Question

Clinopyroxene crystallizing from a basaltic magma has Sm concentration of 24 ppm. If the clinopyroxene-melt partition coefficient for Sm is 1.2, the concentration of Sm in the basaltic magma will be ______ ppm. (In integer)

Answer 1

Correct Answer: 20

Calculating the Concentration of Sm in Basaltic Magma 

Step 1: Understanding the Formula

The concentration of Sm in the basaltic magma can be calculated using the partition coefficient formula:

\[ K_d = \frac{C_{\text{clinopyroxene}}}{C_{\text{magma}}} \]

Where:

• K_d is the partition coefficient.
• C_{clinopyroxene} is the concentration of Sm in the clinopyroxene.
• C_magma is the concentration of Sm in the magma.

Step 2: Rearranging the Equation to Solve for C_magma

Rearranging the equation to solve for C_magma:

\[ C_{\text{magma}} = \frac{C_{\text{clinopyroxene}}}{K_d} \]

Step 3: Substituting the Given Values

Substitute the given values into the equation:

\[ C_{\text{magma}} = \frac{24 \, \text{ppm}}{1.2} = 20 \, \text{ppm} \]

Final Answer:

The concentration of Sm in the basaltic magma is: 20 ppm.