Questions on the Maxwell–Boltzmann distribution, temperature and catalysts

Question 1

Discuss the advantages and disadvantages, to a company making a product by an exothermic reversible reaction between gases, of using a heterogeneous catalyst rather than a higher temperature to obtain a useful rate.

Accepted Answer

Indicative content

a catalyst provides a route with a lower activation energy, so a useful rate is reached at a lower temperature
less fuel is burnt to heat the plant, which lowers the energy cost and the carbon dioxide released
the reaction is exothermic, so a lower temperature gives a higher equilibrium yield, while a catalyst does not change the position of equilibrium
the catalyst is not used up, and as a solid it stays in the reactor and does not need separating from the products
against that, the catalyst costs money and must be replaced, and impurities in the feed can poison its surface
on balance a catalyst is preferred where the saving in energy and the gain in yield outweigh its cost, as in the Haber process, where iron gives a useful rate at about 450 °C

Levels

Level 3 (5–6 marks) the advantages of the catalyst over a higher temperature are all explained, the lower activation energy, the saving in fuel and carbon dioxide, and the higher equilibrium yield of the exothermic reaction, together with its ease of separation and the disadvantages of cost and poisoning, ending with a justified conclusion
Level 2 (3–4 marks) the lower activation energy and the energy saving are explained and one drawback is given; the higher equilibrium yield for an exothermic reaction, or the conclusion, is not there
Level 1 (1–2 marks) the catalyst is said to lower the activation energy or save energy, often with the claim that it also shifts the equilibrium to the right

Question 2

Draw a Maxwell–Boltzmann distribution for a sample of gas, labelling both axes. Mark the most probable energy, the mean energy and an activation energy, Ea, and shade the area that represents the molecules able to react.

Accepted Answer

B1 axes labelled number of molecules, vertical, and energy, horizontal; ignore units B1 the curve starts at the origin, rises to a single peak and falls in a long tail to the right B1 the tail approaches the energy axis but does not touch or cross it; a tail that meets the axis loses this mark B1 the most probable energy is marked at the peak and the mean energy to the right of the peak B1 Ea is marked well to the right of the peak, with the area under the curve beyond it shaded

Question 3

Draw an enthalpy profile for an exothermic reaction with and without a catalyst, labelling the activation energy of each route and ΔH, and explain why the catalyst does not change the equilibrium yield of a reversible reaction.

Accepted Answer

B1 axes labelled enthalpy and progress of reaction, with the product level below the reactant level B1 two humps between the same reactant and product levels, the catalysed one lower B1 the activation energy of each route drawn from the reactant level to the top of its own peak B1 a single ΔH arrow from the reactants to the products, the same for both routes B1 the catalyst lowers the activation energy of the forward and reverse reactions equally, so the position of equilibrium is unchanged and is only reached sooner

Question 4

Evaluate a student's sketch of the Maxwell–Boltzmann distribution, shown in the figure.

Accepted Answer

B1 the curve should start at the origin, because no molecule has zero energy, so starting part of the way up is wrong B1 the tail should approach the axis without meeting it, because there is no maximum energy B1 the peak is the most probable energy; the mean energy lies to the right of the peak because the curve is not symmetrical B1 the axes should be number of molecules and energy; reject 'rate', which the vertical axis does not show, so the sketch would earn none of these marks as drawn

Question 5

Compare the effect of raising the temperature with the effect of adding a catalyst on the Maxwell–Boltzmann distribution and on the rate of a reaction.

Accepted Answer

B1 raising the temperature changes the distribution: the peak moves right and lower, with the same area B1 a catalyst leaves the distribution unchanged and moves the activation energy to a lower value B1 in both cases more molecules have energy at least equal to the activation energy that applies, so more collisions are successful per unit time and the rate rises B1 raising the temperature also makes collisions slightly more frequent, whereas a catalyst does not change the collision frequency

Question 6

Explain why a Maxwell–Boltzmann distribution starts at the origin and never meets the energy axis at high energy, and state what the total area under the curve represents.

Accepted Answer

B1 it starts at the origin because no molecules have zero energy B1 it never meets the axis because there is no maximum energy: a very small number of molecules have very high energies B1 the total area under the curve is the total number of molecules in the sample

Question 7

Describe how the Maxwell–Boltzmann distribution for a sample of gas changes when its temperature is raised from T₁ to T₂, as in the graph.

Accepted Answer

B1 the peak moves to a higher energy, to the right B1 the peak is lower and the curve is broader, lying above the original curve at high energies B1 the area under the curve is unchanged, because the number of molecules is the same

Question 8

Explain why increasing the temperature increases the rate of a reaction between two gases.

