201. Which set of statements is correct for a reaction that is spontaneous in the forward direction under standard conditions?
ⓐ. \(E^\circ_{\text{cell}} 0\), \(K < 1\)
ⓑ. \(E^\circ_{\text{cell}} > 0\), \(\Delta G^\circ > 0\), \(K < 1\)
ⓒ. \(E^\circ_{\text{cell}} = 0\), \(\Delta G^\circ = 0\), \(K > 1\)
ⓓ. \(E^\circ_{\text{cell}} > 0\), \(\Delta G^\circ 1\)
Correct Answer: \(E^\circ_{\text{cell}} > 0\), \(\Delta G^\circ 1\)
Explanation: Under standard conditions, a spontaneous forward reaction has positive standard emf. From \(\Delta G^\circ = -nF E^\circ_{\text{cell}}\), that means \(\Delta G^\circ\) is negative. Also, from \(E^\circ_{\text{cell}} = \frac{0.0591}{n}\log K\) at \(298\,\text{K}\), a positive \(E^\circ_{\text{cell}}\) gives \(\log K > 0\), so \(K > 1\).
202. A cell reaction involves transfer of \(3\) electrons and has \(E^\circ_{\text{cell}} = 0.40\,\text{V}\). What is the value of \(\Delta G^\circ\)?
(Use \(F = 96500\,\text{C mol}^{-1}\))
ⓐ. \(-115.8\,\text{kJ mol}^{-1}\)
ⓑ. \(+115.8\,\text{kJ mol}^{-1}\)
ⓒ. \(-38.6\,\text{kJ mol}^{-1}\)
ⓓ. \(-57.9\,\text{kJ mol}^{-1}\)
Correct Answer: \(-115.8\,\text{kJ mol}^{-1}\)
Explanation: \(\textbf{Given:}\)
\[n = 3\]
\[E^\circ_{\text{cell}} = 0.40\,\text{V}\]
\[F = 96500\,\text{C mol}^{-1}\]
\(\textbf{Required:}\)
\[\Delta G^\circ\]
\(\textbf{Relevant formula:}\)
\[\Delta G^\circ = -nF E^\circ_{\text{cell}}\]
\(\textbf{Why this formula applies:}\)
This relation connects standard Gibbs energy change with standard cell emf.
\(\textbf{Substitution:}\)
\[\Delta G^\circ = -(3)(96500)(0.40)\]
\(\textbf{Intermediate simplification:}\)
\[(96500)(0.40) = 38600\]
\(\textbf{Now multiply by 3:}\)
\[\Delta G^\circ = -115800\,\text{J mol}^{-1}\]
\(\textbf{Convert to kilojoule:}\)
\[\Delta G^\circ = -115.8\,\text{kJ mol}^{-1}\]
\(\textbf{Unit check:}\)
\(1\,\text{V} \cdot 1\,\text{C} = 1\,\text{J}\), so the unit is correct.
\(\textbf{Final Answer:}\)
\[\Delta G^\circ = -115.8\,\text{kJ mol}^{-1}\]
203. For a cell reaction, \(\Delta G^\circ = +38.6\,\text{kJ mol}^{-1}\) and \(n = 2\). What is the value of \(E^\circ_{\text{cell}}\)?
(Use \(F = 96500\,\text{C mol}^{-1}\))
ⓐ. \(+0.40\,\text{V}\)
ⓑ. \(-0.20\,\text{V}\)
ⓒ. \(-0.40\,\text{V}\)
ⓓ. \(+0.20\,\text{V}\)
Correct Answer: \(-0.20\,\text{V}\)
Explanation: \(\textbf{Given:}\)
\[\Delta G^\circ = +38.6\,\text{kJ mol}^{-1} = +38600\,\text{J mol}^{-1}\]
\[n = 2\]
\[F = 96500\,\text{C mol}^{-1}\]
\(\textbf{Required:}\)
\[E^\circ_{\text{cell}}\]
\(\textbf{Relevant formula:}\)
\[\Delta G^\circ = -nF E^\circ_{\text{cell}}\]
\(\textbf{Why this formula applies:}\)
The problem gives standard Gibbs energy change, so the standard emf can be found directly from this relation.
