Final answer:
To find the pH after adding NaOH to HNO₂, calculate the moles of NaOH, determine if NaOH or HNO₂ is in excess after the reaction, and then calculate the new concentration of the remaining reactant to find the pH. However, without the Kₚ of HNO₂, we cannot provide the exact pH value.
Step-by-step explanation:
To calculate the pH of a solution made by adding 3.266 g of solid NaOH to 675 ml of 0.400 M HNO₂, we need to first determine the number of moles of NaOH added, which can be calculated using the molar mass of NaOH (about 40.00 g/mol).
The moles of NaOH are calculated as follows:
3.266 g NaOH × (1 mol NaOH / 40.00 g NaOH) = 0.08165 mol NaOH
Since NaOH is a strong base, it will react completely with HNO₂, a weak acid. The reaction between NaOH and HNO₂ forms water and the salt sodium nitrite, NaNO₂. This reaction can be represented as:
NaOH + HNO₂ → NaNO₂ + H₂O
We need to determine whether the reaction goes to completion or if there's any excess reactant. To do this, we calculate the moles of HNO₂ in 675 ml (or 0.675 L) of the solution:
0.675 L HNO₂ × 0.400 mol/L = 0.270 mol HNO₂
Comparing the moles of NaOH to the moles of HNO₂, we have more moles of NaOH (0.08165 mol) than moles of HNO₂ (0.270 mol). Thus, NaOH is in excess and the solution will be basic after the reaction goes to completion.
To find the concentration of OH⁻ ions, we subtract the moles of HNO₂ from the moles of NaOH and then divide by the total volume of the solution (which assumes that the volume doesn't change significantly upon the addition of the solid NaOH).
(0.08165 mol NaOH - 0.270 mol HNO₂) / 0.675 L = -0.18835 mol / 0.675 L = -0.279 M OH⁻ (which isn't possible since concentration can't be negative, indicating there was a mistake in calculation since NaOH cannot be in excess of HNO₂; actually, we would take the difference other way around, 0.270 mol HNO₂ - 0.08165 mol NaOH, which gives us the number of moles of unreacted HNO₂).
After finding the correct excess amount of HNO₂, we would then calculate the new concentration of HNO₂ and determine the pH level from there using the Ka value for HNO₂ and an ICE table.
However, without the given Kₚ of HNO₂, further calculations cannot be provided.