The electrical resistance of a column of $0.05 \ mol \ L^{-1}$ $NaOH$ solution of diameter $1 \ cm$ and length $50 \ cm$ is $5.55 \times 10^{3} \ \Omega$. Calculate its resistivity,conductivity and molar conductivity.
$A = \pi r^{2} = 3.14 \times (0.5 \ cm)^{2} = 0.785 \ cm^{2} = 0.785 \times 10^{-4} \ m^{2}$
$l = 50 \ cm = 0.5 \ m$
$\rho = \frac{R A}{l} = \frac{5.55 \times 10^{3} \ \Omega \times 0.785 \ cm^{2}}{50 \ cm} = 87.135 \ \Omega \ cm$
$\kappa = \frac{1}{\rho} = \frac{1}{87.135} \ S \ cm^{-1} = 0.01148 \ S \ cm^{-1}$
$\Lambda_{m} = \frac{\kappa \times 1000}{c} = \frac{0.01148 \ S \ cm^{-1} \times 1000 \ cm^{3} \ L^{-1}}{0.05 \ mol \ L^{-1}} = 229.6 \ S \ cm^{2} \ mol^{-1}$
$l = 50 \ cm = 0.5 \ m$
$\rho = \frac{R A}{l} = \frac{5.55 \times 10^{3} \ \Omega \times 0.785 \ cm^{2}}{50 \ cm} = 87.135 \ \Omega \ cm$
$\kappa = \frac{1}{\rho} = \frac{1}{87.135} \ S \ cm^{-1} = 0.01148 \ S \ cm^{-1}$
$\Lambda_{m} = \frac{\kappa \times 1000}{c} = \frac{0.01148 \ S \ cm^{-1} \times 1000 \ cm^{3} \ L^{-1}}{0.05 \ mol \ L^{-1}} = 229.6 \ S \ cm^{2} \ mol^{-1}$
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View SolutionAn aqueous solution of $X$ is added slowly to an aqueous solution of $Y$ as shown in List-$I$. The variation in conductivity of these reactions is given in List-$II$. Match List-$I$ with List-$II$ and select the correct answer using the code given below the lists :
List-$I$ List-$II$ $P$. $\underset{X}{(C_2H_5)_3N} + \underset{Y}{CH_3COOH}$ $1$. Conductivity decreases and then increases $Q$. $\underset{X}{KI (0.1 \ M)} + \underset{Y}{AgNO_3 (0.01 \ M)}$ $2$. Conductivity decreases and then does not change much $R$. $\underset{X}{CH_3COOH} + \underset{Y}{KOH}$ $3$. Conductivity increases and then does not change much $S$. $\underset{X}{NaOH} + \underset{Y}{HI}$ $4$. Conductivity does not change much and then increases
Codes: $P \quad Q \quad R \quad S$
| List-$I$ | List-$II$ |
|---|---|
| $P$. $\underset{X}{(C_2H_5)_3N} + \underset{Y}{CH_3COOH}$ | $1$. Conductivity decreases and then increases |
| $Q$. $\underset{X}{KI (0.1 \ M)} + \underset{Y}{AgNO_3 (0.01 \ M)}$ | $2$. Conductivity decreases and then does not change much |
| $R$. $\underset{X}{CH_3COOH} + \underset{Y}{KOH}$ | $3$. Conductivity increases and then does not change much |
| $S$. $\underset{X}{NaOH} + \underset{Y}{HI}$ | $4$. Conductivity does not change much and then increases |
Codes: $P \quad Q \quad R \quad S$
Match List-$I$ with List-$II$:
List-$I$ (Parameter) List-$II$ (Unit) $a$. Cell constant $i$. $S\, cm^{2}\, mol^{-1}$ $b$. Molar conductivity $ii$. Dimensionless $c$. Conductivity $iii$. $m^{-1}$ $d$. Degree of dissociation of electrolyte $iv$. $\Omega^{-1}\, m^{-1}$
Choose the most appropriate answer from the options given below:
| List-$I$ (Parameter) | List-$II$ (Unit) |
| $a$. Cell constant | $i$. $S\, cm^{2}\, mol^{-1}$ |
| $b$. Molar conductivity | $ii$. Dimensionless |
| $c$. Conductivity | $iii$. $m^{-1}$ |
| $d$. Degree of dissociation of electrolyte | $iv$. $\Omega^{-1}\, m^{-1}$ |
Choose the most appropriate answer from the options given below:
What is the molar conductivity of $0.1 \ M$ $NaCl$ if its conductivity is $1.06 \times 10^{-2} \ \Omega^{-1} \ cm^{-1}$?
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