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
| 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
Correct Answer: 7
Solution and Explanation
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.
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