Question

Distilled water at 25 0C, in which the only ions are H+ and OH-, is placed in contact with a gas at atmospheric pressure containing CO2 at a partial pressure of 1.0 x 10-3 atm (approximately equal to some projections for atmospheric CO2 by 2200). a) What is the concentration of carbonic acid, (H2CO3*), in the water when it has come to equilibrium with the gas? (Hint: Equilibrium constants for 25 0C are listed in Table 18.1 of S&Z). b) Assuming that the dominant ionic (charged) species of dissolved inorganic carbon, (CO3)T, is bicarbonate, HCO3 -, estimate the pH of the water when it has come to equilibrium with the gas. For this estimate, assume that the ionic strength of the water is low enough to neglect activity corrections. (Hint: Start by writing a “charge balance” equation, recognizing that all negative charges in solution must be balanced by a positive charge and that the only cation in your water will be H+. You should be able to use equilibrium relations from Table 18.1 to derive equations for the anions in your charge balance as functions of (H+)). c) Check the assumption of bicarbonate being the dominant ionic species of dissolved inorganic carbon by using your estimated pH to determine [HCO3 -] and the ratio [CO3 2-]/[HCO3 -]. d) Check the assumption of negligible activity corrections by calculating the ionic strength of the water and the activity coefficients (s) for H+ and HCO3 -. e) What is the total dissolved inorganic carbon concentration in the water expressed in terms of mg/L of carbon (Note: You will need first to determine the total moles of carbon, then convert to mg. This is a common way of reporting concentrations of dissolved inorganic carbon.)

Answer 1

Step 1

A

Concentration of H_2CO­­_3 can be determined as:

n is number of mole = m /M

Step 2

Now,

Thus, concentration of

Step 3

B

Average limit of

It indicates maximum capacity or limit of intake of

Concentration = n /V

Thus, pH is 5.78

Step 4

C

Concentration of

Ratio,

Step 5

D

Ionic strength of water is:

From equation (1)

Total alkalinity

Thus, total carbon dioxide concentration is 5.64 mmol.

Activity coefficient for

Activity coefficient for H^+ = 0.1624 /45 = 0.0036