A mixture of 2.002.00 moles of "H"_2H2, 3.003.00 moles of "NH"_3NH3, 4.004.00 moles of "CO"_2CO2, and 5.005.00 moles of "N"_2N2 exerts a total pressure of "800. mmHg"800. mmHg. What is the partial pressure of each gas?
1 Answer
Here's what I got.
Explanation:
The idea here is that the partial pressure of each gas will be proportional to the mole fraction each gas has in the mixture
P_ "gas i" = chi_ "gas i" * P_"total"Pgas i=χgas i⋅Ptotal
Here
P_"gas i"Pgas i is the partial pressure of gasii chi_"gas i"χgas i is the mole fraction of gasii P_"total"Ptotal is the total pressure of the mixture
In other words, the partial pressure of a given gas will be equal to the pressure that gas would have if it were to occupy the same volume alone.
Consequently, the sum of these partial pressures must be equal to the total pressure exerted by the mixture.
P_"total" = P_( "H"_ 2) + P_ ("NH"_ 3) + P_ ("CO"_ 2) + P_ ("N"_ 2)Ptotal=PH2+PNH3+PCO2+PN2
Now, the mole fraction of a component of this mixture is calculated by dividing the number of moles of said component by the total number of moles of gas present in the mixture.
For hydrogen gas, you will have
chi_ ("H"_ 2) = (2.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.1429
Similarly, for ammonia, you will have
chi_ ("NH"_ 3) = (3.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.2143
For carbon dioxide, you will have
chi_ ("CO"_ 2) = (4.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.2857
Finally, for nitrogen gas, you will have
chi_ ("N"_ 2) = (5.00 color(red)(cancel(color(black)("moles"))))/((2.00 + 3.00 + 4.00 + 5.00)color(red)(cancel(color(black)("moles")))) = 0.3571
To find the partial pressure of hydrogen gas, simply multiply the mole fraction of hydrogen gas by the total pressure of the mixture.
P_ ("H"_ 2) = 0.1429 * "800m mmHg" = color(darkgreen)(ul(color(black)("114 mmHg")))
Similarly, the partial pressure of ammonia will be
P_ ("NH"_ 3) = 0.2143 * "800. mmHg" = color(darkgreen)(ul(color(black)("171 mmHg")))
Use the same approach to find the partial pressures of carbon dioxide and nitrogen gas.
Don't forget to round the answers to three sig figs and make sure to double-check your calculations by using the fact that all the partial pressures must add up to give the total pressure of the mixture.