\(\textbf{Rearrangement:}\)
\[E^\circ_{\text{cell}} = -\frac{\Delta G^\circ}{nF}\]
\(\textbf{Substitution:}\)
\[E^\circ_{\text{cell}} = -\frac{38600}{(2)(96500)}\]
\(\textbf{Intermediate simplification:}\)
\[(2)(96500) = 193000\]
So,
\[E^\circ_{\text{cell}} = -\frac{38600}{193000}\]
\(\textbf{Final simplification:}\)
\[E^\circ_{\text{cell}} = -0.20\,\text{V}\]
\(\textbf{Unit check:}\)
Gibbs energy per mole divided by coulomb per mole gives volt.
\(\textbf{Final Answer:}\)
\[E^\circ_{\text{cell}} = -0.20\,\text{V}\]
204. At \(298\,\text{K}\), a cell reaction has \(\Delta G^\circ = -11.42\,\text{kJ mol}^{-1}\). What is the value of the equilibrium constant \(K\)?
ⓐ. \(10\)
ⓑ. \(100\)
ⓒ. \(0.01\)
ⓓ. \(1000\)
Correct Answer: \(100\)
Explanation: \(\textbf{Given:}\)
\[\Delta G^\circ = -11.42\,\text{kJ mol}^{-1} = -11420\,\text{J mol}^{-1}\]
\[T = 298\,\text{K}\]
\(\textbf{Required:}\)
Equilibrium constant, \(K\)
\(\textbf{Relevant formula:}\)
\[\Delta G^\circ = -RT\ln K\]
\(\textbf{Why this formula applies:}\)
This relation directly connects standard Gibbs energy change with the equilibrium constant.
\(\textbf{Identify constants:}\)
\[R = 8.314\,\text{J mol}^{-1}\text{K}^{-1}\]
\[T = 298\,\text{K}\]
\(\textbf{Substitution:}\)
\[-11420 = -(8.314)(298)\ln K\]
\(\textbf{Intermediate simplification:}\)
\[(8.314)(298) \approx 2477.6\]
So,
\[11420 = 2477.6 \ln K\]
\(\textbf{Now divide:}\)
\[\ln K \approx \frac{11420}{2477.6} \approx 4.61\]
\(\textbf{Convert to common value:}\)
\(\ln K \approx 4.61\) corresponds to \(K \approx 100\)
\(\textbf{Final Answer:}\)
\[K \approx 100\]
205. Assertion: If \(K\) is very large at \(298\,\text{K}\), then \(E^\circ_{\text{cell}}\) is positive.
Reason: A large value of \(K\) means products are favored at equilibrium, so \(\log K\) is positive.
ⓐ. Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
ⓑ. Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
ⓒ. Assertion is true, but Reason is false.
ⓓ. Assertion is false, but Reason is true.
Correct Answer: Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
Explanation: At \(298\,\text{K}\), the relation \(E^\circ_{\text{cell}} = \frac{0.0591}{n}\log K\) shows that the sign of \(E^\circ_{\text{cell}}\) depends on the sign of \(\log K\). When \(K\) is very large, products are strongly favored and \(\log K\) is positive. Therefore \(E^\circ_{\text{cell}}\) is positive.
