# Question ddef4

Oct 18, 2016

Deviation from ideal behaviour means the difference between the ideal value and the experimental value of a property.

#### Explanation:

At ordinary temperatures, real gases behave almost like ideal gases.

For example, the volume of 1.00 mol of an ideal gas at 1 bar and 0 °C. is 22.7 L.

The volume of 1 mol of ${\text{CO}}_{2}$ under the same conditions is 22.6 L.

At low temperatures and high pressures, the differences become much larger.

For example, let's calculate the volume of 1.00 mol of carbon dioxide as an ideal gas at 150 bar and 200 K.

$P V = n R T$

V = (nRT)/P = (1.00 color(red)(cancel(color(black)("mol"))) × "0.083 14"color(red)(cancel(color(black)("bar")))·"L"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 200 color(red)(cancel(color(black)("K"))))/(150 color(red)(cancel(color(black)("bar")))) = "0.111 L" = "111 mL"

The actual volume under these conditions is 51 mL.

The actual volume is less than half of the ideal volume, because of the attractive forces of the molecules for each other

Now, let's repeat the calculation at a pressure of 900 bar and 200 K..

V = (nRT)/P = (1.00 color(red)(cancel(color(black)("mol"))) × "0.083 14" color(red)(cancel(color(black)("bar")))·"L"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 200 color(red)(cancel(color(black)("K"))))/(900 color(red)(cancel(color(black)("bar")))) = "0.0185 L" = "18.5 mL"#

The actual volume under these conditions is 48 mL.

The actual volume is 2.5 times greater than the ideal volume, because at this high pressure the volumes of the molecules themselves are a large proportion of the space.