301. A weak-electrolyte solution has conductivity \(5.0\times10^{-4}\,S\,cm^{-1}\) at \(0.10\,mol\,L^{-1}\). After dilution to \(0.010\,mol\,L^{-1}\), its conductivity becomes \(1.5\times10^{-4}\,S\,cm^{-1}\). Its molar conductivity:
ⓐ. decreases from \(50\) to \(15\,S\,cm^2\,mol^{-1}\)
ⓑ. remains unchanged at \(5\,S\,cm^2\,mol^{-1}\)
ⓒ. increases from \(50\) to \(150\,S\,cm^2\,mol^{-1}\)
ⓓ. increases from \(5\) to \(15\,S\,cm^2\,mol^{-1}\)
Correct Answer: increases from \(5\) to \(15\,S\,cm^2\,mol^{-1}\)
Explanation: For the original solution:
\[
\Lambda_{m,1}=\frac{1000(5.0\times10^{-4})}{0.10}
\]
\[
\Lambda_{m,1}=5.0\,S\,cm^2\,mol^{-1}
\]
For the diluted solution:
\[
\Lambda_{m,2}=\frac{1000(1.5\times10^{-4})}{0.010}
\]
\[
\Lambda_{m,2}=15\,S\,cm^2\,mol^{-1}
\]
The conductivity decreases:
\[
5.0\times10^{-4}\rightarrow1.5\times10^{-4}\,S\,cm^{-1}
\]
but the concentration decreases by a factor of \(10\).
Consequently, the conductivity per mole increases by a factor of \(3\).
This is consistent with improved mobility and increased ionisation on dilution.
302. Assertion: The molar conductivity of a strong electrolyte increases only moderately on dilution.
Reason: A strong electrolyte is already largely dissociated, so dilution mainly reduces interionic interactions rather than producing many additional ions.
ⓐ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓑ. Both Assertion and Reason are true, and Reason explains 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 explains Assertion
Explanation: Strong electrolytes exist predominantly as ions even before extensive dilution. Adding water therefore causes little additional dissociation. The major effect is an increase in ionic mobility as interionic forces become weaker. This produces a gradual rather than dramatic increase in molar conductivity. The Reason directly explains the trend stated in the Assertion.
303. In the relation \(\Lambda_m=\frac{1000\kappa}{C}\), the factor \(1000\) is required mainly because \(C\) is expressed in:
ⓐ. \(mol\,cm^{-3}\)
ⓑ. \(mol\,L^{-1}\)
ⓒ. \(mol\,m^{-3}\)
ⓓ. \(g\,L^{-1}\)
Correct Answer: \(mol\,L^{-1}\)
Explanation: Conductivity in this practical relation is expressed per centimetre. Concentration in \(mol\,L^{-1}\) refers to a litre of solution. Since \(1\,L=1000\,cm^3\), the numerical factor converts between these volume scales. The resulting molar-conductivity unit is \(S\,cm^2\,mol^{-1}\). The factor would not be inserted in the same form if fully SI concentration units were used.
304. Equal-concentration solutions of a strong electrolyte and a weak electrolyte are diluted by the same factor. Which observation is most reasonable?
ⓐ. Both show identical changes in conductivity and molar conductivity
ⓑ. The strong electrolyte shows a much larger ionisation increase than the weak electrolyte
ⓒ. The weak electrolyte shows decreasing molar conductivity because its ions recombine
ⓓ. Both lose conductivity, but the weak electrolyte gains more molar conductivity
Correct Answer: Both lose conductivity, but the weak electrolyte gains more molar conductivity
Explanation: Dilution lowers the concentration of ions per unit volume in both solutions, so conductivity generally decreases. Molar conductivity rises because ionic movement becomes less hindered. The strong electrolyte is already substantially dissociated and gains relatively few additional ions. The weak electrolyte undergoes significant further ionisation. Its molar conductivity consequently shows the larger increase.
305. A researcher records the following observations for an electrolyte as water is added: resistance in the same cell rises, conductivity falls, but molar conductivity rises sharply. The electrolyte is most likely:
ⓐ. a non-electrolyte that produces no ions
ⓑ. a metal conducting through free electrons
ⓒ. a weak electrolyte undergoing increased ionisation
ⓓ. a strong electrolyte whose ions disappear on dilution
Correct Answer: a weak electrolyte undergoing increased ionisation
Explanation: In the unchanged cell, rising resistance corresponds to falling conductance and conductivity. The sharp increase in molar conductivity shows that the conducting contribution per mole is increasing substantially. Weak electrolytes become much more ionised as they are diluted. This creates additional ions while interionic interactions also weaken. The combined effect explains the steep rise in molar conductivity despite the fall in conductivity.
