(a)The table below gives the volume/pressure data for a particular sample of a gas-at a given temperature.
| Volumedm\(^3\) (V) |
4.00 |
2.00 |
1.00 |
| Pressure/atm (P) |
1.00 |
2.00 |
4.00 |
(i) Deduce a mathematical relationship between volume (V) and pressure (P).
(ii) Name law that can be deduced from the data.
(iii) Calculate the pressure of the gas when the volume is 3.20 dm\(^3\)
(b)(i) What is the role of a salt bridge in an electrochemical cell?
(ii) What type of ions must flow into the cathode? Give a reason for your answer.
(iii)A standard galvanic cell constructed with \( \mathrm{Ag^+_{(aq)}} \) \( \mathrm{Ag_{(s)}} \) and \( \mathrm{Zn^{2+}_{(aq)}} \) couple is discharged until 3.3 g of Ag forms.
I. Write the overall cell reaction and standard cell potential?
II. How many moles of electrons flowed through the circuit during the discharge?
III. How many coulombs of charges flowed through the circuit?
\( \mathrm{Ag^+_{(aq)} + e^- \rightleftharpoons Ag_{(s)}} \); E° = + 0.80V
\( \mathrm{Zn^{2+}_{(aq)} + 2^- \rightleftharpoons Zn_{(s)}} \), E° = – 0.76 V [Ag = 108]
(c)(i) Define each of the following terms: I. Activation energy; II. Exothermic reaction.
(ii) Give one example of an endothermic process.
(iii) What is the significance of activated complex in a chemical reaction?
(a) Volume-pressure data
| Volume/dm\(^3\) (V) | 4.00 | 2.00 | 1.00 |
|---|
| Pressure/atm (P) | 1.00 | 2.00 | 4.00 |
(a)(i) Relationship between V and P
The product PV is constant (4.00, 4.00, 4.00), so:
\[ PV = \text{constant} \qquad \Rightarrow \qquad V \propto \frac{1}{P} \]
(a)(ii) Law: Boyle's law.
(a)(iii) Pressure when V = 3.20 dm\(^3\)
\[ PV = 4.00 \Rightarrow P = \frac{4.00}{3.20} = 1.25\ \text{atm} \]
(b)(i) Role of a salt bridge: it completes the electrical circuit by allowing ions to flow between the two half-cells, and it keeps each solution electrically neutral (preventing a build-up of charge).
(b)(ii) Ions that flow into the cathode: cations (positive ions). Reason: reduction (gain of electrons) takes place at the cathode, so positive ions migrate there to collect electrons.
(b)(iii) Galvanic cell: Ag\(^+\)/Ag and Zn\(^{2+}\)/Zn; 3.3 g of Ag deposited
I. Overall reaction and standard cell potential
Silver has the higher (more positive) potential, so it is reduced (cathode) and zinc is oxidised (anode):
\[ \text{Zn} + 2\text{Ag}^+ \rightarrow \text{Zn}^{2+} + 2\text{Ag} \]
\[ E^{o}_{cell} = E^{o}_{cathode} - E^{o}_{anode} = (+0.80) - (-0.76) = +1.56\ \text{V} \]
II. Moles of electrons that flowed
\[ \text{Moles of Ag} = \frac{3.3}{108} = 0.0306\ \text{mol} \]
Since Ag\(^+\) + e\(^-\) \(\rightarrow\) Ag needs one electron per silver atom, moles of electrons = 0.0306 mol.
III. Quantity of charge (coulombs)
\[ Q = n \times F = 0.0306 \times 96500 = 2.95 \times 10^{3}\ \text{C} \ (\approx 2949\ \text{C}) \]
(c)(i) Definitions
- I. Activation energy: the minimum energy that the reacting particles must acquire before they can react to form products.
- II. Exothermic reaction: a reaction in which heat energy is given out (released) to the surroundings, so \(\Delta H\) is negative.
(c)(ii) One example of an endothermic process: the dissolving of ammonium nitrate (or ammonium chloride) in water; photosynthesis is also acceptable.
(c)(iii) Significance of the activated complex: it is the short-lived, high-energy species formed at the peak of the energy barrier, in which old bonds are partly broken and new bonds are partly formed; it is the state through which reactants must pass to become products.
(a) Volume-pressure data
| Volume/dm\(^3\) (V) | 4.00 | 2.00 | 1.00 |
|---|
| Pressure/atm (P) | 1.00 | 2.00 | 4.00 |
(a)(i) Relationship between V and P
The product PV is constant (4.00, 4.00, 4.00), so:
\[ PV = \text{constant} \qquad \Rightarrow \qquad V \propto \frac{1}{P} \]
(a)(ii) Law: Boyle's law.
(a)(iii) Pressure when V = 3.20 dm\(^3\)
\[ PV = 4.00 \Rightarrow P = \frac{4.00}{3.20} = 1.25\ \text{atm} \]
(b)(i) Role of a salt bridge: it completes the electrical circuit by allowing ions to flow between the two half-cells, and it keeps each solution electrically neutral (preventing a build-up of charge).
(b)(ii) Ions that flow into the cathode: cations (positive ions). Reason: reduction (gain of electrons) takes place at the cathode, so positive ions migrate there to collect electrons.
(b)(iii) Galvanic cell: Ag\(^+\)/Ag and Zn\(^{2+}\)/Zn; 3.3 g of Ag deposited
I. Overall reaction and standard cell potential
Silver has the higher (more positive) potential, so it is reduced (cathode) and zinc is oxidised (anode):
\[ \text{Zn} + 2\text{Ag}^+ \rightarrow \text{Zn}^{2+} + 2\text{Ag} \]
\[ E^{o}_{cell} = E^{o}_{cathode} - E^{o}_{anode} = (+0.80) - (-0.76) = +1.56\ \text{V} \]
II. Moles of electrons that flowed
\[ \text{Moles of Ag} = \frac{3.3}{108} = 0.0306\ \text{mol} \]
Since Ag\(^+\) + e\(^-\) \(\rightarrow\) Ag needs one electron per silver atom, moles of electrons = 0.0306 mol.
III. Quantity of charge (coulombs)
\[ Q = n \times F = 0.0306 \times 96500 = 2.95 \times 10^{3}\ \text{C} \ (\approx 2949\ \text{C}) \]
(c)(i) Definitions
- I. Activation energy: the minimum energy that the reacting particles must acquire before they can react to form products.
- II. Exothermic reaction: a reaction in which heat energy is given out (released) to the surroundings, so \(\Delta H\) is negative.
(c)(ii) One example of an endothermic process: the dissolving of ammonium nitrate (or ammonium chloride) in water; photosynthesis is also acceptable.
(c)(iii) Significance of the activated complex: it is the short-lived, high-energy species formed at the peak of the energy barrier, in which old bonds are partly broken and new bonds are partly formed; it is the state through which reactants must pass to become products.
