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I am helping my friend's 16 year old prepare for her GCSE chemistry exam. This question was on an AQA GCSE Chemistry past paper but I do not know the year and could not find a markscheme for it on the AQA site. They publish markschemes for the previous three years there. How does she do this question and how can I explain what is happening please?

When hydrochloric acid dissolves in water H+ions and Cl- ions are produced.

A solution of hydrochloric acid with pH 4.5 has a concentration of H+ ions of $\pu{3.16E-5}$ mol/dm³

What is the concentration of H+ ions in a solution of hydrochloric acid with pH 2.5?

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    $\begingroup$ Start from : $\pu{10^{-4.5} = 3.16 10^{-5}}$. Use the same approach to get $\pu{[H^+] = 10^{-2.5}}$. $\endgroup$
    – Maurice
    Apr 1 at 18:21
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    $\begingroup$ You have it backwards, pH depends on H+ concentration, not vice versa. $\endgroup$
    – Poutnik
    Apr 1 at 18:30
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    $\begingroup$ The question has it backwards! $\endgroup$
    – jimchmst
    Apr 1 at 19:34
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    $\begingroup$ $10^{-2.5}$ = 0.00316 so concentation of H+ ions is 3.16 x $10^{-3}$ mol/dm³to 2 d..p If I got that right the H+ ion concentration that gives a pH of 2.5 is 100 times larger than that which gives a pH Thanks everybody for the help.Is the pattern that whenever the concentration is multiplied by ten, the pH drops by 1? The 16 year old would be more likely to understand that, her maths is not great. $\endgroup$ Apr 1 at 20:50
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    $\begingroup$ I just googled is the pH scale logarithmic and it confirmed it it. $\endgroup$ Apr 1 at 20:52

2 Answers 2

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What is the concentration of H+ ions in a solution of hydrochloric acid with pH 2.5?

Using the definition of pH $= -\log(\frac{[\ce{H+}]}{\pu{1 mol L-1}})$, you can easily calculate this as long as you have (are allowed to have) a scientific calculator.

A solution of hydrochloric acid with pH 4.5 has a concentration of H+ ions of 3.16×10−5 mol/dm³

This additional information allows you to do the math in your head, and shows you the units they want. As discussed in the comments, a change in pH by one unit corresponds to a change in H+ ions by a factor 10. Lower pH means higher H+ ion concentration. So you multiply the given concentration by 100, or change the exponent from -5 to -3.

How does the concentration of H+ ions in HCl change as the pH changes?

Technically, once you have the HCl in water (hydrochloric acid rather than hydrogen chloride gas), the hydrochloric acid dissociates:

$$\ce{HCl(g) -> HCl(aq) -> Cl-(aq) + H+(aq)}$$

So the H+ ions are in the water, not really in HCl. However, we still label the bottle as hydrochloric acid and might use the chemical formula HCl(aq), knowing full well it's a strong acid and has long since dissociated.

For students past the intro chemistry college stage

The pH is defined as the negative base-10 logarithm of the hydrogen ion activity. At low concentrations and low ionic strength, the concentration divided by 1 mol/L is a good estimate.

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This question changes a simple definition of: [pH = the negative logarithm of the hydrogen ion activity in M/L], into a puzzle or possibly an IQ test.

Knowing nothing about pH the relationship between 4.5 and 3.16x10^-5 might be confusing but after some pondering you will think the -5 is an exponent so maybe 4.5 is a negative exponent and can be written +.5-5 and 0.5 is the square root of 10 = ~3.16 so a pH of 4.5 means a hydrogen ion activity of 3.16 x10^-5M. I REMEMBER now; pH is the negative logarithm of the hydrogen ion activity so the second part is simple! A pH of 2.5 means a hydrogen ion activity of 3.16 x 10^-3. The IQ test part is that someone much smarter than the rest of us could figure this out knowing no chemistry. The question really is: " If 4.5 = 3.16x10^-5 what is 2.5 equal to?"; nothing to do with chemistry.

Lets discuss Chemistry. HCl is a gas consisting of HCl molecules it is covalent not ionic. HCl dissolves in water and reacts to give hydrated hydronium ions, H3O+, and hydrated chloride ions, Cl-. These are commonly referred to as hydrogen ions and chloride ions. HCl gas dissolved in water has been given the name Hydrochloric Acid because at reasonable concentrations at least, say below one[1] Molar, there are very few HCl molecules remaining. HCl and similar acids such as nitric, sulfuric, perchloric and some others are strong acids and the concentration of hydrogen ion in reasonably dilute solutions can be determined by formulation or by titration. Formulation or titration measure total acid. For strong acids this is the hydrogen ion concentration; for weak acids such as acetic acid this is the sum of molecular acid and hydrogen ion. Since the molecular acid and the hydrogen ions react differently in some reactions it is useful to measure both. The hydrogen ion activity is measured electrochemically with the hydrogen electrode, the quinhydrone electrode, or most commonly with the glass electrode. The pH scale was devised to simplify the exponents in the huge range of hydrogen activities in water and also because it fits in naturally with the logarithmic nature of the Nernst Equation.

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