50 cm cubed of 0.10 mol per dm cubed hydrochloric acid is diluted with water to a total volume of 500 cm cubed. What is the pH of the diluted solution?

1. Diluting a solution adds water but does not change the number of moles of acid present. 2. First find those moles. Fifty cubic centimetres is 0.050 cubic decimetres. 3. Moles equals concentration multiplied by volume, so it is 0.10 multiplied by 0.050, which is 0.0050 moles. 4. The new volume is 500 cubic centimetres, which is 0.500 cubic decimetres. 5. The new concentration is 0.0050 moles divided by 0.500 cubic decimetres, which is 0.010 moles per cubic decimetre. 6. Hydrochloric acid is a strong acid that releases one hydrogen ion per molecule, so the hydronium concentration is also 0.010 moles per cubic decimetre. 7. The pH is the negative logarithm of that concentration, and 0.010 is ten to the power minus two, so the pH is 2. 8. A pH of 1 is the trap for using the original concentration before dilution, a pH of 3 dilutes by a hundred times instead of ten, and a pH of 4 dilutes twice over. _Source: Siyavula Physical Sciences Grade 12 (Everything Science, CC BY 4.0), Chapter 9: Acids and bases_