Chapter 7 · Carbon in the Low-Temperature Environment

Answer 1

Not printed in the 1st ed. [Constructed: Δδ¹³C = 40 × (−0.006) = −0.24‰, a ≈0.24‰ shift over the glacial–interglacial cycle.]

Answer 2

1. The atmosphere has 775·10¹⁵ g C with a δ¹³C value of −8‰. If we add 5.4·10¹⁵ g of −25‰ carbon to the atmosphere, the new value will be
   (775 × (−8) + 5.4 × (−25)) / (775 + 5.4) = −8.11‰
   It will change by ~0.11‰/year. Over 20 years, it should change by ~2‰. There will be some exchange with the oceans, so that the change should be slightly less than this.
2. Not printed in the 1st ed.

[Worked grid for part (a) (constructed).]

Answer 3

The stomates will close down as much as possible to prevent water loss. As a result, only a small amount of CO₂ will be admitted into the cell. The internal partial pressure of CO₂ will be far less than the external pressure. From equation (7.4), it is clear that for low internal pressures, the fractionation approaches the value for constant a.

Answer 4

The mass-balance equation for this problem is

Thus, x = −1.7‰.

Answer 5

Methane will have an extremely low carbon isotope ratio. If the methane is later oxidized to CO₂ or bicarbonate, it will form a carbonate with a very low δ¹³C value. Likewise, the removal of methane from a system will leave behind CO₂ or bicarbonate with a very high δ¹³C value. If this is converted to carbonate, it will have a high value as well.

Answer 6

There are two boxes: shallow and deep ocean. Input flux to the shallow ocean is riverine. There is a diffusional exchange between shallow and deep ocean, but the flux of the biological pump (shallow to deep ocean) is larger than the diffusion exchange flux. Both shallow and deep ocean can lose carbon as either carbonates or organic matter.

[Diagram redrawn from the printed figure (constructed); reservoir sizes and δ values as printed.]

Answer 7

1. The burial of carbonates has very little effect on the δ¹³C values of the ocean, but the burial of organic matter removes light carbon from the ocean, leaving the ocean heavier. If burial shuts down, the δ¹³C of the ocean will decrease due to light influx of riverine input until it has the same value as that of the river. As long as productivity is active, the biological pump is going to cause a difference between shallow and deep ocean.
2. Similar to the answer to part (a), but without productivity, the difference between shallow and deep ocean will disappear, with the shallow ocean quickly assuming the same value as the deep ocean.
3. In this case, the removal of light carbon continues, so that the overall value of the ocean will not change. But without productivity, the difference between shallow and deep ocean disappears.

[The printed sketch panels (δ¹³C vs time, shallow and deep curves for each case) are not reproduced; check the print copy.]

Answer 8

Not printed in the 1st ed.

Answer 9

The atomic weight of carbon is given by 12x + 13.00335(1 − x) = 12.0107, so x = 0.989336. The ¹³C/¹²C ratio of typical “periodic table” carbon is (1 − 0.989336)/0.989336 = 0.0107789. Using the definition of δ¹³C, we have

far lower than the Earth’s average value.