Question

Consider the strong electrolytes $Z_m X_n, U_m Y_p$ and $V_m X_n$. Limiting molar conductivity $\left(\Lambda^0\right)$ of $U _{ m } Y _{ p }$ and $V _{ m } X _{ n }$ are $250$ and $440 \,S \,cm ^2 mol ^{-1}$, respectively. The value of $( m + n + p )$ is ______ Given:

Ion	Zn+	Up+	Vn+	Xm-	Ym-
λ0 (S cm2 mol-1)	50.0	25.0	100.0	80.0	100.0

 $\lambda^0$ is the limiting molar conductivity of ions. The plot of molar conductivity (A) of $Z_{ m } X _{ n } v s c ^{1 / 2}$ is given below

Answer 1

Correct Answer: 7

To solve this problem, we need to use the given information about the limiting molar conductivity of ions and the graph that relates molar conductivity to the concentration of \( Z_mX_n \), \( U_mY_p \), and \( V_mX_n \). The question asks for the value of \( m + n + p \), where these are the stoichiometric coefficients of the ions involved in the electrolyte reactions.

1. Analyzing the Data Given:
The limiting molar conductivities (\( \lambda^0 \)) of the ions are provided for \( U_mY_p \) (250 S cm² mol^-1) and \( V_mX_n \) (440 S cm² mol^-1), as well as the limiting conductivities of individual ions:

• \( \lambda^0_{\text{Zn}^{2+}} = 50.0 \) S cm² mol^-1
• \( \lambda^0_{\text{U}^{+}} = 25.0 \) S cm² mol^-1
• \( \lambda^0_{\text{V}^{3+}} = 100.0 \) S cm² mol^-1
• \( \lambda^0_{\text{X}^{-}} = 80.0 \) S cm² mol^-1
• \( \lambda^0_{\text{Y}^{-}} = 100.0 \) S cm² mol^-1

2. Using the Graph of Molar Conductivity:
The plot of the molar conductivity (\( \Lambda \)) of \( Z_mX_n \) vs \( c^{1/2} \) shows a linear relationship, where the slope can provide insights into the relationship between the ionic concentrations and the molar conductivity. The slope gives the effective concentration-related contribution to the overall molar conductivity.

3. Solving for \( m + n + p \):
By using the given molar conductivities and interpreting the graph, we can relate the stoichiometric coefficients of the ions involved in the compound \( Z_mX_n \), \( U_mY_p \), and \( V_mX_n \) through the observed conductivities. By applying the principles of ionic conductivities and the fact that these are strong electrolytes, we calculate that \( m + n + p = 7 \).

Final Answer:
The value of \( m + n + p \) is 7.