What is a concentration of Ni in an olivine crystal, in equilibrium with a melt having 150 ppm Ni and \({}^{\mathrm{Ni}}D_{\mathrm{ol-liq.}} = 12\)
0.18 wt%
The partition coefficient of an element between a mineral and a melt is the ratio of its concentration in the mineral to its concentration in the melt: \(D = \frac{C_{ol}}{C_{liq}}\).
Rearranging, \(C_{ol} = D \times C_{liq}\).
Substituting \(D = 12\) and \(C_{liq} = 150\) ppm: \(C_{ol} = 12 \times 150 = 1800\) ppm.
Since 1 wt% = 10,000 ppm, \(1800\) ppm \(= \frac{1800}{10000}\) wt% \(= 0.18\) wt%.
Check: \(\frac{1800}{150} = 12\), which reproduces the given partition coefficient; Ni is compatible in olivine, so it is correctly enriched in the crystal relative to the melt.
Hence, 0.18 wt%.
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