Question

Question #d5762

Answer 1

`P_"total" = "36 atm"`

Explanation:

Your strategy here will be to

• use the molar masses of oxygen gas and hydrogen gas to determine how many moles of gas you have in that sample

• use the ideal gas law equation to determine the partial pressure of each gas in the mixture

• use Dalton's Law of Partial Pressures to find the total pressure of the mixture

The idea here is that since the volume of the container is the same for both gases, you can calculate the pressure each gas would exert if isolated in that volume and at that temperature.

So, this gaseous mixture will contain

`4 color(red)(cancel(color(black)("g"))) * "1 mole O"_2/(32.0color(red)(cancel(color(black)("g")))) = "0.125 moles O"_2`

`3color(red)(cancel(color(black)("g"))) * "1 mole H"_2/(2.016color(red)(cancel(color(black)("g")))) = "1.49 moles H"_2`

Use the ideal gas law equation

`color(blue)(PV = nRT)`

to determine the pressure each gas would exert if alone in the given volume - do no forget to convert the temperature from degrees Celsius to Kelvin!

`PV = nRT implies P = (nRT)/V`

For oxygen gas, you will have

`P_(O_2) = (0.125color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * (273.15 + 0)color(red)(cancel(color(black)("K"))))/(1color(red)(cancel(color(black)("L"))))`

`P_(O_2) = "2.8 atm"`

For hydrogen gas, you will have

`P_(H_2) = (1.49color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * (273.15 + 0)color(red)(cancel(color(black)("K"))))/(1color(red)(cancel(color(black)("L"))))`

`P_(H_2) = "33.4 atm"`

Now, Dalton's Law of Partial Pressures states that the total pressure of a gaseous mixture is equal to the sum of the partial pressures of each individual gas that makes up that mixture.

`color(blue)(P_"total" = sum_i P_i)" "`, where

`P_i` - the partial pressure of gas `i`

In your case, the mixture contains two gases, oxygen as and hydrogen gas. This means that the total pressure of the mixture will be

`P_"total" = P_(O_2) + P_(H_2)`

`P_"total" = "2.8 atm" + "33.4 atm" = "36.2 atm"`

Now, you should round this off to one sig fig, but I'll leave it rounded to two sig figs, just for good measure

`P"_total" = color(green)("36 atm")`