Read the passage carefully and answer the Questions.
Molar conductivity (\( Λ_m \)) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar conductivity (\( Λ^0_m \)). For a strong electrolyte, \( Λ_m \) increases linearly with dilution and is given by \( Λ_m = Λ^0_m -Ac^{1/2} \). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \( Λ^0_m \) for an electrolyte is \( Λ^0_m=v_+λ^0_+ + v_-λ^0_- \), where \( v_+ \) and \( v_- \) are the number of cations and anions, respectively, per molecule of the electrolyte and \( λ^0_+ \) and \( λ^0_- \) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation (\( Λ_m/Λ^0_m \)) and the dissociation constant of a weak electrolyte.
The plot between \( Λ_m \) and \( c^{1/2} \) is a straight line with
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Slope = -A and intercept = \(Λ^0_m\)
The equation of a straight line is \( y = mx + b \), where m is the slope and b is the intercept on the y-axis. Write the equation for a strong electrolyte in the same form:
\( \displaystyle \Lambda_m = \Lambda^{0}_m - A\,c^{1/2} \)
\( \displaystyle \Lambda_m = (-A)\,c^{1/2} + \Lambda^{0}_m \)
With \( \Lambda_m \) on the y-axis and \( c^{1/2} \) on the x-axis, the coefficient of \( c^{1/2} \) is the slope, and the constant term is the intercept. So the plot is a straight line with slope −A (the line falls as the concentration rises) and intercept \( \Lambda^{0}_m \). This is how the limiting molar conductivity of a strong electrolyte is found: the line is extended back to zero concentration.
NCERT (2026-27 edition):
Strong Electrolytes