206. Which statement is correct if \(\Delta G^\circ = 0\) for a cell reaction?
ⓐ. \(E^\circ_{\text{cell}} < 0\) and \(K < 1\)
ⓑ. \(E^\circ_{\text{cell}} = 0\) and \(K = 1\)
ⓒ. \(E^\circ_{\text{cell}} > 0\) and \(K > 1\)
ⓓ. \(E^\circ_{\text{cell}} = 0\) and \(K > 1\)
Correct Answer: \(E^\circ_{\text{cell}} = 0\) and \(K = 1\)
Explanation: If \(\Delta G^\circ = 0\), then from \(\Delta G^\circ = -nF E^\circ_{\text{cell}}\), the standard emf must also be zero. Also, from \(\Delta G^\circ = -RT\ln K\), a zero value of \(\Delta G^\circ\) gives \(\ln K = 0\), so \(K = 1\).
207. At \(298\,\text{K}\), for a cell reaction with \(n = 2\), the equilibrium constant is \(K = 10^{-6}\). The value of \(E^\circ_{\text{cell}}\) is
ⓐ. \(+0.1773\,\text{V}\)
ⓑ. \(-0.3546\,\text{V}\)
ⓒ. \(-0.1773\,\text{V}\)
ⓓ. \(+0.3546\,\text{V}\)
Correct Answer: \(-0.1773\,\text{V}\)
Explanation: \(\textbf{Given:}\)
\[K = 10^{-6}\]
\[n = 2\]
\[T = 298\,\text{K}\]
\(\textbf{Required:}\)
\[E^\circ_{\text{cell}}\]
\(\textbf{Relevant formula:}\)
At \(298\,\text{K}\),
\[E^\circ_{\text{cell}} = \frac{0.0591}{n}\log K\]
\(\textbf{Why this formula applies:}\)
This equation directly relates standard emf with equilibrium constant.
\(\textbf{Identify the logarithmic value:}\)
\[\log(10^{-6}) = -6\]
\(\textbf{Substitution:}\)
\[E^\circ_{\text{cell}} = \frac{0.0591}{2}(-6)\]
\(\textbf{Intermediate simplification:}\)
\[\frac{0.0591}{2} = 0.02955\]
So,
\[E^\circ_{\text{cell}} = 0.02955 \times (-6)\]
\(\textbf{Final simplification:}\)
\[E^\circ_{\text{cell}} = -0.1773\,\text{V}\]
\(\textbf{Unit check:}\)
Standard emf is measured in volt.
\(\textbf{Final Answer:}\)
\[E^\circ_{\text{cell}} = -0.1773\,\text{V}\]
208. A cell reaction has \(\Delta G = -57.9\,\text{kJ mol}^{-1}\) under given conditions and involves transfer of \(1\) electron. What is the value of \(E_{\text{cell}}\)?
(Use \(F = 96500\,\text{C mol}^{-1}\))
ⓐ. \(-0.60\,\text{V}\)
ⓑ. \(+0.30\,\text{V}\)
ⓒ. \(-0.30\,\text{V}\)
ⓓ. \(+0.60\,\text{V}\)
Correct Answer: \(+0.60\,\text{V}\)
Explanation: \(\textbf{Given:}\)
\[\Delta G = -57.9\,\text{kJ mol}^{-1} = -57900\,\text{J mol}^{-1}\]
\[n = 1\]
\[F = 96500\,\text{C mol}^{-1}\]
\(\textbf{Required:}\)
\[E_{\text{cell}}\]
\(\textbf{Relevant formula:}\)
\[\Delta G = -nF E_{\text{cell}}\]
\(\textbf{Why this formula applies:}\)
The problem gives Gibbs energy change under actual conditions, so the actual cell emf is required.
\(\textbf{Rearrangement:}\)
\[E_{\text{cell}} = -\frac{\Delta G}{nF}\]
\(\textbf{Substitution:}\)
\[E_{\text{cell}} = -\frac{-57900}{(1)(96500)}\]
\(\textbf{Intermediate simplification:}\)
\[E_{\text{cell}} = \frac{57900}{96500}\]
\(\textbf{Final simplification:}\)
\[E_{\text{cell}} = 0.60\,\text{V}\]
\(\textbf{Unit check:}\)
Joule per coulomb gives volt.
