Did you know that the pH of seawater is 8? Find the pH of seawater by giving the partial pressure of carbon dioxide in the atmosphere (pCO2) and the concentration of total carbonic acid (DIC).

Below we have written out the definition of DIC, the equations for the dissolution equilibrium of carbon dioxide and the dissociation equilibrium of carbonic acid system components and water.

[DIC] = [HCO3-] + [CO32-] + [H2CO3]  Equation(1)

K0 = [H2CO3]/pCO2            Equation(2)

K1 = [HCO3-]・[H+]/[H2CO3]    Equation(3)

K2 = [CO32-]・[H+]/[HCO3-]    Equation(4)

Kw = [H+]・[OH-]             Equation(5)

 K0 = 10-1.489、K1 = 10-5.882、K2 = 10-9.035、Kw = 10-13.409  (Temperature: 20°C)

Equations (6) through (8) below were derived by calculating the ratio of each carbonic acid component to DIC at a given pH.

Equation (7) is used here.

[HCO3-]=  K1・[H+]・[DIC]/( [H+]2 + K1[H+]+ K1K2 )      Equation (6)

[H2CO3]= [H+]2・[DIC]/( [H+]2 + K1[H+]+ K1K2 )        Equation (7)

[CO32-]=  K1・K2・[DIC]/( [H+]2 + K1[H+]+ K1K2 )           Equation (8)

Step 1: Substitute equation (7) into equation (2).

    Transform this into the form of a quadratic equation for [H+], including pCO2 and [DIC].

   (That is, transform it to A[H+]2 + B[H+] + C = 0  A, B, and C on the left are for you all to find.)

Step 2) Solve the quadratic equation for [H+] above according to the solution formula.

    [H+] = ~~~

I (Ooki) tend to forget the solution formula, so I will note it so that I do not make a mistake.
ax^2 + bx + c = 0,     solution:x=( -b ± (b^2  -4ac )^0.5 ) / (2a)

Step 3) 2.09 x 10-3 (mol/L) as [DIC] of seawater and 380 x 10-6 (atm) as pCO2 of atmosphere,

    Substitute the formula" H+ = ~~~~ "to obtain the value of [H+].

    Since it is impossible to calculate by hand, please create this formula in Excel (*) and have it calculated.

Step 4: Substitute into equation "pH = -Log10[H+]" to obtain the pH of seawater.

Did you obtain pH = 8.06?

760×10-6 (atm), the value at which atmospheric pCO2 doubled
190×10-6 (atm), the value at which atmospheric pCO2 was halved.  
Find also the pH at this time.

*You can create a formula by typing "=" into an Excel cell, with each cell as an argument.

If you type the Excel function, =Log(argument) into the cell, it will calculate the ordinary logarithm of the argument.

By the way, =Ln(argument) will calculate the logarithm with e as the base. Get used to Excel calculations.

Last modified: Tuesday, 18 July 2023, 10:35 AM