How this instrument works
pH was invented specifically because hydrogen ion concentrations in everyday solutions span an enormous range — from about 1 mol/L in strong acid down to 10^-14 mol/L in strong base — which is unwieldy to write and compare directly. Taking -log10 of the concentration compresses that whole range into a tidy 0-to-14 scale. This instrument reverses that compression: given a pH value, it computes [H+] = 10^(-pH), the actual molar concentration of hydrogen ions the pH number represents.
Because the relationship is logarithmic, each single step of pH corresponds to a tenfold change in [H+], not a proportional one. A solution at pH 3 doesn't have '4 units more acid' than one at pH 7 — it has a hydrogen ion concentration 10,000 times greater, since the difference of 4 pH units means 10^4. This is the detail that trips people up most often when reasoning about pH informally, and it's exactly what converting back to [H+] makes concrete.
Converting pH to [H+] matters whenever a downstream calculation needs the actual concentration rather than the log-scale number — reaction rate expressions, equilibrium constant calculations, or buffer capacity work all use [H+] directly, not pH. Reporting pH is convenient for communicating acidity at a glance; reporting or computing with [H+] is what the underlying chemistry actually operates on.
- Enter the solution's pH value into the pH field — any real number, including negative values for extremely concentrated strong acids.
- Read Hydrogen ion concentration [H+] (mol/L) directly beneath it — the instrument computes 10 raised to the negative of your pH value.
- Watch the exponent, not just the digits: [H+] is reported in scientific notation because the concentrations involved routinely span many orders of magnitude.
- Remember each single pH unit is a 10x change in [H+] — moving pH from 5 to 4 multiplies [H+] by 10, not by a small increment.
Worked example — pH 3, a moderately strong acid
Enter 3 into pH. [H+] reads 0.001 mol/L, since 10^(-3) = 0.001. That's a concentration of one thousandth of a mole of hydrogen ions per liter of solution — roughly the acidity of a dilute solution of a strong acid like hydrochloric acid.
Compare that to neutral water at pH 7, where [H+] = 10^(-7) = 0.0000001 mol/L. The pH 3 solution's hydrogen ion concentration is 10^4, or 10,000 times, larger than neutral water's — a difference the two nearby-looking numbers '3' and '7' completely disguise until you convert both to actual concentrations.
Questions
Why is [H+] reported in scientific notation instead of a plain decimal?
Because hydrogen ion concentrations routinely span more than a dozen orders of magnitude — from about 1 mol/L in concentrated strong acid down to roughly 10^-14 mol/L in concentrated strong base. Writing out 0.00000000000001 by hand invites miscounted zeros, so scientific notation (1 x 10^-14) is the standard, unambiguous way chemists report it.
Does a pH of 4 mean twice the acid of a pH of 8?
No — it means 10,000 times the hydrogen ion concentration, not twice. Each single pH unit represents a tenfold change in [H+] because the scale is logarithmic (base 10). The gap between pH 4 and pH 8 is 4 units, so [H+] differs by 10^4 = 10,000, one of the most common misreadings of the pH scale.
Can pH be negative, and what does that mean for [H+]?
Yes, in sufficiently concentrated strong acid, pH can go below zero — for example, pH -1 corresponds to [H+] = 10^1 = 10 mol/L, an extremely concentrated acid solution. The formula [H+] = 10^(-pH) still applies without modification; a negative pH simply means the exponent -pH becomes positive, pushing [H+] above 1 mol/L.
What's the [H+] of pure neutral water?
1 x 10^-7 mol/L, at pH 7 and 25 degrees C. That figure comes directly from water's own autoionization equilibrium (2 H2O ⇌ H3O+ + OH-), where the hydrogen and hydroxide ion concentrations are equal at exactly 10^-7 mol/L each — which is also why pH 7 is defined as the neutral point on the scale.
How is this different from an ionic-strength calculation?
Ionic strength accounts for every dissolved ion in a solution, weighted by the square of its charge, to describe the solution's overall electrolyte environment. This instrument converts only the pH value into the concentration of one specific ion, H+. They answer different questions: this one asks 'how much H+ is actually present,' ionic strength asks 'how does the whole ionic mixture affect activity and equilibrium behavior.'