Determining the pH and Buffering Capacities of Buffer Solutions Report

Abstract

A buffer is a solution that weathers changes in pH when an acid or base is added. Buffers are usually made from combinations of weak acids and their corresponding bases or weak bases and their equivalent acids. The Henderson-Hasselbalch equation is often employed in working out the pH of buffers. This experiment intended to establish the variations in pH of acetate and ammonium buffers after the addition of hydrochloric acid and sodium hydroxide. It also aimed at making comparisons between experimentally obtained changes in pH and values calculated using the Henderson-Hasselbalch equation. There were disparities between the measured and calculated pH values due to accidental and systematic uncertainties. However, the observed trend was in accordance with the expected behavior of buffers. It was concluded that experimental techniques were convenient in establishing the buffering capabilities of weak acids and bases.

Introduction

A buffer may be described as a solution that withstands alterations in pH upon the addition of an acid or base. In living systems, buffers are particularly important because they cushion the body from shifts in pH that may have adverse effects on biological processes. Buffer solutions are composed of conjugate weak acids or weak base pairs of chemical species.¹ The addition of a strong acid to a buffer causes the conjugate base in the buffer to react with the acid thereby eliminating it. Consequently, the conjugate base is converted to the conjugate acid. In the same manner, the conjugate acid in a buffer neutralizes hydroxide ions from the added base. Part of the conjugate acid is converted into the corresponding base leading to a slight elevation in the pH of the solution.

K_a denotes the dissociation constant of an acid, which is the measure of the potency of the acid in solution. This value is sometimes indicated as pK_a, which is the logarithm of K_a. A large value of pK_a (small K_a value) is characteristic of a weak acid. It shows that an acid dissociates to a small extent. K_b, conversely, is the dissociation constant of a base. Large K_b values (small pK_b values) are typical of strong bases.

The pH of buffers can be computed using the Henderson-Hasselbalch equation, which is written as pH = pK_a + log ([A^–]/[HA]). In this equation, pK_a is the logarithm of the acid’s K_a value, [A^–] is the concentration of the conjugate base in moles and [HA] is the strength of the acid in moles (before the dissociation). The ability of a weak acid or base to act as a buffer can be determined experimentally by the addition of a strong acid or base and measuring the resultant pH.

This practical aimed at using the Henderson-Hasselbalch equation to calculate the changes in pH of acetate and ammonium buffers after the addition of small quantities of hydrochloric acid and sodium hydroxide. It also sought to compare the experimental and calculated pH values.

Procedure

All solutions were prepared in volumetric flasks using appropriate techniques. It was assumed that the change in volume of the buffer was negligible when the solid conjugate base was added to the measured volume of the acid. The number of moles of sodium acetate was calculated from its molecular weight. One hundred milliliters of 0.1M acetic acid were measured into a 250 ml beaker. The pH of the acid was measured and recorded. Thereafter, the appropriate quantity of sodium acetate was weighed and added to the acetic acid. The mixture was stirred until all the sodium acetate dissolved in the acid. The pH of the resulting buffer was then measured and recorded.

The pK_a of the ammonia/ammonium buffer was 9.26 according to equation 7.¹ One hundred milliliters of 0.1M ammonia were measured and transferred to a 250 ml beaker. The pH of the solution was measured and recorded. The appropriate amount of ammonium chloride (10 mmoles) was measured and added to the ammonia solution. The mixture was stirred until all the ammonium chloride dissolved. The pH of the buffer was also measured and recorded.

To investigate the changes in the pH of the buffers upon the addition of strong acids and bases, 50 ml of the acetate buffer was added to each of two 100 ml beakers. Small amounts of hydrochloric acid (a strong acid) ranging from 1 ml to 4 ml were added to the buffer 1 ml at a time from a burette. The pH values of the resultant solutions were measured and recorded. Similarly, 1 ml to 4 ml of sodium hydroxide (a strong base) was added to the acetate buffer in the second beaker. The pH of the solution was also measured and recorded. The same procedure was repeated for the ammonium buffer in two 100 ml beakers. The measured pH values were then compared to values calculated using the Henderson-Hasselbalch equation.

Data and Results

Acetate Buffer

pH of acetic acid solution= 2.7.

pH of acetate buffer= 3.99.

Table 1: Changes in the pH of the acetate buffer after the addition of various volumes of HCl and NaOH.

Table 1 above showed that the addition of HCl to the buffer led to small decreases in the pH of the buffer, whereas the addition of small volumes of NaOH caused slight increases in the pH of the acetate buffer.

Ammonium Buffer

PH of ammonia solution= 10.55.

PH of ammonium buffer= 9.7.

Table 2: Changes in the pH of the ammonium buffer following the addition of varying volumes of HCl and NaOH.

Table 2 above showed that adding HCl to the ammonium buffer lowered the pH of the buffer while the addition of NaOH raised the pH of the buffer.

Calculations

Acetate Buffer System

1. pH of acetic acid solution

CH₃COOH _(aq)→ H⁺_(aq) + CH₃COO^-(aq)

The formula for K_a is given by K_a= [H⁺][B^–]/[HB] where [H⁺]= concentration of H⁺ ions,

[B^–]= concentration of conjugate base ions and [HB]= concentration of undissociated acid molecules for the reaction HB → H⁺ + B^–.

