Question

In a hypothetical rock, the Kd values of element E in minerals M1, M2, and M3 are 1.5, 1.0, and 0.5, respectively. The modal abundances of M1, M2, and M3 are 10%, 40%, and 50%, respectively. The bulk partition coefficient of element E in this rock is ________

Hint:

To calculate the bulk partition coefficient, take the weighted average of the individual partition coefficients based on the modal abundances of the minerals.

Answer 1

Step 1: Understanding the formula for the bulk partition coefficient. 
The bulk partition coefficient (\(K_d\)) for the rock is calculated as a weighted average based on the modal abundances and the partition coefficients of each mineral: \[ K_{{bulk}} = (f_1 \times K_{d1}) + (f_2 \times K_{d2}) + (f_3 \times K_{d3}) \] Where:
\(f_1, f_2, f_3\) are the modal abundances of M1, M2, and M3, respectively.
\(K_{d1}, K_{d2}, K_{d3}\) are the partition coefficients of element E in M1, M2, and M3, respectively. 
Step 2: Applying the values. 
Given:
\(K_{d1} = 1.5, K_{d2} = 1.0, K_{d3} = 0.5\)
\(f_1 = 10% = 0.1, f_2 = 40% = 0.4, f_3 = 50% = 0.5\)
The bulk partition coefficient is: \[ K_{{bulk}} = (0.1 \times 1.5) + (0.4 \times 1.0) + (0.5 \times 0.5) = 0.15 + 0.4 + 0.25 = 0.8 \] Thus, the bulk partition coefficient of element E in the rock is \(0.80\).