(a)(i) State three postulates of the kinetic theory of gases. (ii) Draw a sketch to illustrate Boyle's law. (iii) Explain what is meant by "absolute zero of...
Question 1 Report
(a)(i) State three postulates of the kinetic theory of gases.
(ii) Draw a sketch to illustrate Boyle's law.
(iii) Explain what is meant by "absolute zero of temperature".
(b) Equal volumes of a gas X and oxygen are at the same pressure but temperature of 200 K and 800K respectively.
(i) Giving reason for your answer, state which of the gas samples contains the greater number of molecules.
(ii) If the mass of one molecule of the gas X is \(2.19 x 10^{-22}\) g, determine the molar mass of X. [Avogadro constant = \(6.02 x 10^{-23}\)]
(iii) Hence, state with reason which of X and oxygen will diffuse faster under the same conditions. [O = 16].
(c)(i) Mention two reaction conditions that can increase the yield of ammonia in the reaction represented by the following equation: \(N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}\ \Delta H = -46\text{kJmol}^{-1}\). Draw a labelled energy profile diagram for an endothermic reaction.
(iii) A solid W decomposes on heating according to the following equation: \(W_{(s)} \to Y_{(s)} + Z_{(g)}\) List two factors apart from temperature, which can affect the rate of the reaction.
Answer Details
(a)(i) Postulates of the kinetic theory of gases
- A gas consists of a very large number of tiny particles which are in continuous rapid random motion.
- The actual volume of the gas particles is negligible compared with the volume of the container, and intermolecular forces are negligible.
- Collisions between gas particles and with the walls of the container are perfectly elastic. The average kinetic energy of the particles is proportional to the absolute temperature.
(a)(ii) Boyle's law
At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: \(P \propto \frac{1}{V}\), or \(PV=\text{constant}\).
(a)(iii) Absolute zero
Absolute zero is the lowest theoretically attainable temperature, \(0\text{ K}\) or approximately \(-273^\circ\text{C}\), at which the volume of an ideal gas would theoretically become zero and molecular motion is at its minimum.
(b)(i)
Gas X contains the greater number of molecules. For equal volumes at the same pressure,
\[n=\frac{PV}{RT}\]
Hence, \(n\propto \frac{1}{T}\). Since X is at \(200\text{ K}\), whereas oxygen is at \(800\text{ K}\), X has more molecules.
(b)(ii)
Mass of one molecule of X \(=2.19\times10^{-22}\text{ g}\).
\[M=2.19\times10^{-22}\times6.02\times10^{23}\]
\[M=(2.19\times6.02)\times10=131.8\text{ g mol}^{-1}\]
Therefore, the molar mass of X is approximately \(132\text{ g mol}^{-1}\).
(b)(iii)
\[M(\mathrm{O_2})=2(16)=32\text{ g mol}^{-1}\]
By Graham's law, rate of diffusion is inversely proportional to the square root of molar mass. Since \(32<132\), oxygen diffuses faster than X.
(c)(i) Conditions for increasing the equilibrium yield of ammonia
- Use a high pressure, because the forward reaction changes four moles of gaseous reactants into two moles of gaseous product.
- Use a low temperature, because the forward reaction is exothermic, \(\Delta H=-46\text{ kJ mol}^{-1}\).
Continuous removal of ammonia as it is formed also increases its yield.
(c)(ii) Labelled energy profile diagram for an endothermic reaction
(c)(iii)
Two factors, apart from temperature, which affect the rate of decomposition of W are:
- Surface area (particle size) of W. A finely divided solid decomposes faster.
- Presence of a catalyst.
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