Question

If the concentration of DIC in the ocean was 2040 micromole/L, what would the pH of the ocean be? Remember this is a scenario where PCO₂ = 560 ppm.Hint: Use algebra to combine the equations given above to solve for [H⁺].

Answer 1

With a DIC concentration of 2040 micromole/L and PCO₂ of 560 ppm, the pH of the ocean would be approximately 7.88

Determining the pH of the ocean with DIC and PCO₂

Given that the DIC concentration is 2040 micromole/L and PCO₂ is 560 ppm, we can calculate the pH of the ocean using the following steps:

Calculate Total Carbonate Concentration (CT):

DIC represents Dissolved Inorganic Carbon, which includes carbonic acid (H₂CO₃), bicarbonate (HCO₃⁻), and carbonate (CO₃²⁻) ions. To determine the total carbonate concentration (CT), we need to account for the contribution of CO₂ from PCO₂ through Henry's Law and the equilibrium reactions between these species.

The equation for CT is:

CT = DIC + 2 * K₁ * PCO₂ / (1 + K₁ * PCO₂)

where:

K₁ is the first dissociation constant of carbonic acid (≈ 0.001008)

PCO₂ is the partial pressure of CO₂ (560 ppm)

Plugging in the values:

CT = 2040 + 2 * 0.001008 * 560 / (1 + 0.001008 * 560) ≈ 2125 micromole/L

Calculate Hydrogen Ion Concentration ([H⁺]):

The pH is determined by the hydrogen ion concentration ([H⁺]). We can calculate [H⁺] using the second dissociation constant of carbonic acid (K₂) and CT:

[H⁺] = √
`√((K_2 * CT))`

where:

K₂ is the second dissociation constant of carbonic acid (≈ 0.000094996)

Substituting the CT value:

[H⁺] =
`√((0.000094996 * 2125))` ≈ 0.133 mol/L

Calculate pH:

Finally, we can calculate the pH using the following equation:

pH = -log₁₀([H⁺])

pH = -log₁₀(0.133) ≈ 7.88

Therefore, in this scenario with a DIC concentration of 2040 micromole/L and PCO₂ of 560 ppm, the pH of the ocean would be approximately 7.88.