Geochemistry: Calculating Rb Enrichment Factor
This solution explains how to calculate the enrichment factor for an element (Rubidium, Rb) during the partial melting of a source rock using the batch melting model.
Batch Melting Formula
The enrichment factor ($C_L/C_o$) for an element in the melt during batch melting is determined by the formula:
$ \frac{C_L}{C_o} = \frac{1}{F + D_o(1 - F)} $
Where:
- $C_L$ = Concentration of the element in the melt.
- $C_o$ = Initial concentration of the element in the source rock.
- $F$ = Fraction of melt (as a decimal).
- $D_o$ = Bulk distribution coefficient for the element.
Enrichment Calculation Steps
Given values:
- Partial melt fraction, $F = 5\% = 0.05$.
- Bulk distribution coefficient for Rb, $D_o = 0.045$.
Substitute these values into the batch melting formula:
- Calculate the term $D_o(1 - F)$:
$ D_o(1 - F) = 0.045 \times (1 - 0.05) $
$ D_o(1 - F) = 0.045 \times 0.95 $
$ D_o(1 - F) = 0.04275 $
- Calculate the denominator $F + D_o(1 - F)$:
$ F + D_o(1 - F) = 0.05 + 0.04275 $
$ F + D_o(1 - F) = 0.09275 $
- Calculate the enrichment factor $C_L/C_o$:
$ \frac{C_L}{C_o} = \frac{1}{0.09275} $
$ \frac{C_L}{C_o} \approx 10.7816711... $
- Round the result to 2 decimal places as required:
$ \frac{C_L}{C_o} \approx 10.78 $
Final Result
The enrichment factor ($C_L/C_o$) for Rb during batch melting is approximately 10.78.
Important Questions from Igneous Petrology (Trace Elements/Melting/Evolution)
- Choose the explanation(s) for negative Eu anomalies in upper crustal rocks like granite and granodiorite.
- A basaltic magma has an initial nickel concentration of 300 ppm. Olivine crystallizes from this magma by equilibrium crystallization (Case I) or fractional crystallization (Case II). Then, the absolute value of the difference between the nickel concentrations of the liquids remaining after 25% crystallization in these two cases is ________.
(Use $K_{D,Ni}$ olivine/melt = 10). - The modal abundance in an ultramafic rock and the partition coefficients of lutetium (Lu) in clinopyroxene, orthopyroxene, olivine and plagioclase are tabulated below. The bulk distribution coefficient of lutetium ($D_{Lu}$) in the ultramafic rock is ________.
Mineral Modal abundance (%) Partition coefficient Clinopyroxene 45 0.506 Orthopyroxene 40 0.42 Olivine 10 0.045 Plagioclase 05 0.019 A hypothetical garnet peridotite composed of 60% olivine, 25% orthopyroxene, 10% clinopyroxene and 5% garnet undergoes 10% batch melting described by $\frac{C_L}{C_o} = \frac{1}{F+D-F*D}$ where F is degree of melting and D is bulk partition coefficient. The ratio of Ce in the melt to the original rock will be ___________ (round off to 2 decimal places).
(The $K_D$ values of Ce for olivine, orthopyroxene, clinopyroxene and garnet are 0.001, 0.003, 0.10 and 0.02, respectively)
Choose the CORRECT combination for the following four statements.
Statement I: Anhydrous partial melting of peridotites produces basaltic magma.
Statement II: Hydrous melting of peridotites produces andesitic magma.
Statement III: Congruent melting of minerals produces liquids of compositions identical to the minerals.
Statement IV: Incongruent melting of minerals produces liquids of different compositions and new solids.
