Question

The conductivity of KCl solution of 0.02 mol/dm[sup]3[/sup] is 0.2768 s/m A measuring cell filled with this solution has resistance of 453 Onm/m. The same measuring cell is filled with a CaCl[sub]2[/sub] solution of 0.555 g/dm[sup]3[/sup], the resistance is measured as 1050 ohm/m. Calculate, (1) Cell constant, (2) The conductivity of the CaCl[sub]2[/sub] solution, (3) The molar conductivity of the CaCl solution. Molecular Weight of CaCl[sub]2[/sub] is 111 g/mol)

Answer 1

Answer on Question #53063 – Chemistry – General chemistry

Question:

The conductivity of KCl solution of $0.02\ \mathrm{mol/dm^3}$ is $0.2768\ \mathrm{s/m}$. A measuring cell filled with this solution has resistance of 453 Ohm/m. The same measuring cell is filled with a $\mathrm{CaCl_2}$ solution of $0.555\ \mathrm{g/dm^3}$, the resistance is measured as 1050 ohm/m. Calculate, (1) Cell constant, (2) The conductivity of the $\mathrm{CaCl_2}$ solution, (3) The molar conductivity of the $\mathrm{CaCl_2}$ solution. Molecular Weight of $\mathrm{CaCl_2}$ is 111 g/mol.

Solution:

1) The cell constant can be found according to the equation:

$$K = \chi(KCl) \times R(KCl), \text{ where } \chi\text{-conductivity, } R\text{-resistance}.$$ $$K = 0.2768\ \mathrm{s/m} \times 453\ \mathrm{Ohm/m} = 125.39\ \mathrm{s\ Ohm/m^2}$$

2) Since the same cell is used, $K$ has the same value. The conductivity of the $\mathrm{CaCl_2}$ solution is calculated according to an equation: $\chi(\mathrm{CaCl_2}) = K/R(\mathrm{CaCl_2})$

$$\chi(\mathrm{CaCl_2}) = 125.39\ \mathrm{s\ Ohm/m^2} / 1050\ \mathrm{Ohm/m} = 0.1194\ \mathrm{s/m}$$

3) The molar conductivity of $\mathrm{CaCl_2}$ is: $\lambda_{\mathrm{m}} = \chi(\mathrm{CaCl_2})/(1000 \times C_{\mathrm{m}})$, where $C_{\mathrm{m}} = C/M_{\mathrm{w}}$, $C_{\mathrm{m}}$ - molar concentration and $C$ - weight concentration $(0.555\ \mathrm{g/dm^3})$, $M_{\mathrm{w}}$ - molecular weight of $\mathrm{CaCl_2}$ (111 g/mol).

$$\lambda_{\mathrm{m}} = (0.1194\ \mathrm{s/m} \times 111\ \mathrm{g/mol}) / (1000 \times 0.555\ \mathrm{g/dm^3}) = 23.88 \times 10^{-3}\ \mathrm{s\ m^2/mol}$$

Answers:

(1) 125.39 s Ohm/m²

(2) 0.1194 s/m

(3) $23.88 \times 10^{-3}\ \mathrm{s\ m^2/mol}$

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