Question #bf70b
1 Answer
Explanation:
The idea here is that you need to use the ideal gas law equation to calculate the number of moles of helium present in the sample, then use the molar mass of helium to convert the number of moles to grams.
The ideal gas law equation looks like this
#color(blue)(ul(color(black)(PV = nRT)))#
Here
#P# is the pressure of the gas#V# is the volume it occupies#n# is the number of moles of gas present in the sample#R# is the universal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is the absolute temperature of the gas
Now, you are told that the partial pressure of helium is equal to
This value was calculated by taking into account the partial pressures of the other gases present in the mixture and the total pressure of the mixture
#P_"total" = P_ ("CO"_ 2) + P_ "Ar" + P_ ("O"_ 2) + P_ "He"#
This resulted in
#P_ "He" = P_ "total" - (P_ ("CO"_ 2) + P_ "Ar" + P_ ("O"_ 2))#
which got you
#P_ "He" = "745 mmHg" - ("133 mmHg" + "214 mmHg" + "195 mmHg")#
#P_ "He" = "203 mmHg"#
So, rearrange the ideal gas law equation to solve for
#PV = nRT implies n = (PV)/(RT)#
Plug in your values to find--do not forget to convert the pressure of the gas to atm!
#n = (203/760 color(red)(cancel(color(black)("atm"))) * 11.1 color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * 273 color(red)(cancel(color(black)("K")))) = "0.1323 moles He"#
Since helium has a molar mass of
#0.1323 color(red)(cancel(color(black)("moles He"))) * "4.0026 g"/(1color(red)(cancel(color(black)("mole He")))) = color(darkgreen)(ul(color(black)("0.530 g")))#
The answer is rounded to three sig figs.