The first step in calculating buffer ingredients is to determine the ratio between acid (HA) and base (A–) concentration using the Henderson-Hasselbalch equation. The pKa of phosphoric acid is 7.21. For a phosphate buffer of pH 7, what is the ratio of [A-]/[HA] (i.e. the base to acid concentration ratio)?

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BlackTom AI · Accepted Answer

Henderson–Hasselbalch: pH = pKa + log([A–]/[HA]), so use this to find the base/acid ratio. 1. Relevant knowledge points and concepts - The Henderson–Hasselbalch equation links pH, pKa and the ratio of conjugate base ([A–]) to acid ([HA]): pH = pKa + log10([A–]/[HA]). - If pH < pKa, the acid form predominates and the ratio [A–]/[HA] will be less than 1; if pH > pKa the ratio exceeds 1. 2. Step-by-step reasoning - Rearrange the equation to solve for the ratio: log10([A–]/[HA]) = pH − pKa. - Substitute the given values: pH = 7.00, pKa = 7.21. 3. Calculation with intermediate steps - Compute the log term: log10([A–]/[HA]) = 7.00 − 7.21 = −0.21. - Convert from log form to ratio: [A–]/[HA] = 10^(−0.21). - Evaluate 10^(−0.21): - Using e: 10^(−0.21) = e^(−0.21 · ln 10) = e^(−0.21 · 2.302585) = e^(−0.483543) ≈ 0.6169. - Rounded to three significant figures: 0.617. 4. Why this is correct - The algebraic manipulation of Henderson–Hasselbalch is straightforward and the numeric evaluation yields ~0.617. The ratio is less than 1 because pH (7.00) is lower than pKa (7.21), so the protonated (acid) form HA is more abundant than the deprotonated base A–. 5. Why other answers would be incorrect - Any ratio = 1 would correspond to pH = pKa (7.21), not pH 7. Any ratio >1 contradicts pH < pKa. Lower or higher numeric values not equal to 10^(−0.21) are simply not the result of the correct substitution and evaluation. 6. Conclusion - The base-to-acid concentration ratio [A–]/[HA] = 10^(7.00−7.21) ≈ 0.617, which matches the provided answer (0.617).

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