A flask contains three times as many moles as #H_2# as it does #O_2# gas. If hydrogen and oxygen are the only present gases, what is the total pressure flask if the partial pressure due to oxygen is #P#?
1 Answer
Explanation:
According to Dalton's Law of Partial Pressures, the total pressure of a gaseous mixture will be equal to the individual partial pressure of each component of the mixture.
Simply put, to get the total pressure of a gaseous mixture, you add up the partial pressure you'd get for each component of that mixture if it occupied the volume of the mixture alone.
Mathematically, this can written as
#color(blue)(|bar(ul(color(white)(a/a)P_"total" = sum_i P_icolor(white)(a/a)|)))" "# , where
In your case, the mixture is said to contain hydrogen gas,
This means that if you take
#n_(H_2) = 3 xx n_(O_2)" "color(purple)("(*)")#
Now, let's assume that the mixture is being held in a container that has a volume of
#color(blue)(|bar(ul(color(white)(a/a)PV = nRT color(white)(a/a)|)))#
to express
#P * V = n_(O_2) * RT implies V = n_(O_2)/P * RT" "color(red)("(*)")#
Now, you can write the same thing for
#P^' * V = n_(H_2) * RT implies V = n_(H_2)/P^' * RT#
Use equation
#n_(O_2)/P * color(red)(cancel(color(black)(RT))) = n_(H_2)/P^' * color(red)(cancel(color(black)(RT)))#
Rearrange to find
#P^' = n_(H_2)/n_(O_2) * P#
Use equation
#P^' = (3 xx color(red)(cancel(color(black)(n_(O_2)))))/color(red)(cancel(color(black)(n_(O_2)))) * P#
#P^' = 3 xx P#
Finally, plug this into the equation that describes Dalton's Law of Partial Pressures to get the total pressure of the mixture,
#P_"total" = P^' + P#
#P_"total" = 3 xx P + P = color(green)(|bar(ul(color(white)(a/a)4 xx Pcolor(white)(a/a)|)))#