What is a weak electrolyte? Explain the relation between the concentration of a weak electrolyte and molar conductivity with a suitable graph.
(N/A) Weak electrolyte: Electrolytes that undergo partial ionization in their aqueous solution are known as weak electrolytes. They exhibit ionic equilibrium in their aqueous solution. For example,$CH_{3}COOH$,$NH_{4}OH$,etc.
$(b)$ $\Lambda_{m}$ of weak electrolyte solution and concentration: For such electrolytes,the change in $\Lambda_{m}$ with dilution is due to the increase in the degree of dissociation and consequently the number of ions in the total volume of solution that contains $1 \ mol$ of electrolyte.
According to Ostwald's dilution law,the molar conductivity of a weak electrolyte solution increases significantly with a decrease in the concentration of the solution.
$(c)$ Explanation of conductivity on dilution: The dissociation constant of a weak electrolyte like acetic acid is low at higher concentrations. As the solution is diluted,the degree of dissociation increases. Consequently,the total volume of solution containing $1 \ mol$ of weak electrolyte increases,and molar conductivity increases significantly due to the increase in the number of ions.
Limiting molar conductivity of weak electrolyte: The graph of $\Lambda_{m}$ versus $c^{1/2}$ is not linear; it is a curve. Because the curve does not intersect the y-axis at zero concentration,we cannot obtain the value of limiting molar conductivity $\Lambda_{m}^{\circ}$ by extrapolation.
$(b)$ $\Lambda_{m}$ of weak electrolyte solution and concentration: For such electrolytes,the change in $\Lambda_{m}$ with dilution is due to the increase in the degree of dissociation and consequently the number of ions in the total volume of solution that contains $1 \ mol$ of electrolyte.
According to Ostwald's dilution law,the molar conductivity of a weak electrolyte solution increases significantly with a decrease in the concentration of the solution.
$(c)$ Explanation of conductivity on dilution: The dissociation constant of a weak electrolyte like acetic acid is low at higher concentrations. As the solution is diluted,the degree of dissociation increases. Consequently,the total volume of solution containing $1 \ mol$ of weak electrolyte increases,and molar conductivity increases significantly due to the increase in the number of ions.
Limiting molar conductivity of weak electrolyte: The graph of $\Lambda_{m}$ versus $c^{1/2}$ is not linear; it is a curve. Because the curve does not intersect the y-axis at zero concentration,we cannot obtain the value of limiting molar conductivity $\Lambda_{m}^{\circ}$ by extrapolation.
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The conductivity of $0.01 \ M$ aqueous acetic acid measured with a conductivity cell of cell constant $0.5 \ cm^{-1}$ at $298 \ K$ is $3.12 \times 10^{-4} \ S$. If the limiting molar conductivities of $H^{+}$ and $CH_3COO^{-}$ at the same temperature are $349$ and $41 \ S \ cm^2 \ mol^{-1}$ respectively,the dissociation constant of acetic acid is
Consider the following two half-cell reactions:
$CO_2 + 6H^+ + 6e^- \rightarrow CH_3OH + H_2O$ $(E^{\ominus} = 0.02 \text{ V})$
$\frac{1}{2}O_2 + 2H^+ + 2e^- \rightarrow H_2O$ $(E^{\ominus} = 1.23 \text{ V})$
$A$ fuel cell was set up such that the cell operates under standard conditions. The fuel cell works with $80\%$ efficiency. If the work derived from the cell using $1 \text{ mol}$ of $CH_3OH$ is used to compress an ideal gas isothermally against a constant pressure of $1 \text{ kPa}$, then the change in the volume of the gas, $\Delta V =$ . . . . . . $\text{m}^3$. (nearest integer) Given: $F = 96500 \text{ C mol}^{-1}$
$CO_2 + 6H^+ + 6e^- \rightarrow CH_3OH + H_2O$ $(E^{\ominus} = 0.02 \text{ V})$
$\frac{1}{2}O_2 + 2H^+ + 2e^- \rightarrow H_2O$ $(E^{\ominus} = 1.23 \text{ V})$
$A$ fuel cell was set up such that the cell operates under standard conditions. The fuel cell works with $80\%$ efficiency. If the work derived from the cell using $1 \text{ mol}$ of $CH_3OH$ is used to compress an ideal gas isothermally against a constant pressure of $1 \text{ kPa}$, then the change in the volume of the gas, $\Delta V =$ . . . . . . $\text{m}^3$. (nearest integer) Given: $F = 96500 \text{ C mol}^{-1}$
DifficultJEE MAIN 2026
View SolutionWhy is electrochemistry important for the invention of the latest technology?
Easy
View SolutionConsider a $70 \%$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1 \ bar$ and $298 \ K$. Its cell reaction is
$H_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow H_2O(\ell)$
The work derived from the cell on the consumption of $1.0 \times 10^{-3} \ mol$ of $H_{2(g)}$ is used to compress $1.00 \ mol$ of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in $K$) of the ideal gas?
The standard reduction potentials for the two half-cells are given below.
$O_{2(g)} + 4H^{+}(aq.) + 4e^- \rightarrow 2H_2O(\ell), E^{\circ} = 1.23 \ V$
$2H^{+}(aq.) + 2e^- \rightarrow H_{2(g)}, E^{\circ} = 0.00 \ V$
Use $F = 96500 \ C \ mol^{-1}, R = 8.314 \ J \ mol^{-1} \ K^{-1}$
$H_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow H_2O(\ell)$
The work derived from the cell on the consumption of $1.0 \times 10^{-3} \ mol$ of $H_{2(g)}$ is used to compress $1.00 \ mol$ of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in $K$) of the ideal gas?
The standard reduction potentials for the two half-cells are given below.
$O_{2(g)} + 4H^{+}(aq.) + 4e^- \rightarrow 2H_2O(\ell), E^{\circ} = 1.23 \ V$
$2H^{+}(aq.) + 2e^- \rightarrow H_{2(g)}, E^{\circ} = 0.00 \ V$
Use $F = 96500 \ C \ mol^{-1}, R = 8.314 \ J \ mol^{-1} \ K^{-1}$
MediumIIT 2020
View SolutionConsider the strong electrolytes $Z_{m}X_{n}$,$U_{m}Y_{p}$ and $V_{m}X_{n}$. Limiting molar conductivity $(\Lambda^0)$ of $U_{m}Y_{p}$ and $V_{m}X_{n}$ are $250 \ S \ cm^2 \ mol^{-1}$ and $440 \ S \ cm^2 \ mol^{-1}$,respectively. The value of $(m + n + p)$ is . . . . . Given:
$Ion$ $\lambda^0 \ (S \ cm^2 \ mol^{-1})$ $U^{p+}$ $50.0$ $Y^{m-}$ $50.0$ $V^{n+}$ $60.0$ $X^{m-}$ $50.0$ $Z^{n+}$ $40.0$
$\lambda^0$ is the limiting molar conductivity of ions. The plot of molar conductivity $(\Lambda)$ of $Z_{m}X_{n}$ $vs$ $c^{1/2}$ is given below.
| $Ion$ | $\lambda^0 \ (S \ cm^2 \ mol^{-1})$ |
|---|---|
| $U^{p+}$ | $50.0$ |
| $Y^{m-}$ | $50.0$ |
| $V^{n+}$ | $60.0$ |
| $X^{m-}$ | $50.0$ |
| $Z^{n+}$ | $40.0$ |
$\lambda^0$ is the limiting molar conductivity of ions. The plot of molar conductivity $(\Lambda)$ of $Z_{m}X_{n}$ $vs$ $c^{1/2}$ is given below.
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