For a strong electrolyte, a plot of molar conductivity against \( (\text{concentration})^{1/2} \) is a straight line, with a negative slope, the correct unit for the slope is:
- S cm\(^2\) mol\(^{-3/2}\) L\(^{1/2}\)
- S cm\(^2\) mol\(^{-1}\) L\(^{1/2}\)
- S cm\(^2\) mol\(^{-3/2}\) L
- S cm\(^2\) mol\(^{-3/2}\) L\(^{-1/2}\)
The Correct Option is A
Approach Solution - 1
For a strong electrolyte, the molar conductivity \(\Lambda_m\) can be expressed as:
\[\Lambda_m = \Lambda_m^0 - A\sqrt{C}\]
where \(\Lambda_m^0\) is the molar conductivity at infinite dilution, \(A\) is a constant, and \(C\) is the concentration.
The term \(A\sqrt{C}\) has units of \(\text{S cm}^2 \text{mol}^{-1}\), so the units of \(A\) must be \(\text{S cm}^2 \text{mol}^{-3/2} \text{L}^{1/2}\) to ensure dimensional consistency when multiplied with \(\sqrt{C}\) (units of \(\text{mol}^{1/2} \text{L}^{-1/2}\)).
Approach Solution -2
For a strong electrolyte, molar conductivity (\( \Lambda_m \)) varies with the square root of concentration (\( c^{1/2} \)) according to the Kohlrausch’s law of independent migration of ions. The relationship is expressed as:
\[ \Lambda_m = \Lambda_m^0 - K \sqrt{c} \] where:
- \( \Lambda_m \) = molar conductivity at concentration \(c\),
- \( \Lambda_m^0 \) = molar conductivity at infinite dilution,
- \( K \) = slope of the line (a proportionality constant),
- \( c \) = concentration in mol L\(^{-1}\).
Step 2: Analyze the equation for the slope
From the above equation, if we plot \(\Lambda_m\) (in S cm² mol\(^{-1}\)) on the y-axis against \(c^{1/2}\) (in mol\(^{1/2}\) L\(^{-1/2}\)) on the x-axis, we get a straight line with:
- Intercept = \(\Lambda_m^0\)
- Slope = \(-K\)
Step 3: Determine the unit of the slope
To find the unit of slope \(K\), consider:
\[ \text{Unit of } K = \frac{\text{Unit of } \Lambda_m}{\text{Unit of } c^{1/2}} \] Now substitute the respective units:
\[ \text{Unit of } \Lambda_m = \text{S cm}^2 \text{mol}^{-1} \] and \[ \text{Unit of } c^{1/2} = (\text{mol L}^{-1})^{1/2} = \text{mol}^{1/2} \text{L}^{-1/2}. \] Hence, \[ \text{Unit of } K = \frac{\text{S cm}^2 \text{mol}^{-1}}{\text{mol}^{1/2} \text{L}^{-1/2}} = \text{S cm}^2 \text{mol}^{-3/2} \text{L}^{1/2}. \]
Step 4: Final conclusion
Therefore, the correct unit of the slope for the plot of molar conductivity vs. \((\text{concentration})^{1/2}\) is:
Top JEE Main Chemistry Questions
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- At equilibrium the concentrations of and in a sealed vessel at . What will be for the reaction
- Find out the major products from the following reactions
Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
- The correct order of atomic radii is:
Top JEE Main Electrochemistry Questions
- $\text{The hydrogen electrode is dipped in a solution of pH = 3 at } 25^{\circ}\text{C. The potential of the electrode will be } -\_\_\_\_\_ \times 10^{-2} \text{ V.}$
$\left( \frac{2.303RT}{F} = 0.059 \, \text{V} \right)$ - The mass of zinc produced by the electrolysis of zinc sulfate solution with a steady current of 0.015 A for 15 minutes is _____ \( \times \, 10^{-4} \) g.
(Atomic mass of zinc = 65.4 amu) - The mass of silver (Molar mass of Ag : 108 gmol–1 ) displaced by a quantity of electricity which displaces 5600 mL of O2 at S.T.P. will be _____ g.
- The potential for the given half cell at 298 K is\[(-) \ldots \times 10^{-2} \, \text{V}.\]\[2\text{H}^+ (\text{aq}) + 2e^- \rightarrow \text{H}_2 (\text{g})\]\[[\text{H}^+] = 1M, \, P_{\text{H}_2} = 2 \, \text{atm}\](Given: \( 2.303 \frac{RT}{F} = 0.06 \, \text{V}, \log 2 = 0.3 \))
- The metals that are employed in the battery industries are
A. Fe
B. Mn
C. Ni
D. Cr
E. Cd
Choose the correct answer from the options given below:
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.