\(\textbf{Final Answer:}\)
\[E_{\text{cell}} = +0.60\,\text{V}\]
209. Which statement correctly distinguishes metallic conduction from electrolytic conduction?
ⓐ. In metallic conduction, current is carried by ions, whereas in electrolytic conduction it is carried by electrons only.
ⓑ. In both metallic and electrolytic conduction, current is carried only by free electrons.
ⓒ. In metallic conduction, current is carried by electrons, whereas in electrolytic conduction it is carried by ions.
ⓓ. In metallic conduction, current is always accompanied by chemical decomposition, whereas in electrolytic conduction it is not.
Correct Answer: In metallic conduction, current is carried by electrons, whereas in electrolytic conduction it is carried by ions.
Explanation: In metals, electrical conduction occurs because free electrons move through the metallic lattice. In electrolytes, conduction takes place due to the movement of cations and anions in solution or molten state. This is the basic difference between the two types of conduction.
210. Which substance can show electrolytic conduction?
ⓐ. Aqueous NaCl
ⓑ. Solid copper wire
ⓒ. Solid sulfur crystal
ⓓ. Dry wooden rod
Correct Answer: Aqueous NaCl
Explanation: Electrolytic conduction requires the presence of mobile ions. In aqueous sodium chloride, \(Na^+\) and \(Cl^-\) ions are free to move and carry current. Solid copper conducts through electrons, while sulfur and dry wood do not provide mobile ions for electrolytic conduction.
211. Why does an electrolyte conduct electricity in aqueous solution?
ⓐ. Because the solution contains free electrons moving between molecules
ⓑ. Because water itself is always a strong metallic conductor
ⓒ. Because neutral molecules of the solute move toward the electrodes
ⓓ. Because ions migrate under an electric field
Correct Answer: Because ions migrate under an electric field
Explanation: When an electrolyte dissolves in water, it produces ions. Under an applied potential difference, cations move toward the cathode and anions move toward the anode. This ionic migration causes the solution to conduct electricity.
212. Which statement about chemical change during conduction is correct?
ⓐ. Metallic conduction always produces new substances at the ends of the wire.
ⓑ. Electrolytic conduction is commonly accompanied by chemical change at the electrodes.
ⓒ. Metallic and electrolytic conduction both occur without any material change.
ⓓ. Electrolytic conduction can occur only when no reaction takes place at electrodes.
Correct Answer: Electrolytic conduction is commonly accompanied by chemical change at the electrodes.
Explanation: In electrolytic conduction, ions are discharged at the electrodes and may form new substances. That is why electrolysis is associated with chemical change. Metallic conduction, in contrast, usually involves electron flow without decomposition of the conductor.
213. Which of the following is a correct comparison?
ⓐ. Metals conduct as solids; many electrolytes conduct when molten or aqueous.
ⓑ. Metals conduct only when dissolved, whereas electrolytes conduct only in solid state.
ⓒ. Metals and electrolytes both require mobile ions in solid state for conduction.
ⓓ. Metals and electrolytes both conduct only because of neutral particle motion.
Correct Answer: Metals conduct as solids; many electrolytes conduct when molten or aqueous.
Explanation: Metals possess mobile electrons even in the solid state, so they conduct without melting. Electrolytes generally need their ions to be free to move, which happens in molten state or in aqueous solution. In solid ionic compounds, ions are fixed and conduction is poor or absent.
214. Which statement is correct for molten sodium chloride?
ⓐ. It conducts electricity because sodium atoms move to one electrode and chlorine atoms to the other.
ⓑ. It does not conduct because the compound is ionic.
ⓒ. It conducts exactly like a copper wire, by movement of free electrons alone.
ⓓ. It conducts because \(Na^+\) and \(Cl^-\) ions become mobile in the molten state.
Correct Answer: It conducts because \(Na^+\) and \(Cl^-\) ions become mobile in the molten state.
