Choosing and Stress-Testing an Assay Buffer
You are preparing 500 mL of assay buffer for a kinase experiment. The enzyme loses 40% activity in phosphate buffer and is inhibited when chloride exceeds 50 mmol/L. The assay also requires 10 mmol/L MgCl2. You have 1.0 M HEPES free acid (MW 238.3; pKa 7.55 at 25°C), 1.0 M NaOH and solid anhydrous MgCl2 (MW 95.2). The target is 0.050 M HEPES at pH 7.40 at 25°C. A colleague suggests Tris (pKa 8.06) because it is cheaper per litre. You also need to know how the buffer will behave when 2.5 mL of 0.10 M HCl is added during a timed acid-stress step. The pH meter is calibrated and the room is at 25°C. Assume activities equal concentrations and ignore MgCl2's contribution to ionic strength in the pH calculation.
1. Calculate the volumes of 1.0 M HEPES stock and 1.0 M NaOH, and the mass of anhydrous MgCl2 needed for 500 mL. Show the Henderson–Hasselbalch reasoning.
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Henderson–Hasselbalch: pH = pKa + log([A−]/[HA]). So 7.40 = 7.55 + log(r), giving log(r) = −0.15 and r = 10^−0.15 = 0.708. With total buffer concentration 0.050 M, [A−] = 0.050 × 0.708 / 1.708 = 0.0207 M and [HA] = 0.0293 M. In 0.500 L, total HEPES = 0.0250 mol, so the 1.0 M stock volume is 25.0 mL.
NaOH must convert 0.0207 × 0.500 = 0.01035 mol of free acid to the salt form, so 10.35 mL of 1.0 M NaOH is required. Add the HEPES stock and NaOH to about 450 mL water, mix, check pH, then make to 500 mL. MgCl2 needed = 10 mmol/L × 0.500 L = 5.0 mmol; mass = 5.0 × 95.2 = 476 mg, or 0.476 g. Add MgCl2 after pH adjustment to avoid confusing the electrode response.
2. Evaluate the colleague's Tris suggestion and decide whether 50 mM HEPES has enough buffer capacity at pH 7.40.
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Tris is a poor choice here. At pH 7.40, Tris (pKa 8.06) is 0.66 pH units below its pKa. The ratio [A−]/[HA] = 10^(7.40−8.06) = 10^−0.66 = 0.219, so only about 18% of Tris is deprotonated and buffer capacity is well below its maximum. Tris also has a strongly temperature-dependent pKa and can interfere with some enzyme assays. HEPES is chemically suitable and is not phosphate; its chloride contribution is negligible if the pH is adjusted with NaOH rather than HCl.
For 50 mM HEPES at pH 7.40, the deprotonated fraction f = 1/(1 + 10^(pKa−pH)) = 1/(1 + 10^0.15) = 0.414. Buffer capacity β = 2.303 × C × f × (1−f) = 2.303 × 0.050 × 0.414 × 0.586 = 0.0279 M per pH unit, about 28 mM/pH. That is close to the theoretical maximum of 28.8 mM/pH, so 50 mM HEPES is adequate for the planned acid challenge.
3. Calculate the pH after 2.5 mL of 0.10 M HCl is added to the 500 mL buffer. Interpret the result for the acid-stress step.
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Initial moles: A− = 0.01035 mol and HA = 0.01465 mol. HCl added = 0.0025 L × 0.10 M = 0.00025 mol H+. This converts A− to HA: new A− = 0.01035 − 0.00025 = 0.01010 mol; new HA = 0.01465 + 0.00025 = 0.01490 mol. The ratio is 0.01010 / 0.01490 = 0.678. New pH = 7.55 + log(0.678) = 7.55 − 0.169 = 7.38. The total volume rises to 502.5 mL, but both species are diluted equally, so the ratio and hence pH are unaffected.
The pH falls by only about 0.02 units, so the buffer absorbs the acid challenge well. This assumes the enzyme is stable at pH 7.38 and that the added HCl does not introduce inhibitory chloride: 0.00025 mol in 0.5025 L gives about 0.5 mM chloride, far below the 50 mM limit. If the stress step were repeated many times, capacity would eventually be exhausted.