306. Solution P has \(\kappa=1.0\times10^{-2}\,S\,cm^{-1}\) at \(0.10\,mol\,L^{-1}\). Solution Q has \(\kappa=4.0\times10^{-3}\,S\,cm^{-1}\) at \(0.020\,mol\,L^{-1}\). Which comparison is correct?
ⓐ. P and Q have equal conductivity and equal molar conductivity
ⓑ. P has higher conductivity, but Q has higher molar conductivity
ⓒ. Q has higher conductivity, but P has higher molar conductivity
ⓓ. P has both higher conductivity and higher molar conductivity
Correct Answer: P has higher conductivity, but Q has higher molar conductivity
Explanation: Compare the conductivities directly:
\[
\kappa_P=1.0\times10^{-2}\,S\,cm^{-1}
\]
\[
\kappa_Q=4.0\times10^{-3}\,S\,cm^{-1}
\]
Therefore, P has the higher conductivity.
For P:
\[
\Lambda_{m,P}=\frac{1000(1.0\times10^{-2})}{0.10}
\]
\[
\Lambda_{m,P}=100\,S\,cm^2\,mol^{-1}
\]
For Q:
\[
\Lambda_{m,Q}=\frac{1000(4.0\times10^{-3})}{0.020}
\]
\[
\Lambda_{m,Q}=200\,S\,cm^2\,mol^{-1}
\]
Q therefore has the lower conductivity but the higher molar conductivity.
The comparison shows why \(\kappa\) and \(\Lambda_m\) must not be treated as interchangeable quantities.
307. For a strong electrolyte at sufficiently low concentration, the approximate relation between molar conductivity and concentration is:
ⓐ. \(\Lambda_m=\Lambda_m^\circ+A\sqrt{c}\)
ⓑ. \(\Lambda_m=A-\Lambda_m^\circ\sqrt{c}\)
ⓒ. \(\Lambda_m=\Lambda_m^\circ-A\sqrt{c}\)
ⓓ. \(\Lambda_m=\frac{\Lambda_m^\circ}{A\sqrt{c}}\)
Correct Answer: \(\Lambda_m=\Lambda_m^\circ-A\sqrt{c}\)
Explanation: A strong electrolyte is already almost completely dissociated in solution. Its molar conductivity decreases approximately linearly with \(\sqrt{c}\) over the low-concentration range used in this treatment. The limiting molar conductivity \(\Lambda_m^\circ\) is the value approached as concentration tends to zero. The term \(A\sqrt{c}\) represents the reduction from this limiting value at finite concentration. The negative sign therefore agrees with the observation that \(\Lambda_m\) increases when the solution is diluted.
308. In a graph of \(\Lambda_m\) on the vertical axis against \(\sqrt{c}\) on the horizontal axis for a strong electrolyte, the vertical intercept represents:
ⓐ. \(\Lambda_m^\circ\)
ⓑ. \(A\)
ⓒ. \(-A\)
ⓓ. the conductivity \(\kappa\) at the highest concentration
Correct Answer: \(\Lambda_m^\circ\)
Explanation: The graph follows \(\Lambda_m=\Lambda_m^\circ-A\sqrt{c}\). At the vertical intercept, \(\sqrt{c}=0\). The concentration is therefore at the infinite-dilution limit. Substitution gives \(\Lambda_m=\Lambda_m^\circ\). The intercept is not the measured conductivity of a concentrated solution.
309. The slope of a \(\Lambda_m\) versus \(\sqrt{c}\) graph for a strong electrolyte is:
ⓐ. \(\Lambda_m^\circ\)
ⓑ. \(+\Lambda_m^\circ\)
ⓒ. \(+A\)
ⓓ. \(-A\)
Correct Answer: \(-A\)
Explanation: The relation has the straight-line form \(y=b+mx\). Here, \(y=\Lambda_m\), \(x=\sqrt{c}\), and the intercept is \(\Lambda_m^\circ\). The coefficient multiplying \(\sqrt{c}\) is \(-A\). Hence, the graph has a negative slope. This means molar conductivity decreases as concentration increases.
