Explain (using equations) how a solution of 1.0 mol dm^-3 in both CH3COOH and CH3COONa is resistant to changes n pH when we add either small amounts of acid or small amount of base (such solution is called a buffer)
continued from above calculate the initial pH of the acetic acid-sodium acetate solution above.The pKa of acetic acid is 4.76
To do the second part from first principles. Start with the acid dissociation equation:
HAc -> H+ + Ac-
Ka is then
[H+][Ac-]/[HAc]
at the start
HAc -> H+ + Ac-
1.0 M ___0__1.0M
at the end
HAc -> H+ + Ac-
1.0-x__x___1.0+x
so Ka is
Ka=(x)(1.0+x)/(1.0-x)
we can treat this in two ways, we can solve for x
or
Assume that x is small so that
Ka=x(1.0)/(1.0)=x
thus pKa = pH =4.76
To give another perspective, you can calculate the pH of a buffer using the Henderson-Hasselbalch equation.
To understand why a solution of CH3COOH (acetic acid) and CH3COONa (sodium acetate) is resistant to changes in pH when small amounts of acid or base are added, we need to consider the properties of acids, bases, and the Henderson-Hasselbalch equation.
Acetic acid (CH3COOH) is a weak acid, meaning it only partially dissociates in water, releasing a small number of hydrogen ions (H+). Sodium acetate (CH3COONa) is the salt of acetic acid, and when dissolved in water, it dissociates completely into sodium ions (Na+) and acetate ions (CH3COO-).
To analyze the resistance to pH changes of the buffer solution, we start with the equilibrium equation for the dissociation of acetic acid:
CH3COOH ⇌ CH3COO- + H+
This equation represents the equilibrium between undissociated acetic acid, acetate ions, and hydrogen ions in the solution. The equilibrium constant for this dissociation is denoted by Ka.
Ka = [CH3COO-][H+]/[CH3COOH]
Now, using the Henderson-Hasselbalch equation, we can express the pH of a buffer solution as a function of the concentrations of the acid and its conjugate base:
pH = pKa + log([CH3COO-]/[CH3COOH])
where pKa is the negative logarithm of Ka.
The Henderson-Hasselbalch equation shows that the pH of the buffer solution is determined by the ratio of the concentrations of the conjugate base (CH3COO-) to the weak acid (CH3COOH). When both the acid and its conjugate base are present in significant amounts, even small additions of acid or base can be absorbed by the buffer solution without causing a drastic change in pH. This is due to the common ion effect, where the added acid or base reacts with the corresponding conjugate base or acid in the solution, keeping the overall concentration ratio relatively constant.
For example, if we add a small amount of acid, it will react with the acetate ions (CH3COO-) present, converting them into acetic acid (CH3COOH) through the equation:
H+ + CH3COO- ⇌ CH3COOH
This reaction relieves the excess hydrogen ions from the added acid, preventing a sharp decrease in pH. Similarly, if we add a small amount of base, it will react with the acetic acid (CH3COOH) present, converting it into acetate ions (CH3COO-) through the equation:
OH- + CH3COOH ⇌ CH3COO- + H2O
This reaction consumes the excess hydroxide ions from the added base, preventing a significant increase in pH.
Therefore, a solution of CH3COOH and CH3COONa acts as a buffer because the presence of a weak acid and its conjugate base allows for the absorption of small amounts of acid or base, keeping the pH relatively constant. The effectiveness of the buffer is primarily determined by the ratio of the concentrations of the weak acid and its conjugate base.