Calculate the pH of a buffer formed by mixing 85 mL of 0.16 M nitrous acid (HNO2, Ka = 4.6X10^-4) with 94 mL of 0.15 M sodium nitrate (NaNo2)
Note that NaNO2 is sodium NITRITE.
Use pH = pKa + log [(base)/(acid)].
To calculate the pH of a buffer solution, we need to determine the concentration of the acid and its conjugate base. We can use the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log([A-]/[HA])
Where:
- pH is the measure of acidity or alkalinity of the solution.
- pKa is the negative logarithm of the acid dissociation constant.
- [A-] is the concentration of the conjugate base.
- [HA] is the concentration of the acid.
To solve this problem, we need to find the concentrations of HNO2 and NO2- in the solution after mixing.
Step 1: Calculate the moles of HNO2 and NaNO2:
Moles of HNO2 = volume (L) x concentration (mol/L)
= 0.085 L x 0.16 mol/L
= 0.0136 mol
Moles of NaNO2 = volume (L) x concentration (mol/L)
= 0.094 L x 0.15 mol/L
= 0.0141 mol
Step 2: Determine the concentration of HNO2 and NO2-:
Using the balanced chemical equation for the ionization of HNO2:
HNO2 ⇌ H+ + NO2-
The stoichiometry of the equation tells us that one mole of HNO2 yields one mole of H+ and one mole of NO2-. Therefore, the concentration of HNO2 and NO2- are both equal to the moles of HNO2 and NaNO2 divided by the total volume (179 mL = 0.179 L) of the solution:
[HNO2] = 0.0136 mol / 0.179 L
= 0.076 mol/L
[NO2-] = 0.0141 mol / 0.179 L
= 0.079 mol/L
Step 3: Calculate the pH of the buffer solution using the Henderson-Hasselbalch equation:
pH = pKa + log([NO2-]/[HNO2])
= -log(4.6x10^-4) + log(0.079/0.076)
= -log(4.6x10^-4) + log(1.039)
Using the logarithmic identity: log(a/b) = log(a) - log(b), we can rewrite the equation:
pH = -log(4.6x10^-4) + log(1.039)
= -log(4.6x10^-4 / 1.039)
Now we can use a scientific calculator to evaluate the expression:
pH = -log(4.6x10^-4 / 1.039)
= 3.95
Therefore, the pH of the buffer solution is approximately 3.95.