A water containing 1x10^-4 mol CO2/L and having an alkalinity of 2.5x10^-4 eq/L has a pH of 6.7. The pH is to be raised to pH 8.3 with NaOH. How many moles of NaOH per liter of water are needed for this pH adjustment? (pK1=6.3 and pK2=10.3)
To determine the amount of NaOH required to adjust the pH of the water, we need to consider the equilibrium reactions involving CO2 (carbon dioxide), NaOH (sodium hydroxide), and the carbonate system.
First, let's write the relevant chemical equations:
1. The dissociation of water:
H2O ↔ H+ + OH-
2. The reaction of CO2 with water:
CO2 + H2O ↔ HCO3- + H+
3. The reaction of bicarbonate (HCO3-) with water:
HCO3- ↔ H+ + CO32-
4. The reaction of sodium hydroxide (NaOH) with water:
NaOH → Na+ + OH-
The pH of the solution can be calculated from the concentration of H+. The pK1 and pK2 values given are the negative logarithms of the acid dissociation constants (Ka) for the reactions involving CO2 in water.
To determine the concentration of H+ in the solution, we need to equate the total concentrations of H+ from all the equilibrium reactions involved. In this case, we have:
[H+] = [H+] from the dissociation of water + [H+] from the reaction of CO2 + [H+] from the reaction of bicarbonate
Now, let's break down the steps to calculate the amount of NaOH required to adjust the pH from 6.7 to 8.3:
Step 1: Calculate [H+] at pH 6.7:
pH = -log[H+]
6.7 = -log[H+]
[H+] = 10^(-pH)
[H+] = 10^(-6.7)
Step 2: Calculate [HCO3-] based on alkalinity:
Alkalinity is a measure of the amount of acid needed to neutralize the basic components in the water. In this case, the alkalinity is given as 2.5x10^-4 eq/L. Since the alkalinity is due to bicarbonate (HCO3-), the concentration of HCO3- can be assumed to be the same as the alkalinity:
[HCO3-] = 2.5x10^-4
Step 3: Calculate [CO32-] from [HCO3-]:
[HCO3-] → [H+] + [CO32-]
Here, the initial concentration of HCO3- is equal to [HCO3-] calculated in Step 2.
Step 4: Calculate the amount of NaOH required to adjust the pH to 8.3:
For every mole of NaOH added, it reacts with one mole of H+ and results in an increase in pH.
Since the desired pH is 8.3, we need to calculate the [H+] required at pH 8.3:
[H+] = 10^(-pH)
[H+] = 10^(-8.3)
The difference in [H+] between the desired pH and the initial pH needs to be neutralized by adding NaOH.
Now, you can calculate the moles of NaOH required using the stoichiometry of the reaction between NaOH and H+.
Note: The pK1 and pK2 values are given, but they are not directly used in calculating the amount of NaOH. They are used to understand the equilibrium reactions involving CO2 in water.