Question #c0267

Jun 7, 2017

The total volume of the mixture is 118.6 L. All the gases exert the same pressure: 1 bar.

Explanation:

STP is a pressure of 1 bar and a temperature of 0 °C.

At STP the volume of 1 mol of any gas is 22.71 L.

So, we can find the moles of each gas and then calculate the volumes.

Hydrogen

$\text{Moles" = 6.50 color(red)(cancel(color(black)("g"))) × "1 mol"/(2.016 color(red)(cancel(color(black)("g")))) = "3.224 mol}$

$\text{Volume" = 3.224 color(red)(cancel(color(black)("mol"))) × "22.71 L"/(1 color(red)(cancel(color(black)("mol")))) = "73.22 L}$

Nitrogen dioxide

$\text{Moles" = 6.50 color(red)(cancel(color(black)("g"))) × "1 mol"/(46.01 color(red)(cancel(color(black)("g")))) = "0.1413 mol}$

$\text{Volume" = 0.1413 color(red)(cancel(color(black)("mol"))) × "22.71 L"/(1 color(red)(cancel(color(black)("mol")))) = "3.208 L}$

Carbon monoxide

$\text{Moles" = 6.50 color(red)(cancel(color(black)("g"))) × "1 mol"/(28.01 color(red)(cancel(color(black)("g")))) = "0.2321 mol}$

$\text{Volume" = 0.2321 color(red)(cancel(color(black)("mol"))) × "22.71 L"/(1 color(red)(cancel(color(black)("mol")))) = "5.270 L}$

Helium

$\text{Moles" = 6.50 color(red)(cancel(color(black)("g"))) × "1 mol"/(4.003 color(red)(cancel(color(black)("g")))) = "1.624 mol}$

$\text{Volume" = 1.624 color(red)(cancel(color(black)("mol"))) × "22.71 L"/(1 color(red)(cancel(color(black)("mol")))) = "36.88 L}$

Total volume

The total volume of the gases is

$V = \text{(73.22 + 3.208 + 5.270 + 36.88) L" = "118.6 L}$

Gas Pressure

All gases are at STP, so they each exert the same pressure: 1 bar.