# Question #4d7ef

##### 1 Answer

#### Explanation:

The idea here is that the **number of moles** of hydrogen gas, **constant** when going from the initial state of the gas to the final state of the gas.

Your starting point here will be the **ideal gas law** equation, which looks like this

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#

Here you have

#P# - the pressure of the gas

#V# - the volume it occupies

#n# - the number of moles of gas

#R# - theuniversal gas constant

#T# - theabsolute temperatureof the gas

Now, you know that when the gas is first generated in a volume **total pressure** of the gas + air mixture goes from

This means that the pressure of hydrogen gas is equal to

#P_("H"_2) = P_f - P_a#

In other words, the **total pressure** of the hydrogen gas + air mixture is given by the sum of the **partial pressures** of its two components, air and hydrogen gas, as given by **Dalton's Law of Partial Pressures**.

You can thus use the ideal gas law equation to write

#P_("H"_2) * V_1 = n * R * T_1#

which is equivalent to

#(P_f - P_a) * V_1 = n * R * T_1" " " "color(orange)((1))#

Now focus on the second state of the gas. You want **the same number of moles**,

Once again, use the ideal gas law equation to write

#P_2 * V_2 = n * R * T_2" " " "color(orange)((2))#

All you have to do now is divide equation

#((P_f - P_a) * V_1)/(P_2 * V_2) = (color(red)(cancel(color(black)(n))) * color(red)(cancel(color(black)(R))) * T_1)/(color(red)(cancel(color(black)(n))) * color(red)(cancel(color(black)(R))) * T_2)#

Rearrange to isolate

#P_2 * V_2 * T_1 = (P_f - P_a) * V_1 * T_2#

#color(green)(|bar(ul(color(white)(a/a)color(black)(V_2 = (P_f - P_a)/P_2 * T_2/T_1 * V_1)color(white)(a/a)|)))#