What is the pH of a buffer solution prepared from 5.15 g of NH₄NO₃ and 0.10 L of 0.15 M NH₃? What is the new pH if the solution is diluted with pure water to a volume of 5.00 × 10² mL?

Interpretation:

For the buffer solution which is prepared by adding 5.15 g of ammonium nitrate in 0.10 L of 0.15 M NH3 the pH of the buffer solution and after the dilution volume of buffer solution to 5.0×102 mL has to be calculated.

Concept introduction:

The Henderson-Hasselbalch equation relates pOH of a buffer with pKb of base, concentration of conjugate acid and concentration of base. The expression is written as,

pOH=pKb+log[conjugate acid][base] (1)

This equation shows that pOH of buffer solution is controlled by two major factors. First, is strength of the base which can be expressed on terms of pKb and second, the relative concentration of base and its conjugate acid at equilibrium.

The pH value is calculated by expression, pH + pOH = 14.

• The calculation of pH is done by using Henderson-Hasselbalch equation.

Given:

Refer to table 16.2 in the textbook for the value of Kb.

The value of Kb for NH3 is 1.8×10−5.

The pKb value is calculated as follows;

pKb=−log(Kb)

Substitute 1.8×10−5 for Kb.

pKb=−log(1.8×10−5)=4.74

Therefore, pKb value of NH3 is 4.74.

The initial concentration of NH3 is 0.15 mol⋅L−1.

The initial moles of NH4NO3 is 0.0643 mol.

The volume of the buffer solution is 0.10 L.

The concentration of NH4NO3 is calculated as follows;

Molarity=Number of molesvolume of solvent (2)

Substitute 0.0643 mol for number of moles and 0.10 L for volume of solvent in equation (2).

Molarity=0.0643 mol0.10 L=0.643 mol⋅L−1

Therefore, the concentration of NH4NO3 is 0.643 mol⋅L−1.

The value of pH is calculated by using equation (1).

pOH=pKb+log[conjugate acid][base]

Substitute 4.74 for pKb, 0.643 for [conjugate acid], 0.15 for [base].

pOH=4.74+log(0.643)(0.15)=4.74+log(4.2866)=4.74+0.63=5.37

Therefore, pOH value of the buffer solution is 5.37.

The pH value is calculated by using expression,

pH + pOH = 14

Rearrange for pH

pH  = 14−pOH

Substitute 5.37 for pOH

pH  = 14−5.37= 8.63

Therefore value of pH for the buffer solution is 8.63.

Calculation of pH for the buffer solution when it is diluted to 5×102 mL or 0.500 L.

After dilution concentration of ammonia and ammonium nitrate will change as volume of the buffer increases.

Concentration of ammonia after dilution is calculated by using the following expression.

C1V1=C2V2

Here,

• C1 is the initial concentration of ammonia