Mixing pH

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The pH of a solution is defined using logarithms as

$$
pH = -\log_{10}[H^+],
$$
where $[H^+]$ is the concentration of $H^+$ ions in mol/l of the solution.
 

• Given that the pH of a beaker of pure water is 7, work out how many $H^+$ ions there are in 1 litre of the water.
• A strong acid has a pH of 2. If one litre of this acid is diluted with 1 litre of water, what is the pH of the resulting solution?
• A strong acid has a pH of 1.3. If I have 100ml of this acid, how much water needs to be added to create a solution of pH 2?
• 400ml of an acid of pH 3 is added to 300ml of an acid of pH 4. What is the resulting pH?

Make up some of your own mixing pH questions. For example:

• If I start with $1$ litre of acid of pH $1$, what happens to the pH each time I add $100$ml of water? What sort of curve results?
• Is it the case that when mixing two solutions, the resulting pH is always between the pH of the two initial solutions?