Fractional Crystallization Sr Concentration Calculation

This problem requires calculating the concentration of Strontium (Sr) in a residual magma after fractional crystallization, using the Rayleigh equation.

Given Data Identification

• Initial Sr concentration ($C_0$): 400 ppm
• Percentage of fractional crystallization: 60%
• Bulk distribution coefficient ($D$): 0.2

Calculation Steps

1. Determine the fraction of residual liquid ($F$). If 60% has crystallized, the remaining liquid fraction is:

   $ F = 1 - 0.60 = 0.40 $

2. Apply the Rayleigh equation for fractional crystallization to find the Sr concentration in the residual liquid ($C_L$). The formula is:

   $ C_L = C_0 \times F^{(D-1)} $

3. Substitute the known values into the equation:

   $ C_L = 400 \, \text{ppm} \times (0.40)^{(0.2 - 1)} $

   $ C_L = 400 \, \text{ppm} \times (0.40)^{-0.8} $

4. Calculate the value:

   $ (0.40)^{-0.8} \approx 2.09034 $

   $ C_L \approx 400 \times 2.09034 \, \text{ppm} $

   $ C_L \approx 836.14 \, \text{ppm} $

5. Round the result to the nearest integer:

   $ C_L \approx 836 \, \text{ppm} $

The calculated concentration of Sr in the residual liquid is approximately 836 ppm. This value is consistent with the provided answer range.