If the ionic equivalent conductivities of $K^{+} A l^{3 +}, and S O_{4}^{2 -}$ ions are 4, 4, and 1 $S c m^{2} E q^{- 1}$ , respectively. Calculate the value of $\land_{e q}^{0}$ for Potash alum $(K_{2} S O_{4} . A l_{2} {(S O_{4})}_{3} . 24 H_{2} O)$

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Solution

As per the expression:
$\frac{λ_{M}^{o}}{λ_{e q}^{o}} = n - f a c t o r$
$λ_{M_{K^{+}}}^{o} = λ_{e q_{K^{+}}}^{o} \times 1 = 4 S c m^{2} m o l^{- 1}$
Similarly,
$λ_{M_{A l^{3 +}}}^{o} = λ_{e q_{A l^{3 +}}}^{o} \times 3 = 12 S c m^{2} m o l^{- 1}$
and
$λ_{M_{S O_{4}^{2 -}}}^{o} = λ_{e q_{S O_{4}^{2 -}}}^{o} \times 2 = 2 S c m^{2} m o l^{- 1}$
$∴$
$Λ_{M_{K_{2} S O_{4} . A l_{2} (S O_{4})_{3} .24 H_{2} O}}^{o}$ = $2 \times λ_{M_{K^{+}}}^{o} + λ_{M_{S O_{4}^{2 -}}}^{o} + 2 \times λ_{M_{A l^{3 +}}}^{o} + 3 \times λ_{M_{S O_{4}^{2 -}}}^{o}$
$\Rightarrow$ $2 \times 4 + 1 \times 2 + 2 \times 12 + 3 \times 2$
$\Rightarrow$ $40 S c m^{2} m o l^{- 1}$
*NOTE: Since, $H_{2} O$ is neutral therefore will not account for conductivity.
$∴$
$Λ_{e q_{K_{2} S O_{4} . A l_{2} (S O_{4})_{3} .24 H_{2} O}}^{o}$ = $\frac{Λ_{M_{K_{2} S O_{4} . A l_{2} (S O_{4})_{3} .24 H_{2} O}}^{o}}{n - f a c t o r}$
n-factor of Potash Alum is = Total charge on cations
$\Rightarrow$ n-factor = $(+ 1) \times n o . o f K^{+ 1} + (+ 3) \times n o . o f A l^{3 +}$
$\Rightarrow$ $1 \times 2 + 3 \times 2$
$\Rightarrow$ 8
$∴$ Putting values:
$Λ_{e q_{K_{2} S O_{4} . A l_{2} (S O_{4})_{3} .24 H_{2} O}}^{o}$ = $\frac{40}{8}$
= $5 S c m^{2} E q^{- 1}$
Hence, the correct answer is $5 S c m^{2} E q^{- 1}$

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Similar questions

K^{+}

S O_{4}^{2 -}

S c m^{2} e q^{- 1}

Λ_{m}^{0}

Λ_{e q}^{0}

(K_{2} S O_{4} . A l_{2} (S O_{4})_{3} . 24 H_{2} O)

Given the ionic equivalent conductivities for the following ions :

$λ_{e q}^{\circ} K^{\oplus} = 73.5 c m^{2} o h m^{- 1} e q^{- 1}$

$λ_{e q}^{\circ} A l^{3 +} = 189 c m^{2} o h m^{- 1} e q^{- 1}$

$λ_{e q}^{\circ} S O_{4}^{2 -} = 85.8 c m^{2} o h m^{- 1} e q^{- 1}$

The $Λ_{e q}^{\circ}$ for potash alum $(K_{2} S O_{4} . A l_{2} (S O_{4})_{3} . 24 H_{2} O)$ is :

C_{2} O_{4}^{2 -}, K^{+},

N a^{+}

c m^{2} E q^{- 1}

A_{e q}^{0}

(N a O O C - C O O K)

1

N_{A}

= K_{2} S O_{4} . A l_{2} (S O_{4})_{3} . 24 H_{2} O

[K_{2} S O_{4} . A l_{2} (S O_{4})_{3} .24 H_{2} O]

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