C3 Gaseous State

Question 1

Boyle’s Law

Answer 1

At constant temperature, the volume of a fixed mass of gas (i.e. for n is constant) is inversely proportional to its pressure

Question 2

Charles’ Law

Answer 2

At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature (measured in K)

Question 3

Avogadro’s Law

Answer 3

At constant temperature and pressure, the volume of a gas is directly proportional to the number of molecules (or number of moles of gas) present

Question 4

Assumptions of the Kinetic Molecular Theory about ideal gases *(To mem)

Answer 4

1. The gas particles have negligible volume compared to the volume of the container.
2. The intermolecular forces of attraction between gas particles are negligible.
3. Collisions between gas particles, and their collisions with the walls of the container, are perfectly elastic; i.e. there is no net loss or gain of kinetic energy during collision.

Question 5

Conditions for real gases to behave ideally:

Answer 5

At low pressures, the gaseous molecules are relatively far apart. The volume of the molecules themselves is negligible compared to the volume of the container. Thus, real gas molecules at low pressure can be approximated to have negligible volume. Also, intermolecular forces are negligible as the particles are far apart. Hence their behaviour at low pressures would approach that of ideal gases.

At high temperatures, gas particles have enough kinetic energy to overcome intermolecular forces, which can thus be considered insignificant. Thus, the behavior of real gases approach ideal gas behavior at high temperatures.

Question 6

Explaining deviations from ideal gas behaviourr at high pressures

Answer 6

The gas particles can no longer be considered to have negligible volume compared to the volume of the container.
At high pressures, the volume of the container decreases. The molecules are pushed closely together and take up a significant portion of the container volume, resulting in less space in which the molecules can move. Thus, it is no longer valid to assume that its volume is negligible compared to the container volume, and so the gas deviates from ideal behaviour. (In fact, the total volume occupied by a real gas is actually greater than the volume predicted by the ideal gas equation.) Also, since the gas particles are close together, they tend to interact with one another, hence intermolecular attractions are not negligible.

Question 7

Explaining deviations from ideal gas behaviour at low temperatures

Answer 7

The intermolecular forces between gas particles become significant.
As temperature is lowered, the kinetic energy of the gas particles decreases, causing them to move more slowly and intermolecular forces become more significant. This also causes collisions to become inelastic (such that assumption 3 is no longer valid either). Eventually, it reaches a point where the particles can no longer overcome the intermolecular forces, at which point real gases liquefy (condense to form a liquid) when cooled to below its boiling point.

Question 8

Curve for a real gas explanation:

Answer 8

At low external pressures, a real gas behaves almost like an ideal gas. PV/RT is close to 1.

At moderately high external pressures, the gas particles are close together and intermolecular forces of attractions become significant. This lowers the forces of collision of the gas particles with the container’s wall. As a result, a real gas exerts a lower pressure than that predicted by the ideal gas equation.

As P(real) < P(ideal), ((P(real) x V)/ RT) < ((Pv(ideal) x V)/RT)), the curve for a real gas is below the line for ideal gas.

At very high external pressures, the gas particles are so close together, the volume of gas particles become significant. The container volume is larger than the volume of space between the gas particles. Using the container volume as V in the PV/RT ratio gives a value greater than 1. The curve for a real gas is above the line for ideal gas.

Question 9

Molar volume, Vm,

Answer 9

Molar volume, Vm, of any gas is the volume occupied by 1 mole of the gas at a specified temperature and pressure

Question 10

Explain why ammonia (Mr = 17.0) is expected to behave less ideally than neon (Mr = 20.2).

Answer 10

Ammonia is a larger molecule than monoatomic particles of neon.
Ammonia has stronger intermolecular forces (hydrogen bonding) than neon (dispersion) thus ammonia is expected to behave less ideally than neon.

Question 11

In fact, the pressure inside the cylinder is 2.2 x 10^7 Pa under these conditions, Explain why this differs (less than) from the ideal gas pressure you calculated in (b),

Answer 11

Significant dispersion forces between CO2 molecules reduces the collision frequency and force of impact on the walls of container, thus measured pressure is lower than predicted by the ideal gas equation.

Question 12

Explain the following in terms of the behaviour of the gas molecules:
(i) Boiling water in a pressure cooker causes the pressure inside to increase.
(i) Putting a gas under enough pressure causes it to liquefy.

Answer 12

(I): Boiling water increases tempt, resulting in increase in number of gas particles (as more liquid water becomes gaseous steam) and increase in average kinetic energy of gas particles. Overall there’s an increase in frequency of collision of gas particles on walls of cooker and force of impact on walls of the cooker thus pressure increases.

