How do I solve this pH problem?

Question

1. A solution is prepared in which 1.0 mol NaNO2 and 1.5 mol HNO2 are added to a liter of aqueous solution. What is the pH of the solution?

 

2. Suppose 3.65 grams of HCl are added to the solution in #2. What will be the next pH of the solution?

Answer 1

Since HNO2 is a weak acid, you now have a weak acid plus the salt of that acid (NaNO2) which creates a BUFFER.

To find the pH, we need to know the Ka and or pKa for HNO2 and then use the Henderson Hasselbalch equation:

pH = pKa + log [salt]/][acid].   Looking up pKa for HNO2 we find it to be 3.4 (Wikipedia).

pH = 3.4 + log (1.0/1.5) = 3.4 + log 0.667

pH = 3.4 + (-0.18)

pH = 3.2

 

moles HCl added = 3.65 g x 1 mole/36.5 g = 0.1 moles

HCl + NaNO2 = HNO2 + NaCl

So [HNO2] increases by 0.1 M

And [NaNO2] decreases by 0.1 M

New [NaNO2] = 1.0 -0.1 = 0.90 M

New [ HNO2] = 1.5 + 0.1 = 1.6 M

pH = pKa + log [salt]/[acid] = 3.4 + log (0.90/1.60) = 3.4 + log 0.56

pH = 3.4 + (-0.25)

pH = 3.14 = 3.1