Chapter 6 · Biogenic Carbonates: Oxygen

Answers · Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (2007) · ← Problems

Answer 1

With reasonable values of δc and δw, the Epstein equation yields a temperature of 25.8 °C. Substituting this temperature into the aragonite–water equation gives the aragonite value, and comparing the two values yields the ≈0.6‰ aragonite–calcite difference. check vs print [The intermediate values are lost in the extraction, and the printed text cites “Hayes and Grossman” where the problem cites Grossman and Ku.]

Answer 2

  1. From the definition of δ, the water-equilibrated CO2 is (5,986.587/4,116.429)/(5,750.977/4,032.853), giving +19.83‰ vs the reference gas. reconstructed Similarly, for the carbonate, the value is +17.38‰ (printed). Plugging these values into equation (6.4) gives 28 °C.
  2. To convert from one scale to another, we use equation (2.3). On the PDB scale, the calcite is 17.38 + (−19.64) + 0.001(17.38)(−19.64) = −2.60‰ vs VPDB. reconstructed For the water on the VSMOW scale, the printed value is lost in the extraction; carrying the sample CO2 through the PDB-gas to VSMOW conversion and removing the 25 °C CO2–water equilibration factor (α = 1.0412) gives a water near 0‰ vs VSMOW, i.e. a seawater-like value. check vs print
  3. Not printed in the extraction.
  4. Not printed in the extraction. [With T ≈ 28 °C and seawater-like δ18O, Barbados (constructed).]

[Worked grid (constructed), covering part (a) and the calcite half of part (b).]

Answer 3

Not printed in the 1st ed.

Answer 4

The oxygen isotope composition of the water is controlled by that of the inflowing meteoric water (streams, groundwater, or rain) and the degree of evaporation. The isotopic composition of the water is controlled by temperature, distance from the source, and changing sources. The δ18O value of the carbonate is also controlled by temperature, as the fractionation between water and carbonate changes with temperature.

Answer 5

Not printed in the 1st ed.

Answer 6

The δ18O value of meteoric water has a temperature coefficient of 0.69‰/°C (from Chapter 4). The fractionation between carbonate and water has a temperature coefficient of −0.24‰/°C (from equation (6.4)). Therefore, temperature will change the δ18O value of meteoric water almost three times as much as it will the carbonate–water fractionation. Also, carbonates often form only at specific temperature intervals, making water an even stronger control on the δ18O value of the precipitating carbonate.

Answer 7

αacid = (1000 + δCO2)/(1000 + δcalcite), but both must be on the same scale. Convert −2.2‰ vs VPDB to VSMOW and you get +28.64‰, so α = 1038.23/1028.64 = 1.00932. If we now convert to the PDB scale, the sample gas is 7.10‰ (PDB), and α = 1007.10/997.80 = 1.00932, the same. For carbon, α = 1.000, because the δ13C value of the CO2 is identical to that of the carbonate.

Transcribed from Z. Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (Pearson Prentice Hall, 2007), end-of-chapter problem set (published source). Reference-scale names are written VSMOW, VPDB and VCDT where the original used SMOW, PDB and CDT, with the original numerical constants unchanged; historical usages (e.g. Craig's definition of SMOW) are kept as printed.

The source PDF's text layer scrambles mathematics, so equations and some values were reconstructed during transcription. Bracketed notes and anything tagged reconstructed or check vs print are editorial (constructed), not part of the original, and the warn-tagged items should be verified against the print copy.