(a)(i) State Graham's law of diffusion
(ii) If \(100\ \text{cm}^3\) of oxygen diffused in 4 seconds and \(50\text{cm}^3\) of gas Y diffused in 3 seconds, calculate the relative molecular mass of gas Y. (0 = 16)
(b) Consider the following equilibrium reaction: \(X + 2Y_{(g)} \rightleftharpoons XY_{2(9)}\) \(\Delta H = -52\text{KJ mol}^{-1}\)
(i) State what happens to the yield of \(XY_2\) when the temperature is increased
(ii) Explain the effect of decrease in pressure on the equilibrium position.
(iii) State the effect of a catalyst on the I. position of equilibrium II. activation energy
(c)(i) State the differences between the solubilities of solids and gases in liquids.
(ii) Name the physical-properties used it choosing separation techniques for the following mixtures:
I. kerosene and petrol II. calcium trioxocarbonate (IV) and potassium chloride. III. ammonium chloride and sodium chloride.
(d)(i) State a method of preparing each of the following salts:
| Acid |
Basicity |
| \(H_3PO_4\) |
|
| \(CH_3COOH\) |
|
| \(HNO_2\) |
|
(iii) State the difference between anhydrous and hydrated salts.
(a)(i) Graham's law of diffusion
At constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density (or relative molecular mass).
\[ \text{rate} \propto \frac{1}{\sqrt{M}} \]
(a)(ii) Relative molecular mass of gas Y
Rate of oxygen \( = \dfrac{100}{4} = 25\ \text{cm}^3\text{s}^{-1} \); rate of Y \( = \dfrac{50}{3} = 16.67\ \text{cm}^3\text{s}^{-1} \). Relative molecular mass of \( O_2 = 2 \times 16 = 32 \).
\[ \frac{R_{O_2}}{R_Y} = \sqrt{\frac{M_Y}{M_{O_2}}} \]\[ \frac{25}{16.67} = \sqrt{\frac{M_Y}{32}} \;\Rightarrow\; 1.5 = \sqrt{\frac{M_Y}{32}} \]
Squaring both sides: \( 2.25 = \dfrac{M_Y}{32} \), so \( M_Y = 2.25 \times 32 = 72 \).
Relative molecular mass of gas Y = 72.
(b) \( X + 2Y_{(g)} \rightleftharpoons XY_{2(g)} \), \( \Delta H = -52\ \text{kJ mol}^{-1} \) (the forward reaction is exothermic).
(i) An increase in temperature favours the endothermic (backward) direction, so the yield of \( XY_2 \) decreases.
(ii) A decrease in pressure shifts the equilibrium towards the side with the greater number of gas molecules. The left side has 3 gas molecules \( (X + 2Y) \) while the right has 1 \( (XY_2) \); the position of equilibrium therefore moves backward (to the left) and the yield of \( XY_2 \) decreases.
(iii) A catalyst: I. has no effect on the position of equilibrium; II. lowers the activation energy of both the forward and backward reactions equally.
(c)(i) Solubility of solids compared with gases in liquids
- The solubility of most solids increases with a rise in temperature, whereas the solubility of gases decreases with a rise in temperature.
- Pressure has almost no effect on the solubility of solids, but the solubility of gases increases markedly with an increase in pressure.
(c)(ii) Physical property used for separation
- I. Kerosene and petrol: difference in boiling points (fractional distillation).
- II. Calcium trioxocarbonate(IV) and potassium chloride: difference in solubility in water (\( CaCO_3 \) insoluble, \( KCl \) soluble); dissolve, then filter.
- III. Ammonium chloride and sodium chloride: difference in the ability to sublime (\( NH_4Cl \) sublimes); sublimation.
(d)(ii) Basicity of the acids
Basicity is the number of replaceable hydrogen ions produced per molecule of the acid on ionization.
| Acid | Basicity |
|---|
| \( H_3PO_4 \) | 3 |
| \( CH_3COOH \) | 1 |
| \( HNO_2 \) | 1 |
Only the hydrogen of the \( -COOH \) group in ethanoic acid is replaceable, so its basicity is 1.
(d)(iii) Anhydrous and hydrated salts
An anhydrous salt contains no water of crystallization, while a hydrated salt contains a fixed number of molecules of water of crystallization chemically combined with it (for example \( CuSO_4 \) is anhydrous while \( CuSO_4 \cdot 5H_2O \) is hydrated).
(a)(i) Graham's law of diffusion
At constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density (or relative molecular mass).
\[ \text{rate} \propto \frac{1}{\sqrt{M}} \]
(a)(ii) Relative molecular mass of gas Y
Rate of oxygen \( = \dfrac{100}{4} = 25\ \text{cm}^3\text{s}^{-1} \); rate of Y \( = \dfrac{50}{3} = 16.67\ \text{cm}^3\text{s}^{-1} \). Relative molecular mass of \( O_2 = 2 \times 16 = 32 \).
\[ \frac{R_{O_2}}{R_Y} = \sqrt{\frac{M_Y}{M_{O_2}}} \]\[ \frac{25}{16.67} = \sqrt{\frac{M_Y}{32}} \;\Rightarrow\; 1.5 = \sqrt{\frac{M_Y}{32}} \]
Squaring both sides: \( 2.25 = \dfrac{M_Y}{32} \), so \( M_Y = 2.25 \times 32 = 72 \).
Relative molecular mass of gas Y = 72.
(b) \( X + 2Y_{(g)} \rightleftharpoons XY_{2(g)} \), \( \Delta H = -52\ \text{kJ mol}^{-1} \) (the forward reaction is exothermic).
(i) An increase in temperature favours the endothermic (backward) direction, so the yield of \( XY_2 \) decreases.
(ii) A decrease in pressure shifts the equilibrium towards the side with the greater number of gas molecules. The left side has 3 gas molecules \( (X + 2Y) \) while the right has 1 \( (XY_2) \); the position of equilibrium therefore moves backward (to the left) and the yield of \( XY_2 \) decreases.
(iii) A catalyst: I. has no effect on the position of equilibrium; II. lowers the activation energy of both the forward and backward reactions equally.
(c)(i) Solubility of solids compared with gases in liquids
- The solubility of most solids increases with a rise in temperature, whereas the solubility of gases decreases with a rise in temperature.
- Pressure has almost no effect on the solubility of solids, but the solubility of gases increases markedly with an increase in pressure.
(c)(ii) Physical property used for separation
- I. Kerosene and petrol: difference in boiling points (fractional distillation).
- II. Calcium trioxocarbonate(IV) and potassium chloride: difference in solubility in water (\( CaCO_3 \) insoluble, \( KCl \) soluble); dissolve, then filter.
- III. Ammonium chloride and sodium chloride: difference in the ability to sublime (\( NH_4Cl \) sublimes); sublimation.
(d)(ii) Basicity of the acids
Basicity is the number of replaceable hydrogen ions produced per molecule of the acid on ionization.
| Acid | Basicity |
|---|
| \( H_3PO_4 \) | 3 |
| \( CH_3COOH \) | 1 |
| \( HNO_2 \) | 1 |
Only the hydrogen of the \( -COOH \) group in ethanoic acid is replaceable, so its basicity is 1.
(d)(iii) Anhydrous and hydrated salts
An anhydrous salt contains no water of crystallization, while a hydrated salt contains a fixed number of molecules of water of crystallization chemically combined with it (for example \( CuSO_4 \) is anhydrous while \( CuSO_4 \cdot 5H_2O \) is hydrated).