(II): Increasig pressure forces molecules closer together, intermolecular forces of attraction become more significant as molecules get closer, at some point, kinetic energy of particles is no longer large enough to overcome the intermolecular forces and gas liquefies.

Question 13

Compute the PV values for each of the above experiments and use them to identify gases D and E. Explain your reasoning. [3]

Answer 13

The PV values of gas D deviates more from a constant value than gas E. Hence gas D behaves less like an ideal gas than E.

Gas E is H2 which has a smaller electron cloud size and also has weaker dispersion forces between molecules and deviate less from ideal its while gas D is O2 which is a larger molecule with stronger dispersion forces and thus deviates more from ideal its.

Question 14

State and explain the rend in the first ionisation energy of the Group 16 elements down the group. [2]

Answer 14

First IE decreases down the group. As nuclear charge increases, electrons are also added to the next quantum shell thus attraction between the nucleus and the valence electron decreases. Less energy is needed to remove the valence electron.

Question 15

State 2 main assumptions of the kinetic theory and use these to explain why you might expect the behaviour of nitrogen dioxide to be less ideal compared to that of hydrogen. [3]

Answer 15

1. The volume of the gas particles is negligible as compared to the volume of the container.
2. There are no intermolecular forces of attraction between gas particles

NO2 has a larger electron cloud size hence volume of NO2 molecules is more significant compared to the volume of the gas, unlike H2.
Both NO2 and H2 have simplemolecular structure. Since NO2 has stronger permanent dipole-permanent dipole interaction than instantaneous dipole-induced dipole interactions in H2 OR NO2 has a larger number of electrons and hence larger electron cloud size than H2, the electron cloud of NO2 is more Polaris able and hence there is stronger intermolecular forces of attraction, gas deviates more from ideal gas.

Question 16

Under wha conditions of temperature and pressure would you expect the behaviour of gaseous aluminium chloride to be most like that of an ideal gas? [1]

Answer 16

High temperature and low pressure

Question 17

Explain why part of the graph for chloromethane is below that of an ideal gas at low pressure. [1]

Answer 17

At low pressure, when volume increases, pressure of chloromethane falls more than that of ideal gas as permanent dipole-permanent dipole interaction between CH3Cl molecules hold the particles closer together, hence frequency of effective collision between walls of container and CH3Cl molecules is lower, exerting lesser average force on walls of container, resulting in lower pressure.
OR
At low pressure, volume of chloromethane gas is lower/decreasesmore than ideal gas for a given pressure as permanent dipole-permanent dipole interactions between molecules is significant and the molecules are attracted closer to one another.

Question 18

Identify which of the following graphs represent 1 mol of CO2 at 500K.

Answer 18

Graph B.
CO2 at 500K deviates less than CO2 at 298K. At higher temperature, CO2 molecules possess higher average kinetic energy and are more able to overcome forces of attraction between the molecules.

Question 19

Describe 3 ways in which the properties of an ideal gas differ from those of real gases

Answer 19

• Molecules/particles of an ideal gas have zero volume/negligible volume as compared to volume of its container whereas real gases have significant molecular volume.
• There are negligible intermolecular forces between ideal gas molecules/particles whereas real gases have significant intermolecular forces.
• Collisions between ideal gas molecules/particles and those between ideal gas particles and the walls of the container are perfectly elastic (i.e. no loss of energy during collision) whereas those for real gas particles are inelastic (or there is loss of energy during collision).

Question 20

suggest why the volume you calculated is lesser [2]

Answer 20

there really significant dispersion forces between CO2 molecules [0.5]

gas molecules attract more closely together [0.5]

hence actual gas volume is smaller than predicted ideal gas volume [1]

Question 21

When real gas molecules collide, the kinetic energy during collision is not necessarily
conserved.
State two other properties of real gas molecules which could lead to the product pV for a
fixed mass of real gas at constant temperature being different from that for an ideal gas.

Answer 21

gas may have significant intermolecular forces of attraction between real gas particles

real gas particles have non-negligible volume compared to the volume of the container

Question 22

In Fig. 3.1, pV of gas A decreases as p increases, which differs from your sketch in (c)(i)
for an ideal gas. Which one of the properties that you have stated in (c)(ii) results in the
decrease in pV as p increases? Explain your answer briefly.

Answer 22

intermolecular forces of attraction

as pressure increases, gas particles come closer together hence experiences stronger intermolecular forces of attraction, resulting in a decrease in volume as compared to expected ideal gas volume