The pH scale runs from 0 to 14: below 7 is acidic, 7 is neutral and above 7 is basic. Each one-unit step is a tenfold change in hydrogen ion concentration, so pH 3 has 100 times the hydrogen ions of pH 5. Dilution lowers concentration while the amount of solute stays the same: C1V1 = C2V2.
What does the pH scale measure?
pH expresses the hydrogen ion (hydronium) concentration of a water-based solution: [H+] = 10 to the power of minus pH, in moles per liter. At 25 °C, pH 7 is neutral; below 7 is acidic and above 7 is basic (USGS). Each unit is a tenfold change, so pH 4 has 1,000 times the hydrogen ions of pH 7.
Everyday pH values (approximate)
Stomach acid: about 1.5 to 3.5
Lemon juice: about 2
White vinegar: about 2.5 to 3
Acid rain: usually 4.2 to 4.4 (EPA)
Normal rain: about 5.6 (USGS, EPA)
Pure water: 7 (USGS)
Human arterial blood: 7.38 to 7.42 (MedlinePlus)
Ocean surface water: about 8.1 on average (NOAA)
Baking soda in water: about 8.3
Household ammonia: about 11 to 12
Household bleach: about 12 to 13
How do you calculate a dilution?
Concentration is solute divided by total solution volume. When you dilute, the solute amount stays the same: C1 × V1 = C2 × V2. Example: 2 L at 30 g/L contains 60 g; adding 4 L of water gives 6 L, so the new concentration is 60 g ÷ 6 L = 10 g/L.
Questions and answers
Why is each pH unit a tenfold change? pH is a logarithmic scale: pH equals the negative power of ten of the hydrogen ion concentration. USGS puts it this way: water with a pH of five is ten times more acidic than water with a pH of six. Two units apart is 100 times, three units is 1,000 times.
Does a lower pH mean more hydrogen ions? Yes. The scale is inverse: a lower pH means a higher hydrogen ion (hydronium) concentration and a more acidic solution. A higher pH means fewer hydrogen ions and more hydroxide ions relative to them.
How do you compare the acidity of two pH values? Subtract the pH values and raise 10 to that difference. pH 2 versus pH 5 is a 3-unit difference, so the pH 2 solution has 10 to the third, or 1,000, times the hydrogen ion concentration. Do not just subtract or divide the pH numbers.
What is the dilution formula? C1 × V1 = C2 × V2. The amount of solute does not change when you add solvent, so the starting concentration times the starting volume equals the final concentration times the final volume. Tripling the volume makes the concentration one-third as large.
What is normal blood pH? MedlinePlus lists a normal arterial blood pH of 7.38 to 7.42, so blood is very slightly basic. Small changes matter because each pH unit is a tenfold change in hydrogen ion concentration.
Is concentration based on the solvent or the whole solution? The whole solution. Concentration is the amount of solute divided by the total volume of solution. For example, 15 g dissolved to make 3 L of solution is 5 g/L.
Sample questions with explanations
Solution A has a pH of 2. Solution B has a pH of 5. How does the hydrogen ion concentration of Solution A compare with that of Solution B? Answer: B. 1,000 times greater. The pH values differ by 3 units, and each unit is a tenfold change, so the difference is 10³ = 1,000. Solution A has the lower pH, so it has the higher hydrogen ion concentration.
A nurse dilutes 100 mL of a solution that contains 8 g/L of a solute by adding water until the total volume is 400 mL. What is the new concentration? Answer: A. 2 g/L. The solute is conserved: C1V1 = C2V2, so 8 g/L × 100 mL = C2 × 400 mL and C2 = 2 g/L. The volume became four times larger, so the concentration became one-fourth as large.
Which pH describes a basic solution? Answer: D. 8.2. A pH above 7 is basic (alkaline). 7.0 is neutral, and 3.1 and 6.8 are below 7, so they are acidic.
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