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${}_{\text{(Sc}{{\text{m}}^{2}}}{{\wedge }^{\infty }}{}_{\text{mo}{{\text{l}}^{-1}})}$149.9145.0426.291.0126.5

Calculate ${{\wedge }^{\infty }}_{\text{HOAc}}$ using appropriate molar conductance of the electrolytes listed above at infinite dilution in ${{\text{H}}_{2}}\text{O}$ at $25{}^\circ \text{C}$.
A. 517.2
B. 552.7
C. 390.7N
D. 217.5

Last updated date: 18th Jun 2024
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Hint: The ratio of conductivity of an electrolyte and its molar conductance gives the molar conductance, which is denoted by ${{\wedge }_{\text{m}}}\text{ }$. The molar conductance has SI unit, Siemens metre squared per mol $\text{(S}{{\text{m}}^{2}}\text{mo}{{\text{l}}^{-1}})$.

Complete Answer:
-We have to calculate the molar conductance at infinite dilution for $\text{HOAc}$ at a given temperature.
-so, firstly we will write the reaction between hydrochloric acid and $\text{NaOAc}$ i.e.
$\text{HCl + NaOAc }\to \text{ NaCl + HOAc}$
-Now, for the calculating the molar conductance the formula will be written according to the reaction but the temperature will not
-Now, the formula of molar conductance at infinite dilution will be:
$\wedge _{\text{HOAc}}^{\infty }\text{ = }\wedge _{\text{NaOAc}}^{\infty }\text{ + }\wedge _{\text{HCl}}^{\infty }\text{ - }\wedge _{\text{NaCl}}^{\infty }\text{ }....\text{(1)}$
-Here, the molar conductance of sodium chloride is subtracted because molar conductance of sodium chloride is not asked i.e. to remove the sodium from sodium acetate and chlorine from hydrochloric acid.
-It is given in the question that the value of molar conductance of sodium acetate, hydrochloric acid and sodium chloride is 91.0, 426.2 and 126.5 respectively.
-Now, we will put these values in the equation (1) and we will get,
\[91\text{ + 426}\text{.2 - 126}\text{.5 = 390}\text{.7 Sc}{{\text{m}}^{2}}\text{mo}{{\text{l}}^{-1}}\].
Therefore, option C is the correct answer.

Note: According to the theory of electrolysis, dissociation which was given by Arrhenius, if the electrolyte has completely dissociated then the value of molar conductance at infinite dilution will be minimum.