310. For a strong electrolyte, \(\Lambda_m=120\,S\,cm^2\,mol^{-1}\) at \(\sqrt{c}=0.10\), while \(\Lambda_m=110\,S\,cm^2\,mol^{-1}\) at \(\sqrt{c}=0.20\). Assuming linear behaviour, \(\Lambda_m^\circ\) is:
ⓐ. \(110\,S\,cm^2\,mol^{-1}\)
ⓑ. \(130\,S\,cm^2\,mol^{-1}\)
ⓒ. \(140\,S\,cm^2\,mol^{-1}\)
ⓓ. \(100\,S\,cm^2\,mol^{-1}\)
Correct Answer: \(130\,S\,cm^2\,mol^{-1}\)
Explanation: Use the straight-line relation:
\[
\Lambda_m=\Lambda_m^\circ-A\sqrt{c}
\]
Calculate the slope:
\[
\frac{\Delta\Lambda_m}{\Delta\sqrt{c}}
=\frac{110-120}{0.20-0.10}
\]
\[
\frac{\Delta\Lambda_m}{\Delta\sqrt{c}}=-100
\]
Therefore:
\[
-A=-100
\]
\[
A=100
\]
Use the first data point:
\[
120=\Lambda_m^\circ-(100)(0.10)
\]
\[
120=\Lambda_m^\circ-10
\]
Hence:
\[
\Lambda_m^\circ=130\,S\,cm^2\,mol^{-1}
\]
Extrapolating the line to \(\sqrt{c}=0\) gives the limiting molar conductivity.
311. If the concentration of a strong electrolyte is increased from \(c\) to \(4c\), the term \(A\sqrt{c}\) in the relation \(\Lambda_m=\Lambda_m^\circ-A\sqrt{c}\) becomes:
ⓐ. four times its original value
ⓑ. half its original value
ⓒ. twice its original value
ⓓ. unchanged
Correct Answer: twice its original value
Explanation: The concentration-dependent term contains the square root of concentration. Replacing \(c\) by \(4c\) gives \(\sqrt{4c}=2\sqrt{c}\). Therefore, \(A\sqrt{c}\) doubles. The molar conductivity does not necessarily become half its original value because \(\Lambda_m^\circ\) remains present. The change affects only the concentration-dependent subtraction term.
312. Consider the following statements about a strong-electrolyte plot of \(\Lambda_m\) against \(\sqrt{c}\).
Statement I: The plot is approximately linear at low concentration.
Statement II: The slope is negative.
Statement III: Extrapolation to \(\sqrt{c}=0\) gives \(\Lambda_m^\circ\).
ⓐ. Statements I and II only
ⓑ. Statements II and III only
ⓒ. Statement III only
ⓓ. Statements I, II and III
Correct Answer: Statements I, II and III
Explanation: The low-concentration relation predicts an approximately straight line. The negative term \(-A\sqrt{c}\) gives a negative slope. As the horizontal coordinate approaches zero, the concentration approaches the infinite-dilution limit. The vertical intercept is therefore \(\Lambda_m^\circ\). All three statements describe the same graph consistently.
313. A straight-line graph for a strong electrolyte crosses the \(\Lambda_m\)-axis at \(150\,S\,cm^2\,mol^{-1}\). At \(\sqrt{c}=0.25\), the measured molar conductivity is \(135\,S\,cm^2\,mol^{-1}\). The numerical value of \(A\), in the corresponding graph units, is:
ⓐ. \(60\)
ⓑ. \(15\)
ⓒ. \(540\)
ⓓ. \(37.5\)
Correct Answer: \(60\)
Explanation: The vertical intercept gives:
\[
\Lambda_m^\circ=150\,S\,cm^2\,mol^{-1}
\]
Use:
\[
\Lambda_m=\Lambda_m^\circ-A\sqrt{c}
\]
Substitute the measured point:
\[
135=150-A(0.25)
\]
Rearrange:
\[
A(0.25)=150-135
\]
\[
A(0.25)=15
\]
Therefore:
\[
A=\frac{15}{0.25}
\]
\[
A=60
\]
In the corresponding plotted units, the positive coefficient \(A=60\) produces the observed graph slope of \(-60\).
314. For a strong electrolyte, \(\Lambda_m^\circ=150\,S\,cm^2\,mol^{-1}\) and \(A=60\) in a consistent set of concentration units. The molar conductivity at \(c=0.040\) is:
ⓐ. \(126\,S\,cm^2\,mol^{-1}\)
ⓑ. \(144\,S\,cm^2\,mol^{-1}\)
ⓒ. \(138\,S\,cm^2\,mol^{-1}\)
ⓓ. \(90\,S\,cm^2\,mol^{-1}\)
Correct Answer: \(138\,S\,cm^2\,mol^{-1}\)
Explanation: Start with:
\[
\Lambda_m=\Lambda_m^\circ-A\sqrt{c}
\]
The concentration is:
\[
c=0.040
\]
Its square root is approximately:
\[
\sqrt{0.040}=0.20
\]
Substitute the values:
\[
\Lambda_m=150-(60)(0.20)
\]
Calculate the concentration correction:
\[
(60)(0.20)=12
\]
Therefore:
\[
\Lambda_m=150-12
\]
\[
\Lambda_m=138\,S\,cm^2\,mol^{-1}
\]
The finite-concentration value lies below the limiting molar conductivity.
