
#P_"Total"="4 R + 22 R + 4 R"="30 R"#
