Question #5b7ab
1 Answer
Explanation:
For starters, I think that you mistyped the value of the Henry law constant, it should actually be
#K_H = 1 * 10^5"atm" " "# or#" " K_H = 1 * 10^(-5)"atm"^(-1)#
I will use
The idea here is that you can use Dalton's Law of Partial Pressures to determine the partial pressure of nitrogen gas,
As you know, Henry' Law states that the solubility of a gas in a liquid is proportional to the partial pressure of the gas above the liquid.
If you take
#color(purple)(|bar(ul(color(black)(color(white)(a/a)P = K_H xx chi_(N_2))color(white)(a/a)|)))#
This means that the partial pressure of nitrogen gas above the solution depends on its mole fraction in the solution.
Now, the partial pressure of nitrogen gas above the solution will depend on its mole fraction in the air
You will have
#color(purple)(|bar(ul(color(white)(a/a)color(black)(P_(N_2) = chi_("air N"_2) * P_"total")color(white)(a/a)|)))#
Here
Plug in your values to get
#P_(N_2) = 0.8 * "5 atm" = "4 atm"#
Plug this into the equation for Henry's Law to get the mole fraction of nitrogen gas dissolved in the solution
#4 color(red)(cancel(color(black)("atm"))) = 1 * 10^(5)color(red)(cancel(color(black)("atm"))) * chi_(N_2)#
#chi_(N_2) = 4/(1 * 10^(5)) = 4 * 10^(-5)#
SIDE NOTE This is why I said that the value you listed for the Henry law constant is inaccurate. Assuming that you have
#chi_(N_2) = 4/(1 * 10^(-5)) = 4 * 10^(5) -># NOT possible
Now, you know the mole fraction of dissolved nitrogen gas in this solution. This mole fraction tells you the ratio that exists between the number of moles of nitrogen gas and the total number of moles present in the solution.
If you take
#chi_(N_2) = n/(n + 10)#
This is true because you know that you have
You thus have
#4 * 10^(-5) = n/(n + 10)#
Rearrange to get
#n = 4 * 10^(-5) * n + 4 * 10^(-4)#
#n(1 - 4 * 10^(-5)) = 4 * 10^(-4)#
This will be equivalent to
#n = (4 * 10^(-4))/(1 - 4 * 10^(-5)) ~~ color(green)(|bar(ul(color(white)(a/a)4 * 10^(-4)"moles N"_2color(white)(a/a)|)))#