INGENIA
Index/Physical chemistry/CHM-19

CHM-19

Buffer capacity snapshot

β ≈ 2.303 C Ka [H] / ([H] + Ka)². How much acid a buffer soaks.

Reading speed
Acid–baseVan Slyke

Governing equation

β=2.303 CKa[H+]([H+]+Ka)2\beta=2.303\,C\dfrac{K_a[H^+]}{([H^+]+K_a)^2}

[H+]∈[1×10−12,0.1][H^+] \in \left[1\times 10^{-12}, 0.1\right]

where

C
Total buffer (mol/L)
K_a
Ka (—)
[H^+]
Proton concentration (mol/L)
\beta
Buffer capacity (mol/L)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

CHM-19 · gauge
00:0 / 00:08
①

Governing law — red

β=2.303 CKa[H+]([H+]+Ka)2\beta=2.303\,C\dfrac{K_a[H^+]}{([H^+]+K_a)^2}

[H+]∈[1×10−12,0.1][H^+] \in \left[1\times 10^{-12}, 0.1\right]

[H+]=1×10−12[H^+] = 1\times 10^{-12}β=1.32×10−8\beta = 1.32\times 10^{-8}

②

Domain of the variable — blue

[H+]min⁡=1×10−12,[H+]max⁡=0.1[H^+]_{\min} = 1\times 10^{-12},\quad [H^+]_{\max} = 0.1

[H+]∈[1×10−12,0.1][H^+] \in \left[1\times 10^{-12}, 0.1\right]

[H+]=1×10−12[H^+] = 1\times 10^{-12}[H+]=1×10−12[H^+] = 1\times 10^{-12}

③

Response curve — green

β=2.303 CKa[H+]([H+]+Ka)2\beta=2.303\,C\dfrac{K_a[H^+]}{([H^+]+K_a)^2}

[H+]∈[1×10−12,0.1][H^+] \in \left[1\times 10^{-12}, 0.1\right]

[H+]=1×10−12[H^+] = 1\times 10^{-12}β=1.32×10−8\beta = 1.32\times 10^{-8}

④

Rate of change — amber

dβd[H+]\frac{\mathrm{d}\beta}{\mathrm{d}[H^+]}

[H+]∈[1×10−12,0.1][H^+] \in \left[1\times 10^{-12}, 0.1\right]

[H+]=6.29×10−4[H^+] = 6.29\times 10^{-4}β′=2.478\beta^{\prime} = 2.478

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-19 — Buffer capacity snapshot) is the form associated with Van Slyke. Working symbols: CC, KaK_a, [H+][H^+] →\rightarrow β\beta. Van Slyke defined β = dCb / d pH. Maximum at pH = pKa for a monoprotic pair.

Purpose

Purpose: compute β\beta from CC, KaK_a, [H+][H^+] in Physical chemistry via β=2.303 CKa[H+]([H+]+Ka)2\beta=2.303\,C\dfrac{K_a[H^+]}{([H^+]+K_a)^2} β ≈ 2.303 C Ka [H] / ([H] + Ka)². How much acid a buffer soaks. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given C=0.100 mol/LC = 0.100\,\mathrm{mol/L}, Ka=1.750e−5 —K_a = 1.750e-5\,\mathrm{—}, [H+]=1.000e−5 mol/L[H^+] = 1.000e-5\,\mathrm{mol/L}, the governing relation β=2.303 CKa[H+]([H+]+Ka)2\beta=2.303\,C\dfrac{K_a[H^+]}{([H^+]+K_a)^2} yields β=0.05329 mol/L\beta = 0.05329\,\mathrm{mol/L}. Monoprotic, dilute, water terms dropped. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Buffer capacity \beta0.05329 mol/L
Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

CHM-19 · gauge
00:0 / 00:08

Narration of this film

Monoprotic, dilute, water terms dropped.

Van Slyke defined β = dCb / d pH. Maximum at pH = pKa for a monoprotic pair.

Reading speed

Watch on YouTube