Accepted Answer

B1 at the higher temperature more molecules have energy at least equal to the activation energy B1 so a greater proportion of collisions are successful, and there are more successful collisions per unit time B1 molecules also move faster and collide slightly more often, but this is the smaller effect

Question 9

Explain why a rise in temperature of only 10 °C can nearly double the rate of a reaction.

Accepted Answer

B1 the activation energy lies far out in the tail of the distribution, where few molecules have that much energy B1 a small rise in temperature spreads the curve to the right, and the number of molecules with at least Ea rises by a large proportion, nearly doubling B1 the collision frequency rises by only a few per cent, so almost all of the increase in rate comes from the larger number of molecules with at least Ea

Question 10

Explain, with reference to the Maxwell–Boltzmann distribution, how a catalyst increases the rate of a reaction.

Accepted Answer

B1 a catalyst provides an alternative reaction route with a lower activation energy B1 the distribution is unchanged, but the area beyond the lower Ea is larger, so more molecules have energy at least equal to the activation energy B1 a greater proportion of collisions are successful, so there are more successful collisions per unit time

Question 11

Suggest why a car's catalytic converter removes very little carbon monoxide in the first minute after a cold engine is started.

Accepted Answer

B1 the catalyst and the exhaust gases are cold when the engine starts B1 even on the catalysed route few molecules have energy at least equal to the lowered activation energy at that low temperature B1 so few collisions on the catalyst surface succeed and the rate of conversion is low until the hot exhaust has warmed the converter

Question 12

Suggest why raising the temperature from 20 °C to 30 °C increases the rate of a reaction with a large activation energy by a greater factor than the rate of a reaction with a small activation energy.

Accepted Answer

B1 a large Ea lies far out in the tail of the distribution, where the number of molecules falls steeply with energy B1 stretching the curve to the right by warming multiplies the small area beyond a large Ea by a large factor B1 a small Ea lies nearer the peak, where a large share of the molecules already exceeds it, so the same warming changes that area by a smaller proportion

Question 13

Evaluate the statement: 'a catalyst works by giving the reactant molecules the extra energy they need to react'.

Accepted Answer

B1 the statement is wrong: a catalyst does not change the energies of the molecules, so the Maxwell–Boltzmann distribution is unchanged B1 a catalyst provides an alternative route with a lower activation energy B1 more molecules already have enough energy for the lower barrier, so the statement is right that more molecules react but wrong about why

Question 14

Suggest why making ethanoic acid from methanol and carbon monoxide with a rhodium catalyst, CH₃OH(l) + CO(g) → CH₃COOH(l), is more sustainable than oxidising hydrocarbons to a mixture of products.

Accepted Answer

B1 every atom of the reactants ends up in the one product, so the atom economy is 100% B1 there are no by-products to separate or dispose of, so less waste and less energy is spent on separation B1 the catalyst gives a lower activation energy route, so a useful rate is reached at a moderate temperature with less fuel burnt

Question 15

Justify the statement that, for a reaction with a large activation energy, raising the temperature of the mixture by 10 °C increases the rate more than doubling the concentration of a reactant does.

Accepted Answer

B1 doubling the concentration doubles the number of collisions in a given time, so at most it doubles the rate; the fraction of collisions that succeed is unchanged B1 raising the temperature shifts the Maxwell–Boltzmann distribution towards higher energies, and only the tail of the curve lies beyond a large Ea, so the fraction of molecules with energy at least Ea can rise by far more than a factor of two B1 collisions also become a little more frequent at the higher temperature, but for a large Ea the rate more than doubles: for Ea = 100 kJ mol⁻¹, 298 → 308 K multiplies it by about 3.7; accept a numerical estimate

Question 16

State where the most probable energy and the mean energy are found on a Maxwell–Boltzmann distribution.

Accepted Answer

B1 the most probable energy is the energy at the peak of the curve B1 the mean energy lies to the right of the peak, at a higher energy than the most probable energy

Question 17

Identify each catalyst as heterogeneous or homogeneous: chlorine atoms catalysing the decomposition of ozone gas in the stratosphere, and solid nickel catalysing the reaction of hydrogen gas with liquid vegetable oils.

Accepted Answer

B1 chlorine atoms are a homogeneous catalyst, because they are in the gas phase with the ozone B1 nickel is a heterogeneous catalyst, because it is a solid and the reactants are a gas and a liquid