Chapter 3 · Equilibrium Isotope Fractionation

Problem 1

1. Why do anhydrous mineral–mineral fractionation data take the form 10³lnα_m–n = a·10⁶/T², whereas mineral–water fractionations have the additional b term, given in 10³lnα_m–n = a·10⁶/T² + b?
2. Why does the relationship change to 10³lnα_m–n ∝ 1/T at low temperatures?

Problem 2

Mineral–water, mineral–calcite, and mineral–gas exchange experiments have all been used in the experimental calibration of fractionation factors. What are the advantages and disadvantages of each?

Problem 3

Deuterium hydride is the name of the diatomic gas HD and is available commercially.

1. What is the free-energy change for the formation of 1 mole of HD gas by the reaction ½D₂(g) + ½H₂(g) → HD(g), given that ΔG°_f for HD(g), H₂(g) and D₂(g) are −1.464, 0.0, and 0.0 kJ/mole, respectively?
2. What fraction of the gas will be HD at equilibrium?
3. Why is HD(g) commercially available while HDO(l) is not?

[Worksheet constructed.]

Problem 4

What is the equilibrium δD value of water vapor (H₂O gas) in equilibrium with H₂ gas (at 25 °C) if the δD value of the H₂ gas is −600‰? Use the following information:

[Worksheet constructed. The α row is taken as printed (0.289 via equation (3.4)); the printed step from K to α is lost in the extraction, check vs print.]

Problem 5

Calculate the spring constant k_s for ¹²C¹⁶O, given that, for ¹²C¹⁶O, the wave number is 2167.4 cm⁻¹.

[Worksheet constructed. The last row answers the printed answer’s own closing question about the units of k_s.]

Problem 6

Ferrosilite (Fe₂Si₂O₆) is a pyroxene that is stable only at high pressures. If ferrosilite is heated at low pressure, it breaks down to fayalite (Fe₂SiO₄) and quartz (ignoring potential kinetic effects). Likewise, heating calcite to high temperatures produces lime (CaO) and CO₂. Comment on whether laboratory reactions in which these products are produced could be used for calibrating the fractionations between fayalite and quartz, on the one hand, and lime and CO₂, on the other.

Problem 7

Suppose the general enrichment of ¹⁸O is more strongly concentrated in Si–O bonds, then Al–O bonds, and, finally, M²⁺–O = M¹⁺–O bonds. For the following mineral triplets, which would you expect to have the higher ¹⁸O/¹⁶O ratio? (a) albite (NaAlSi₃O₈), microcline (KAlSi₃O₈), and anorthite (CaAl₂Si₂O₈); (b) mullite (Al₆Si₂O₁₃), sillimanite (Al₂SiO₅), and corundum (Al₂O₃).

Problem 8

The fundamental vibrational frequency of ¹⁶O¹⁶O is 1580.4 cm⁻¹. Calculate the fundamental vibrational frequency of ¹⁸O¹⁸O.

[Worksheet constructed.]

Problem 9

Twelve mg of calcite (δ¹⁸O = 24.32‰) and 50 mg of water (δ¹⁸O = −3.65‰) are equilibrated in a sealed gold capsule at 350 °C. At this temperature, α¹⁸O(calcite–water) = 1.00490. What are the δ¹⁸O values of the calcite and water after the equilibration? reconstructed [The assignment of the two printed starting values to calcite and water was reconstructed; check vs print.]

[Worksheet constructed.]