315. A learner extends a straight line fitted to concentrated strong-electrolyte data and treats the intercept as an exact value of \(\Lambda_m^\circ\). The main limitation of this method is that:
ⓐ. the relation is reliable only at low concentration
ⓑ. strong electrolytes become non-electrolytes on dilution
ⓒ. \(\Lambda_m^\circ\) is defined only at maximum concentration
ⓓ. the intercept of every conductivity graph must be zero
Correct Answer: the relation is reliable only at low concentration
Explanation: The linear relation is a limiting treatment for sufficiently dilute strong-electrolyte solutions. At higher concentrations, interionic interactions may produce noticeable deviations from a straight line. Extrapolating only concentrated data can therefore give an inaccurate intercept. Reliable estimation uses low-concentration measurements where the graph is nearly linear. The limiting molar conductivity itself remains associated with \(\sqrt{c}=0\).
316. The graph of \(\Lambda_m\) against \(\sqrt{c}\) for a weak electrolyte is strongly curved mainly because:
ⓐ. the electrode area changes continuously with concentration
ⓑ. the degree of ionisation changes substantially on dilution
ⓒ. weak electrolytes conduct through electrons at high concentration
ⓓ. the limiting molar conductivity is zero
Correct Answer: the degree of ionisation changes substantially on dilution
Explanation: A weak electrolyte is only partially ionised at ordinary concentrations. Dilution shifts the ionisation equilibrium toward the formation of more ions. The number of charge carriers contributed by each mole therefore changes markedly. This effect occurs in addition to the increase in ionic mobility. The resulting concentration dependence is strongly curved rather than approximately linear.
317. Which method is most suitable for obtaining \(\Lambda_m^\circ\) of a weak electrolyte such as \(CH_3COOH\)?
ⓐ. Extrapolate a straight line drawn through any two concentrated-solution points
ⓑ. Set its measured conductivity equal to zero
ⓒ. Use Kohlrausch’s law with suitable strong-electrolyte limiting conductivities
ⓓ. Multiply its molar conductivity by concentration
Correct Answer: Use Kohlrausch’s law with suitable strong-electrolyte limiting conductivities
Explanation: Weak-electrolyte data do not normally produce a dependable straight line against \(\sqrt{c}\). The limiting value therefore cannot be obtained accurately by simple direct extrapolation. Kohlrausch’s law expresses the limiting molar conductivity as the sum of independent ionic contributions. Suitable combinations of strong electrolytes can provide the required ionic terms. This approach yields the weak electrolyte’s infinite-dilution value without extending its curved experimental plot.
318. Assertion: A weak electrolyte can show a large increase in molar conductivity even though its conductivity decreases on dilution.
Reason: Dilution lowers the number of ions per unit volume but increases ionisation and the conducting contribution per mole.
ⓐ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓑ. Both Assertion and Reason are true, and Reason explains 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 explains Assertion
Explanation: Conductivity concerns the concentration of charge carriers in a unit volume. This quantity generally falls as solvent is added. Molar conductivity instead describes the conducting contribution associated with a mole of electrolyte. Greater ionisation and weaker interionic interactions raise that contribution. The Reason directly explains why the two measured trends can occur simultaneously.
319. Two electrolytes give the following observations when diluted by the same factor.
| Electrolyte | Initial \(\Lambda_m\) | Diluted \(\Lambda_m\) | Graph shape |
|---|
| P | \(120\) | \(135\) | Nearly linear against \(\sqrt{c}\) |
| Q | \(20\) | \(90\) | Strongly curved against \(\sqrt{c}\) |
The most reasonable classification is:
ⓐ. P is weak and Q is strong
ⓑ. both P and Q are strong
ⓒ. both P and Q are weak
ⓓ. P is strong and Q is weak
Correct Answer: P is strong and Q is weak
Explanation: Electrolyte P shows a moderate increase in molar conductivity and nearly linear low-concentration behaviour. These are typical features of a strong electrolyte. Electrolyte Q shows a much larger relative rise on dilution. Its strongly curved graph indicates that its ionisation changes substantially. Q is therefore a weak electrolyte.
320. A weak electrolyte has relatively low molar conductivity at moderate concentration because:
ⓐ. only a fraction of its dissolved molecules exist as mobile ions
ⓑ. its ions possess no electrical charge
ⓒ. its solvent prevents all ionic movement
ⓓ. its limiting molar conductivity must be lower than that of every strong electrolyte
Correct Answer: only a fraction of its dissolved molecules exist as mobile ions
Explanation: Weak electrolytes establish an equilibrium between ionised and unionised forms. At moderate concentration, a substantial fraction remains as neutral molecules. These neutral species do not carry current through ionic migration. The number of charge carriers per mole is therefore limited. Dilution increases the ionised fraction and raises the molar conductivity.
