Chapter 6 · Biogenic Carbonates: Oxygen

Problem 1

Show that the aragonite–calcite fractionation of 0.6 per mil at 25 °C determined by Tarutani et al. (1969) is roughly compatible with a combination of the aragonite–water equation of Grossman and Ku (1986) and the calcite–water equation of Epstein et al. (1953). (Hint: start by choosing some reasonable values of δ_c and δ_w and substitute them into the Epstein equation.)

[The Epstein et al. and Grossman and Ku equations are in the chapter text (eqs 6.4 and following).]

Problem 2

A carbonate and a water sample are collected. The water is equilibrated with CO₂ at 25 °C and the calcite is reacted with 100% phosphoric acid at 25 °C, to extract pure CO₂. Both are measured on a mass spectrometer. The δ¹⁸O value of the reference gas on the PDB scale is −19.64‰. The voltages in the following table were obtained:

1. What is the temperature of calcite formation obtained from Epstein’s equation (6.4)?
2. What are the δ¹⁸O values of the calcite and water on the VPDB and VSMOW scales, respectively?
3. What is the temperature of calcite formation obtained from O’Neil’s equation (6.6)? Is the answer the same as in part (a)?
4. Would this carbonate sample be more likely to come from Barbados or the North Atlantic?

[Worksheet constructed, for parts (a) and the calcite half of (b); the water-to-VSMOW chain of part (b) is discussed in the answers. Equation (6.4) is T(°C) = 16.5 − 4.3·(δc − δw) + 0.14·(δc − δw)².]

Problem 3

1. Delta values of marine biogenic carbonate almost always decrease during diagenesis. Under what circumstances could δ¹⁸O increase during diagenesis?
2. A Cretaceous shell comprises high-magnesium calcite. What is the likelihood that it retained its original isotopic composition through time?
3. Is it possible for an organism to deposit its shell in oxygen isotope equilibrium and carbon isotope disequilibrium with ocean water? How about the reverse situation? Explain.

Problem 4

The δ¹⁸O values of marine carbonates are controlled by temperature and the δ¹⁸O value of the ocean. Separating these two factors during a glacial–interglacial period is difficult. Discuss all factors that control the δ¹⁸O values of carbonates in lakes. Recognize that the δ¹⁸O value of meteoric water is related to temperature, etc.

Problem 5

Convert Epstein’s equation (6.4) to a form in which the δ¹⁸O value of carbonate is related to VPDB and the δ¹⁸O value of the water is related to VSMOW. Here is some useful information. The α value for SMOW–PDB is 1.03091; the α value for calcite acid fractionation is α(CO₂–calcite) = 1.01025; the α value for CO₂–water equilibration at 25 °C is 1.0412; the combined fractionation from two factors α₁ and α₂ is given by α₃ = α₁·α₂.

Problem 6

For a carbonate precipitated in a lake, the δ¹⁸O value of the lake water will be controlled by the annual average weighted temperature. The δ¹⁸O value of the carbonate will be controlled by the δ¹⁸O value of the lake water and temperature. These two effects control the δ¹⁸O value of carbonate in an opposite manner. Which factor is more important? Make a semiquantitative assessment of the relative importance of both factors.

[Worksheet constructed; the two coefficients are those cited in the printed answer (Chapter 4 and equation (6.4)).]

Problem 7

Your constant-temperature water bath operates only at 70 °C. In order to determine the fractionation factor during phosphoric acid digestion, you react a sample of NBS-19 (which has a δ¹⁸O value of −2.2‰ vs VPDB) with 100% phosphoric acid at 70 °C and get a δ¹⁸O value for the liberated CO₂ gas of 38.23‰ (vs VSMOW). What is the acid fractionation factor α for calcite at 70 °C? What is the fractionation factor for carbon (e.g., α¹³C(CO₂ gas–calcite)) at 70 °C?

[Worksheet constructed; the scale-conversion constants are the chapter-2 values.]