Explanation: In molten sodium chloride, the ionic lattice breaks down enough for \(Na^+\) and \(Cl^-\) ions to move freely. These ions carry current through the melt. The conduction is therefore ionic, not electronic like in metals.
215. Which observation best indicates electrolytic conduction rather than metallic conduction?
ⓐ. Current passes through a copper wire with no visible electrode change.
ⓑ. Solution electrolysis gives deposition or gas evolution.
ⓒ. Resistance of a metal wire changes slightly with temperature.
ⓓ. Current flows through a metallic strip in solid state.
Correct Answer: Solution electrolysis gives deposition or gas evolution.
Explanation: Electrolytic conduction is usually accompanied by electrode reactions such as metal deposition or gas liberation. These chemical effects are characteristic of ion discharge. Metallic conduction generally does not produce such chemical changes at the ends of the conductor.
216. Which statement about electrolytic and metallic conductors is correct?
ⓐ. Both depend on the movement of the same charge-carrying particles.
ⓑ. An electrolyte conducts in aqueous solution because its atoms become neutral.
ⓒ. A metallic conductor cannot carry current in solid state.
ⓓ. Electrolytes need mobile ions; metals conduct through mobile electrons.
Correct Answer: Electrolytes need mobile ions; metals conduct through mobile electrons.
Explanation: The essential condition for electrolytic conduction is the presence of mobile ions. In a metal, current is carried by delocalized electrons already present in the solid. So the charge carriers are different in the two cases.
217. Why does solid sodium chloride not conduct electricity, while molten sodium chloride does?
ⓐ. In solid sodium chloride, ions are fixed in the lattice, but in molten sodium chloride they become mobile.
ⓑ. In solid sodium chloride, electrons are absent, but in molten sodium chloride free electrons are produced.
ⓒ. In solid sodium chloride, sodium atoms are neutral, but in molten sodium chloride they become positively charged.
ⓓ. In solid sodium chloride, chlorine atoms block current, but in molten sodium chloride they escape as gas.
Correct Answer: In solid sodium chloride, ions are fixed in the lattice, but in molten sodium chloride they become mobile.
Explanation: An ionic solid contains ions, but in the solid state these ions are held in fixed positions and cannot move freely. When the salt is melted, the ions become mobile and can migrate toward opposite electrodes. That mobility allows the molten electrolyte to conduct electricity.
218. Which aqueous solution is least likely to conduct electricity appreciably?
ⓐ. Aqueous hydrochloric acid
ⓑ. Aqueous sodium chloride
ⓒ. Aqueous sugar solution
ⓓ. Aqueous copper sulfate
Correct Answer: Aqueous sugar solution
Explanation: Electrolytic conduction requires mobile ions in solution. Sugar dissolves as neutral molecules and does not furnish ions to any significant extent. Therefore its aqueous solution conducts very poorly compared with solutions of acids, salts, or bases.
219. In an electrolytic conductor, current through the solution is carried by
ⓐ. only cations moving through the solution
ⓑ. cations and anions moving in solution
ⓒ. only anions moving through the solution
ⓓ. electrons moving freely through the solution
Correct Answer: cations and anions moving in solution
Explanation: Electrolytic conduction occurs because positively charged ions move toward the cathode and negatively charged ions move toward the anode. Both types of ions contribute to the flow of charge through the solution. Free electrons are not the main carriers within the electrolyte.
220. Which statement best explains why a dry crystal of an ionic compound usually does not behave as an electrolytic conductor?
ⓐ. It contains no charged particles.
ⓑ. It contains no atoms capable of redox change.
ⓒ. It cannot dissolve in water under any condition.
ⓓ. Its ions are fixed in the solid lattice.
Correct Answer: Its ions are fixed in the solid lattice.
Explanation: Ionic solids contain charged ions, but conduction requires those ions to move. In a rigid crystal, the ions are locked in place by electrostatic attraction. So the solid usually does not conduct well until it is melted or dissolved.
