Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium if the partial pressures of the gases are as follows: #"P"_ ("O"_ 2) = "20.0 kPa"#, #P_ ("N"_ 2) = "46.7 kPa"#, and #P_ "He" = "26.7 kPa"# ?

The idea here is that the total pressure of the gaseous mixture will be equal to the sum of the partial pressures of the constituent gases #-># think Dalton's Law of Partial Pressures here.

In other words, if you add the pressure that each gas would exert if alone in the container, you get the total pressure of the mixture.

So for a mixture that contains #i# gases, you have

#P_"total" = sum_i P_i#

In your case, the mixture contains three gases: oxygen gas, nitrogen gas, and helium. Moreover, you know that

• #P_( "O"_ 2) = "20.0 kPa"#
• #P_ ("N"_ 2) = "46.7 kPa"#
• #P_ "he" = "26.7 kPa"#

  This means that the total pressure of the gas is given by

  #P_"total" = P_ ("O"_ 2) + P_ ("N"_ 2) + P_ "He"#

  which is equal to

  #P_"total" = "20.0 kPa" + "46.7 kPa" + "26.7 kPa"#

  #color(darkgreen)(ul(color(black)(P_"total" = "93.4 kPa")))#