Acetic acid dissociates one H⁺ ion for every CH₃COO^– ion, therefore, [H⁺]= [CH₃COO^–].

Let x denote the concentration of H⁺ that dissociates from HB, then [HB]= C – x where C is the initial concentration.

Entering these values into the K_a equation

K_a= x·x / (C -x)

K_a= x²/(C – x)

(C – x)K_a= x²

x²= CK_a – xK_a

x² + K_ax – CK_a= 0

Substituting the values of K_a and C in the quadratic expression gives

x² + 1.8×10^-5x – 0.1(1.8×10^-5).

Solving for x in the quadratic equation gives X= 1.323610^-3.

pH= -log [H+]

pH= -log1.3236×10^-3

pH= 2.88.

2. pH of acetate buffer

K_a of acetic acid= 1.8×10^-5

CH₃COOH(aq) + H₂O(l) –> H₃O⁺(aq) + CH₃COO^–(aq)

[H₃O⁺]= K_a[CH₃COOH]

[CH₃COO^–]

The number of moles of acetic acid in 100 ml of 0.1M acid= (100ml×0.1M)/1000ml, which is equivalent to 0.01moles.

The number of moles of sodium acetate= 0.01 moles.

[H₃O⁺]= 1.8×10^-5 [0.01]

[0.01] = 1.8×10^-5

pH= -log1.8×10^-5

pH= 4.74

3. One solution with strong acid added to the acetate buffer

Addition of 1mmol HCl

H₃O⁺ + OAc^– → HOAc +H₂O

pH= pK_a+log(mmol OAc-/mmol HOAc)

pH= 4.74+log(4/6) = 4.74+log(0.667) = 4.74+ (-0.18) = 4.56.

4. One solution with strong base added to the acetate buffer

Addition of 1mmol of NaOH

OH^–+HOAc →OAc^–+ H₂O

pH= pK_a+log(mmol OAc-/mmol HOAc)

pH= 4.74+log(6/4) = 4.74+log(1.5) = 4.74+0.176 = 4.92.

Ammonia/Ammonium System

1. pH of ammonia solution

NH₃ +H₂O= NH₄⁺ +OH^–

pK_a= 14-pK_b

pK_a= 9.26. Therefore, pK_b = 14 – 9.26.

pK_b= 4.74

K_b= 10-4.74

= 1.8197 x 10-5

K_b x [ammonia]= [X+][OH-]

[OH^–]= √(K_b x [ammonia]) = √(1.8197 x 10-5 x 0.1) = 1.3489 x 10-3

pOH= -log [OH^–] = -log [1.3489 x 10-3] = 2.87

pH= 14 – 2.87

pH= 11.13.

2. PH of ammonium buffer

K_a of ammonia= 5.6×10^-10

NH₄⁺(aq) + H₂O(l) –> H₃O⁺(aq) + NH₃(aq)

[H₃O⁺]= K_a[NH₄⁺]

[NH₃]

The number of moles of ammonia = (100ml×0.1M)/1000ml, which is equal to 0.01moles.

The number of moles of ammonium ions=0.01 moles.

[H₃O⁺]= 5.6×10^-10 [0.01]

[0.01] = 5.6×10^-10

pH= -log5.6×10^-10

pH= 9.25

3. One solution with strong acid added to the ammonium buffer

Addition of 1mmol of HCl

OH^–+HOAc → OAc^–+ H₂O

pH= pK_a+log(mmol OAc-/mmol HOAc)

pH= 9.26+log(4/6) = 9.26+log(0.667) = 9.26+ (-0.18) = 9.08

4. One solution with strong base added to the ammonium buffer

Addition of 1mmol of NaOH

OH^–+HOAc →OAc^–+ H₂O

pH= pK_a+log(mmol OAc-/mmol HOAc)

pH= 9.26+log(6/4) = 9.26+log(1.5) = 9.26+0.176 = 9.44.

Discussion

There were differences in the measured and calculated pH values. The differences were due to random and systematic errors. Overestimation and underestimation of the quantities of acid and base during the preparation of the buffers was likely to have happened thereby contributing to the random uncertainties. It was also possible that incorrect quantities of hydrochloric acid and sodium hydroxide were added to the buffers. The systematic errors could have occurred from a faulty pH meter or the improper use of the pH meter when measuring the pH of the solutions.

The actual pH values recorded from the experiment were less than the calculated pH values. For example, the actual pH of acetic acid was 2.7 while the calculated pH was 2.88. In addition, the pH of the acetate buffer was 3.99, whereas the calculated pH was 4.74. However, in the ammonium buffer system, the pH of the buffer after adding 1 ml of hydrochloric acid and 1 ml of sodium hydroxide were higher than the computed values. Despite the disparities in the measured and computed pH values, the trend that was observed was what was expected. The addition of HCl led to slight decreases in the pH of the buffers while the addition of NaOH caused the pH of the buffers to increase. It was concluded that experimental techniques were useful in determining the buffering capabilities of weak acids and bases.

Reference

Grossie, A D.; Underwood, K. Laboratory Guide for Chemistry; Hayden-McNeil: Plymouth, MI, 2013.