Buffer Dilution Calculator
Calculate buffer dilution with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Formula
C1 x V1 = C2 x V2 | pH = pKa + log([A-]/[HA])
The dilution equation C1V1 = C2V2 calculates the volume of stock solution needed. The Henderson-Hasselbalch equation determines the conjugate base to acid ratio at a given pH. Buffer capacity measures resistance to pH change based on concentration and the relationship between pH and pKa.
Worked Examples
Example 1: Preparing PBS from 10X Stock
Problem: Prepare 500 mL of 1X PBS (phosphate-buffered saline) from a 10X stock solution.
Solution: Using C1V1 = C2V2:\n(10X)(V1) = (1X)(500 mL)\nV1 = (1 x 500) / 10 = 50 mL\nSolvent needed: 500 - 50 = 450 mL\nDilution factor: 10X / 1X = 10-fold\nPipette 50 mL of 10X PBS stock, add 450 mL of deionized water, mix thoroughly.
Result: Stock volume: 50 mL | Solvent: 450 mL | Dilution factor: 10x
Example 2: Tris-HCl Buffer at pH 7.5
Problem: Calculate the base-to-acid ratio for a 50 mM Tris-HCl buffer at pH 7.5 (pKa of Tris = 8.1).
Solution: Henderson-Hasselbalch: pH = pKa + log([A-]/[HA])\n7.5 = 8.1 + log([Tris]/[TrisH+])\nlog([Tris]/[TrisH+]) = -0.6\n[Tris]/[TrisH+] = 10^(-0.6) = 0.251\nPercent base form: 0.251 / (1 + 0.251) x 100 = 20.1%\nPercent acid form: 79.9%
Result: Base:Acid ratio = 0.251:1 | 20.1% Tris free base | 79.9% TrisH+ (acid form)
Frequently Asked Questions
How does the Henderson-Hasselbalch equation relate to buffer preparation?
The Henderson-Hasselbalch equation (pH = pKa + log([A-]/[HA])) is essential for buffer preparation because it tells you the ratio of conjugate base to weak acid needed to achieve your target pH. When pH equals the pKa, the ratio is 1:1, meaning equal amounts of acid and base forms. As pH increases above pKa, more conjugate base is needed. As pH decreases below pKa, more weak acid is needed. For practical buffer preparation, you calculate the required ratio, then determine the masses or volumes of each component. A buffer works best when pH is within one unit of its pKa, as this is where the buffer has the greatest capacity to resist pH changes.
What is buffer capacity and why does it matter?
Buffer capacity (beta) measures the amount of strong acid or base that must be added to change the pH of one liter of buffer by one unit. It depends on three factors: the total concentration of the buffer components, the pH relative to the pKa, and the specific acid-base equilibrium. Buffer capacity is maximal when pH equals pKa and decreases as pH moves away from pKa. Higher total buffer concentration means greater capacity. For biological work, buffer concentrations of 10-100 mM are typical, providing sufficient capacity without interfering with biochemical reactions. In industrial applications, higher concentrations of 100-500 mM may be used when stronger buffering is needed.
How does the dilution formula work?
The dilution formula is C1V1 = C2V2, where C is concentration and V is volume. If you have 100 mL of 2M HCl and need 0.5M, solve: 2 x 100 = 0.5 x V2, so V2 = 400 mL total volume. Add 300 mL of water to 100 mL of stock solution. Always add acid to water, never the reverse.
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