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How many times more acidic: pH 6.5 and 7.8

Short answer

Sample P (pH 6.5) is about 20 times more acidic than sample Q (pH 7.8) because hydrogen ion concentration ratio is 10^(1.3) ≈ 20.

If there are two samples P and Q from the different treatment plants having the pH values of 6.5 and 7.8, calculate how many times the sample is acidic than sample B [sic].

Acidity is measured by the hydrogen-ion concentration, [H+]=10−pH[H^+] = 10^{-pH}. The pH scale is logarithmic, so each unit of pH changes [H+][H^+] ten times. (The question compares the two samples, P with pH 6.5 and Q with pH 7.8; "sample B" is read as sample Q.)

[H+]P=10−6.5=3.162×10−7 mol/l[H+]Q=10−7.8=1.585×10−8 mol/l\begin{aligned} [H^+]_P &= 10^{-6.5} = 3.162\times10^{-7}\ \text{mol/l} \\ [H^+]_Q &= 10^{-7.8} = 1.585\times10^{-8}\ \text{mol/l} \end{aligned} [H+]P[H+]Q=107.8−6.5=101.3=19.95\frac{[H^+]_P}{[H^+]_Q} = 10^{7.8-6.5} = 10^{1.3} = 19.95

Answer: Sample P (pH 6.5) is about 20 times more acidic than sample Q (pH 7.8).

✓ Answer checked by Claude Opus 5.5 (high effort)

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