INGENIA
Index/Physical chemistry/CHM-18

CHM-18

pH = −log10 a(H+)

pH = −log10 aH. Pedagogue: activity ≈ molarity in dilute water.

Reading speed
Acid–baseSørensen 1909

Governing equation

pH=−log⁡10a(H+)\mathrm{pH}=-\log_{10}a(\mathrm{H}^+)

a(H+)∈[1×10−14,1]a(\mathrm{H}^+) \in \left[1\times 10^{-14}, 1\right]

where

a(\mathrm{H}^+)
Proton activity (—)
pH
pH (—)

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-18 · gauge
00:0 / 00:08
①

Governing law — red

pH=−log⁡10a(H+)\mathrm{pH}=-\log_{10}a(\mathrm{H}^+)

a(H+)∈[1×10−14,1]a(\mathrm{H}^+) \in \left[1\times 10^{-14}, 1\right]

a(H+)=1×10−14a(\mathrm{H}^+) = 1\times 10^{-14}pH=14pH = 14

②

Domain of the variable — blue

a(H+)min⁡=1×10−14,a(H+)max⁡=1a(\mathrm{H}^+)_{\min} = 1\times 10^{-14},\quad a(\mathrm{H}^+)_{\max} = 1

a(H+)∈[1×10−14,1]a(\mathrm{H}^+) \in \left[1\times 10^{-14}, 1\right]

a(H+)=1×10−14a(\mathrm{H}^+) = 1\times 10^{-14}a(H+)=1×10−14a(\mathrm{H}^+) = 1\times 10^{-14}

③

Response curve — green

pH=−log⁡10a(H+)\mathrm{pH}=-\log_{10}a(\mathrm{H}^+)

a(H+)∈[1×10−14,1]a(\mathrm{H}^+) \in \left[1\times 10^{-14}, 1\right]

a(H+)=1×10−14a(\mathrm{H}^+) = 1\times 10^{-14}pH=14pH = 14

④

Rate of change — amber

dpHda(H+)\frac{\mathrm{d}pH}{\mathrm{d}a(\mathrm{H}^+)}

a(H+)∈[1×10−14,1]a(\mathrm{H}^+) \in \left[1\times 10^{-14}, 1\right]

a(H+)=0.006a(\mathrm{H}^+) = 0.006pH′=−961.9pH^{\prime} = -961.9

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-18 — pH = −log10 a(H+)) is the form associated with Sørensen 1909. Working symbols: a(H+)a(\mathrm{H}^+) →\rightarrow pHpH. Defined on the activity of the proton. At 25 °C, pH + pOH = 14 for pure water.

Purpose

Purpose: compute pHpH from a(H+)a(\mathrm{H}^+) in Physical chemistry via pH=−log⁡10a(H+)\mathrm{pH}=-\log_{10}a(\mathrm{H}^+) pH = −log10 aH. Pedagogue: activity ≈ molarity in dilute water. 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 a(H+)=1.000e−7 —a(\mathrm{H}^+) = 1.000e-7\,\mathrm{—}, the governing relation pH=−log⁡10a(H+)\mathrm{pH}=-\log_{10}a(\mathrm{H}^+) yields pH=7.000 —pH = 7.000\,\mathrm{—}. Dilute aqueous, activity coefficient ≈ 1. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • pH pH7.000 —
Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

CHM-18 · gauge
00:0 / 00:08

Narration of this film

Dilute aqueous, activity coefficient ≈ 1.

Defined on the activity of the proton. At 25 °C, pH + pOH = 14 for pure water.

Reading speed

Watch on YouTube