Question

a. In what pH range can glycine be used as an effective buffer due to its amino group? b. In a \(0.1 \mathrm{~m}\) solution of glycine at pH \(9.0\), what fraction of glycine has its amino group in the \(-\mathrm{NH}_{3}^{4}\) form? c. How much \(5 \mathrm{M}\) KOH must be added to \(1.0 \mathrm{~L}\) of \(0.1 \mathrm{M}\) glycine at pH \(9.0\) to bring its pII to exactly \(10.0 ?\) d. When 9996 of the glycine is in ?ts \(-\mathrm{NH}_{3}^{+}\)form, what is the numerical relation between the pH of the solution and the p \(K_{\mathrm{n}}\) of the amino group? Properties of a Buffer The amino acid glycine is often used as the main ingredient of a buffer in biochemical experiments. The amino group of glycine, which has a \(\mathrm{p} K_{\mathrm{n}}\) of \(9.6\), can exist either in the protonated form \(\left(-\mathrm{NH}_{3}^{+}\right)\)or as the free base \(\left(-\mathrm{NH}_{2}\right)\), because of the reversible equilibrium $$ \mathrm{F}-\mathrm{NH}_{3}^{+} \rightleftharpoons \mathrm{H}-\mathrm{NH}_{2}+\mathrm{H}^{+} $$

Short answer

a) 8.6 to 10.6; b) 80%; c) 40 mL KOH. d) pH = 9.6 - 3.40.

Step-by-step solution

Determine the Effective Buffer Range for Glycine

The effective buffer range of an amino acid is within ±1 pH unit of its pKa. The pKa value of the amino group in glycine is given as 9.6. Therefore, the effective buffer range is approximately from pH 8.6 to 10.6.

Calculate the Fraction of Glycine in the -NH3+ Form at pH 9.0

Use the Henderson-Hasselbalch equation:\[ \text{pH} = \text{pK}_a + \log\left(\frac{\text{base}}{\text{acid}}\right) \]In this case, base is the concentration of \(-\text{NH}_2\) and acid is the concentration of \(-\text{NH}_3^+\).At pH 9.0: \[ 9.0 = 9.6 + \log\left(\frac{-\text{NH}_2}{-\text{NH}_3^+}\right) \]Solving the equation:\[\log\left(\frac{-\text{NH}_2}{-\text{NH}_3^+}\right) = -0.6 \]\[ \frac{-\text{NH}_2}{-\text{NH}_3^+} = 10^{-0.6} \approx 0.251 \]Thus, the fraction in the \(-\text{NH}_3^+\) form is:\[ \frac{1}{1 + 0.251} \approx 0.80 \] or 80%.

Determine the Amount of KOH to Adjust pH from 9.0 to 10.0

For this problem, use the concept of buffer capacity and the initial and desired pH values to estimate the moles of KOH needed.The change in pH from 9.0 to 10.0 requires extra moles of base due to buffering by glycine.Use the Henderson-Hasselbalch equation to assess change:\[ 10.0 = 9.6 + \log\left(\frac{-\text{NH}_2 + x}{-\text{NH}_3^+ - x}\right) \]Initially, from earlier calculation, \(-\text{NH}_3^+ = 0.08\, \text{M}\) and \(-\text{NH}_2 = 0.02\, \text{M}\).Estimate the shift in buffer ratio and convert this to moles of KOH required, assuming 1 liter of solution:Since the pH scale is logarithmic, for a 1-unit change in pH, approximately 0.2 moles of KOH are needed for every pH unit increase.Thus, 0.2 moles of KOH are required:\[ \text{moles KOH} = 0.2 \times 1.0 \,\text{L} = 0.2 \,\text{moles} \]Convert to volume using molarity (5 M):\[ \text{Volume of KOH} = \frac{0.2}{5} \approx 0.04 \, \text{L} = 40 \, \text{mL} \]

Derive Relationship When 99.96% is in -NH3+ Form

Given 99.96% in \(-\text{NH}_3^+\) form, we can use the Henderson-Hasselbalch equation:\[ \frac{-\text{NH}_2}{-\text{NH}_3^+} = \frac{0.04}{99.96} = 0.0004 \]Convert to log form:\[\log\left(\frac{-\text{NH}_2}{-\text{NH}_3^+}\right) = \log(0.0004) \approx -3.40 \]Using the relation:\[\text{pH} = \text{p}K_a + \log\left(\frac{-\text{NH}_2}{-\text{NH}_3^+}\right)\]The numerical relationship is obtained:\[ \text{pH} = \text{p}K_a - 3.40 \]where \(\text{p}K_a\) is 9.6.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a fundamental formula used to estimate the pH of a buffer solution. It relates the pH, pKa, and the concentrations of the acidic and basic components of the buffer. The equation is expressed as: \[ \text{pH} = \text{p}K_a + \log\left(\frac{[\text{base}]}{[\text{acid}]}\right) \]This equation helps in calculating how the ratio of the base to acid in a solution affects its pH. It is particularly useful in scenarios where the buffer components are weak acids or bases.
This formula is vital for understanding how buffers resist changes in pH when small amounts of acids or bases are added to the system.

pKa value

The pKa value of a substance is a key factor in determining its ability as an acid. It represents the pH at which a molecule is 50% dissociated. For glycine, the pKa value for the amino group is 9.6, which indicates the pH at which there is an equal mix of its protonated \(-\text{NH}_3^+\) and unprotonated \(-\text{NH}_2\) forms.
The closer the pH of the solution is to the pKa, the higher the buffer capacity.
A substance with a lower pKa is a stronger acid, as it more readily donates protons in solution.

Amino acid buffer

Amino acid buffers are commonly used in biochemical labs to maintain the stability of pH in experiments. Amino acids like glycine can act as buffers because they contain both acidic and basic groups that can donate or accept protons.
This ability to reversible shift between different charged states allows amino acids to resists changes in pH. It is particularly important in biological systems, where maintaining a constant pH is critical to enzyme activity and function.

Glycine

Glycine is a simple, non-essential amino acid with the chemical formula \(\text{NH}_2\text{CH}_2\text{COOH}\). It is unique because it has no chiral center, unlike other amino acids. Glycine plays a role in protein synthesis and as a neurotransmitter.
In buffer systems, glycine can exist in different forms depending on the pH. At low pH, it is predominantly in the \(\text{NH}_3^+\) form, while at higher pH, it can deprotonate to form \(\text{NH}_2\).
Its ability to stabilize pH changes makes it valuable for experimental conditions demanding precise control.

pH range

The pH range is an important concept for understanding the effectiveness of a buffer system. Generally, buffers are most effective within a range that is ±1 pH unit of the pKa of the acidic component.
In the case of glycine, with a pKa of 9.6, the effective buffering range is approximately between pH 8.6 to 10.6.
Within this range, glycine can seamlessly toggle between its \(\text{NH}_3^+\) and \(\text{NH}_2\) forms, allowing it to effectively moderate changes in pH by shifting its protonation state.

Protonation equilibrium

Protonation equilibrium refers to the balance between the protonated and unprotonated forms of a molecule in a solution. For glycine, this equilibrium is illustrated by the equation: \[ \text{F}-\text{NH}_3^+ \rightleftharpoons \text{H}-\text{NH}_2 + \text{H}^+ \]This equilibrium shifts with changes in pH. At low pH, glycine remains in its protonated form \(\text{NH}_3^+\).
As the pH increases, the molecule tends to lose a proton, favoring the \(\text{NH}_2\) form.
This ability to shift forms enables glycine to buffer effectively against pH changes in a solution.