# 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 theuniversal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is theabsolute temperatureof 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 **Dalton's Law of Partial Pressures** here.

#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**.