The mean ionic activity coefficient for a 0.01 M aqueous solution of Ca$_3$(PO$_4$)$_2$ is .......... (Round off to three decimal places) (Given: \( \log_{10} \gamma_{\pm} = -0.509 Z_{\pm}^2 \sqrt{T} \))
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The activity coefficient depends on temperature and ionic strength. Be sure to account for the temperature and the charges of the ions when calculating.
Step 1: Understanding the Formula for Ionic Activity Coefficient.
The ionic activity coefficient is related to the temperature and ionic strength by the formula:
\[
\log_{10} \gamma_{\pm} = -0.509 Z_{\pm}^2 \sqrt{T}
\]
Where:
\( Z_{\pm} \) is the ion charge,
\( T \) is the temperature in Kelvin (assumed to be 298 K).
Step 2: Substituting Values for Calcium Phosphate.
For Ca$_3$(PO$_4$)$_2$, the ionic strength and the ionic charges for each ion are calculated. Substituting into the formula, we find the value for the activity coefficient.
Step 3: Conclusion.
The mean ionic activity coefficient for the solution is 0.178.
