Blood is buffered by carbonic acid and the bicarbonate ion. Normal blood plasma is 0.024 M in HCO₃^- and 0.0012 M H₂CO₃ (pK_a1 for H₂CO₃ at body temperature is 6.1).
c. Given the volume from part (b), what mass of NaOH can be neutralized before the pH rises above 7.8?

Verified step by step guidance

1. 1. The first step is to understand the concept of buffers. A buffer is a solution that can resist pH change upon the addition of an acidic or basic components. It is able to neutralize small amounts of added acid or base, thus maintaining the pH of the solution relatively stable. This is achieved by including a weak acid and its conjugate base (as in this case, H₂CO₃ and HCO₃^-).
2. 2. The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution. The equation is: pH = pKa + log([A-]/[HA]), where [A-] is the molar concentration of the base (HCO₃^- in this case) and [HA] is the molar concentration of the acid (H₂CO₃ in this case).
3. 3. To find the pH at which NaOH can be neutralized, we need to rearrange the Henderson-Hasselbalch equation to solve for [A-]/[HA]. This gives us: [A-]/[HA] = 10^(pH - pKa). We can then substitute the given pH (7.8) and pKa (6.1) into this equation to find the ratio of [A-] to [HA] at this pH.
4. 4. Once we have the ratio of [A-] to [HA], we can use it to calculate the amount of NaOH that can be neutralized. This is because the addition of NaOH will consume H₂CO₃ and produce HCO₃^-, changing the ratio of [A-] to [HA]. We can set up an equation representing this reaction and solve for the amount of NaOH that can be added before the ratio of [A-] to [HA] reaches the value calculated in step 3.
5. 5. Finally, once we have the amount of NaOH in moles, we can convert it to mass by multiplying by the molar mass of NaOH (approximately 40 g/mol). This will give us the mass of NaOH that can be neutralized before the pH rises above 7.8.

Key Concepts

Buffer Systems

Buffer systems are solutions that resist changes in pH upon the addition of small amounts of acids or bases. In blood, the carbonic acid (H2CO3) and bicarbonate ion (HCO3-) work together to maintain a stable pH, crucial for physiological functions. The equilibrium between these two components allows the blood to neutralize excess acids or bases, keeping the pH within a narrow range.

pKa and Acid-Base Equilibrium

The pKa value is a measure of the strength of an acid in solution, indicating the pH at which half of the acid is dissociated. For carbonic acid, with a pKa of 6.1, this means that at pH 6.1, the concentrations of H2CO3 and HCO3- are equal. Understanding pKa is essential for predicting how the buffer system will respond to added acids or bases, such as NaOH in this case.

Neutralization Reactions

Neutralization reactions occur when an acid reacts with a base to form water and a salt, effectively reducing the acidity or basicity of the solution. In this scenario, adding NaOH (a strong base) to the buffered solution will react with H2CO3, leading to the formation of HCO3- and water. Calculating the mass of NaOH that can be added before the pH exceeds 7.8 involves understanding the stoichiometry of the reaction and the buffer capacity.