To create a buffer solution with a pH of 2.88 from 100 mL of 1.50M nitrous acid, the student should dissolve 3.52 g (rounded to 3.5 g to two significant digits) of sodium nitrite (NaNO₂). This calculation uses the Henderson-Hasselbalch equation and considers the molar mass of NaNO₂.
Calculating the Mass of NaNO₂ to Create a Buffer Solution
The student is tasked with finding the mass of sodium nitrite (NaNO₂) to add to a solution of nitrous acid (HNO₂) in order to create a buffer solution with a pH of 2.88. The given Ka for nitrous acid is 4.5 × 10-4. To solve this problem, we'll use the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log ([A-]/[HA])
Where:
- pH is the given pH of the solution
- pKa is the -log(Ka) of the weak acid
- [A-] is the molar concentration of the conjugate base (NaNO₂)
- [HA] is the molar concentration of the weak acid (HNO₂)
First, we calculate the pKa:
pKa = -log(Ka)
= -log(4.5 × 10-4)
= 3.35
Then, we rearrange the Henderson-Hasselbalch equation to solve for [A-]:
[A-] = [HA] × 10(pH-pKa)
For a 1.50M solution of HNO₂:
[A-] = 1.50M × 10(2.88-3.35)
= 1.50M × 10-0.47
= 1.50M × 0.34
= 0.51M
Now, we calculate the moles of NaNO₂ needed:
Moles of NaNO₂ = Volume × Concentration
= 0.100 L × 0.51M
= 0.051 moles
Lastly, we find the mass of NaNO₂ by multiplying the moles by its molar mass (69 g/mol):
Mass of NaNO₂ = Moles × Molar mass
= 0.051 moles × 69 g/mol
= 3.52 g
The student should dissolve 3.52 g of NaNO₂ in the 100 mL solution of HNO₂ to create the desired buffer with a pH of 2.88. It's important to round the final result to two significant digits as the question specifies, so the answer is 3.5 g.