(a) (i) What is diffusion?
(ii) State Charles' law:
(iii) Sketch a graph to illustrate Charles' law.
(iv) A given mass of a gas occupied 150 cm3 at 27 °C and a pressure of \(1.013 \times 10^{5}\ \mathrm{Nm}^{-2}\). Calculate the temperature at which its volume will be doubled at the same pressure.
(v) Arrange the three states of matter in order of increasing: (i) kinetic energy; (ii) forces of cohesion.
(b) (i) State Le Chatelier's principle. (ii) A metal M forms two oxides containing 11.1% and 20.0% of oxygen. Show that these figures agree with the law of multiple proportion.
(c) The table below shows the physical properties of substances A, B and C.
| Substance |
Melting point/°C |
Boiling point/°C |
Solubility in water at 25°C |
| A |
30 |
117 |
Insolube |
| B |
31 |
160 |
Insoluble |
| C |
1200 |
1200 |
Insoluble |
(i) If A and B are miscible when melted and B and C react when heated, describe how a mixture of A, B, and C could be separated.
(ii) When 25.25g of the mixture A, B and C was separated, 7.52 g of A and 8.48 g of B were recovered. Assuming i there was no loss of components during separation, calculate the percentage by mass of C in the mixture
(a)(i) Diffusion
The spontaneous movement of particles of a substance from a region of higher concentration to a region of lower concentration until they are evenly spread.
(a)(ii) Charles' law
The volume of a fixed mass of gas is directly proportional to its absolute (Kelvin) temperature, provided the pressure remains constant.
(a)(iii) Sketch
A straight-line graph of volume (y-axis) against absolute temperature in kelvin (x-axis) that passes through the origin (0 K, 0 volume).
(a)(iv) Temperature at which the volume doubles (constant pressure)
\(V_1 = 150\ \text{cm}^3\), \(T_1 = 27 + 273 = 300\ \text{K}\), \(V_2 = 300\ \text{cm}^3\).
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \Rightarrow T_2 = \frac{V_2 T_1}{V_1} = \frac{300 \times 300}{150} = 600\ \text{K} = 327\ ^{o}\text{C} \]
(a)(v) Order of increasing:
- Kinetic energy: solid < liquid < gas.
- Forces of cohesion: gas < liquid < solid.
(b)(i) Le Chatelier's principle
When a system in equilibrium is subjected to a change in concentration, pressure or temperature, the equilibrium shifts in the direction that tends to oppose (reduce) that change.
(b)(ii) Law of multiple proportions for the two oxides of M
| Oxide | % oxygen | % metal M | Mass of O per 1 g of M |
|---|
| 1 | 11.1 | 88.9 | 11.1 / 88.9 = 0.125 |
| 2 | 20.0 | 80.0 | 20.0 / 80.0 = 0.250 |
\[ \frac{0.250}{0.125} = 2 : 1 \]
The masses of oxygen that combine with a fixed mass of M are in the simple whole-number ratio 2 : 1, which agrees with the law of multiple proportions.
(c) Substances A, B and C
| Substance | m.p./\(^{o}\)C | b.p./\(^{o}\)C | Solubility in water (25 \(^{o}\)C) |
|---|
| A | 30 | 117 | Insoluble |
| B | 31 | 160 | Insoluble |
| C | 1200 | 1200 | Insoluble |
(c)(i) Separation scheme
- Warm the mixture gently to about 35 \(^{o}\)C. A and B (m.p. 30 and 31 \(^{o}\)C) both melt and, being miscible, form one liquid; C (m.p. 1200 \(^{o}\)C) stays solid. Do not overheat, or B would react with C.
- Filter the warm mixture: solid C is retained on the filter paper while the molten A + B mixture passes through. Wash and dry C.
- Separate A and B from the liquid by fractional distillation. A distils over first at 117 \(^{o}\)C and is collected; B distils at 160 \(^{o}\)C and is collected separately.
(c)(ii) Percentage by mass of C
\[ \text{Mass of C} = 25.25 - 7.52 - 8.48 = 9.25\ \text{g} \]
\[ \%\,\text{C} = \frac{9.25}{25.25}\times 100 = 36.6\% \]
(a)(i) Diffusion
The spontaneous movement of particles of a substance from a region of higher concentration to a region of lower concentration until they are evenly spread.
(a)(ii) Charles' law
The volume of a fixed mass of gas is directly proportional to its absolute (Kelvin) temperature, provided the pressure remains constant.
(a)(iii) Sketch
A straight-line graph of volume (y-axis) against absolute temperature in kelvin (x-axis) that passes through the origin (0 K, 0 volume).
(a)(iv) Temperature at which the volume doubles (constant pressure)
\(V_1 = 150\ \text{cm}^3\), \(T_1 = 27 + 273 = 300\ \text{K}\), \(V_2 = 300\ \text{cm}^3\).
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \Rightarrow T_2 = \frac{V_2 T_1}{V_1} = \frac{300 \times 300}{150} = 600\ \text{K} = 327\ ^{o}\text{C} \]
(a)(v) Order of increasing:
- Kinetic energy: solid < liquid < gas.
- Forces of cohesion: gas < liquid < solid.
(b)(i) Le Chatelier's principle
When a system in equilibrium is subjected to a change in concentration, pressure or temperature, the equilibrium shifts in the direction that tends to oppose (reduce) that change.
(b)(ii) Law of multiple proportions for the two oxides of M
| Oxide | % oxygen | % metal M | Mass of O per 1 g of M |
|---|
| 1 | 11.1 | 88.9 | 11.1 / 88.9 = 0.125 |
| 2 | 20.0 | 80.0 | 20.0 / 80.0 = 0.250 |
\[ \frac{0.250}{0.125} = 2 : 1 \]
The masses of oxygen that combine with a fixed mass of M are in the simple whole-number ratio 2 : 1, which agrees with the law of multiple proportions.
(c) Substances A, B and C
| Substance | m.p./\(^{o}\)C | b.p./\(^{o}\)C | Solubility in water (25 \(^{o}\)C) |
|---|
| A | 30 | 117 | Insoluble |
| B | 31 | 160 | Insoluble |
| C | 1200 | 1200 | Insoluble |
(c)(i) Separation scheme
- Warm the mixture gently to about 35 \(^{o}\)C. A and B (m.p. 30 and 31 \(^{o}\)C) both melt and, being miscible, form one liquid; C (m.p. 1200 \(^{o}\)C) stays solid. Do not overheat, or B would react with C.
- Filter the warm mixture: solid C is retained on the filter paper while the molten A + B mixture passes through. Wash and dry C.
- Separate A and B from the liquid by fractional distillation. A distils over first at 117 \(^{o}\)C and is collected; B distils at 160 \(^{o}\)C and is collected separately.
(c)(ii) Percentage by mass of C
\[ \text{Mass of C} = 25.25 - 7.52 - 8.48 = 9.25\ \text{g} \]
\[ \%\,\text{C} = \frac{9.25}{25.25}\times 100 = 36.6\% \]
