Table 8 .4 .1

Van der Waals Constants for Common Gases

The effect of IMF’s and gas volume on real gas behavior becomes quite obvious when you examine a graph of PV/nT versus P for real gases (Figure 8.4.8). Since PV = nRT, PV/nT should equal R

Departure from Ideal Gas Behaviour

Figure 8 .4 .8 As pressure increases, deviation from ideal behavior becomes more pronounced. The deviation is most noticeable for larger gases. This makes sense as larger gases have a greater volume and exert larger London dispersion forces on each other.

The effect is further demonstrated with examination of a graph of PV/RT versus P for one mole of a gas at three different temperatures (Figure 8.4.9). Since PV = nRT, PV/RT should equal 1 for one mole of gas.

Figure 8 .4 .9 As temperature decreases, deviation from ideal behavior becomes more pronounced. Gases behave most ideally when the temperature is high.

Examination of the data in Table 8.4.1 and the graphs in Figure 8.4.8 and Figure 8.4.9 provides support for the statement that gases behave most ideally when pressure is low and temperature is high. Low pressure and high temperature make real gas volume and real gas attractive forces less noticeable

Quick Check

1. Examine the graphs in Figure 8.4.8 and Figure 8.4.9.

(a) Which particle deviates the most from ideal behavior? Give two reasons for this behavior.

(b) What temperature provides the most ideal behavior? Explain.

2. Explain the general pattern for the values of a and b moving down the noble gas family. (A simple statement of the trend is not an adequate answer.)

3. Explain the same pattern moving from N2 to CO2 to CCl4.

4. Explain the same pattern moving from N2 to CO to HCl to H2O.

8.4 Review Questions

1. Calculate the average kinetic energies of Ne(g) and N2(g) at 298 K and 596 K. What pattern is noticeable between kinetic energy and temperature?

4. Consider the van der Waals equation for real gases. (a) Which of the two molecules, H2O or H2S, has the higher value for a and which has the higher value for b? Explain.

2. Calculate the root mean square velocities of Ne(g) and N2(g) at 298 K and 596 K. What pattern is noticeable between root mean square velocities and temperature?

(b) One of the van der Waals constants can be correlated with the boiling point of a substance. Specify which constant and how it is related to the boiling point.

5. Five identical balloons are shown below. Each is filled to the same volume with the pure gases indicated at 25°C and 1.0 atmosphere pressure.

3. At 25°C and 1 atmosphere pressure, which of the following gases shows the greatest deviation from ideal behavior? The least? Give two reasons for your choice.

CH4 SO2 O2 H2

CO2 O2 He N2 CH4

(a) Which balloon contains the greatest mass of gas? Explain.

(b) Compare the average kinetic energies of the gas molecules in the balloons. Explain.

7. Calculate the root mean square velocity and the average kinetic energy of Br2, Cl2, and F2. Which has the greatest: (a) velocity?

(c) Which balloon contains the gas that would be expected to deviate most from the behaviour of an ideal gas? Explain.

(b) kinetic energy?

(d) Twelve hours after being filled, all the balloons have decreased in size. Predict which balloon will be the smallest. Explain your reasoning.

6. Consider a 5.0 L container of helium gas at STP. How will the following be affected by the changes given below?

(a) kinetic energy

(b) average velocity

(c) frequency of collisions

(i) The Kelvin temperature is increased by 100°C.

(c) effusion rate?

8. A sample of neon effuses from a container in 38 s. The same amount of an unknown noble gas requires 77.5 s. What is the unknown gas?

9. The rate of effusion of an unknown gas is four times faster than oxygen gas. Calculate the molar mass and identify the gas.

(ii) The volume is halved.

(iii) The number of moles of gas is doubled.