Water and the pH scale · Chemistry Class 11–12 | StemPy Lab
Course 6.2·Lesson 2 of 3
Water and the pH scale
Water ionises very slightly into H3O+ and OH−. The product of their concentrations, Kw
about 25 min1 simulation2 practice questions1 Python program5 questions to check yourself
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Water ionises too
Even pure water conducts electricity a tiny bit. So it must hold a few ions. One water molecule gives a proton to another:
H2O(l)+H2O(l)⇌H3O+(aq)+OH−(aq)
This is called the self-ionisation of water. Its equilibrium lies very far to the left. The concentration of water hardly changes, so it is folded into the constant. We get the ionic product of water:
Kw=[H3O+][OH−]=1.0×10−14at298K
In pure water the two ions come in equal numbers, so each is 1.0×10−7mol/L.
Kw depends on temperature. Ionisation takes in heat, so warmer water ionises a little more and Kw grows.
Acidic, basic and neutral
Kw holds in every watery solution, not just pure water. Add an acid and [H3O+] rises, so [OH−] must fall to keep the product fixed.
Acidic:[H3O+]>[OH−].
Neutral:[H3O+]=[OH−].
Basic:[H3O+]<[OH−].
The pH scale
Numbers like 10−7 and 10−12 are hard to compare. In 1909, Soren Sorensen suggested a neater way. He defined the pH:
pH=−log10[H3O+]
with the concentration in mol/L. The minus sign makes most values positive. Pure water at 298K has pH=7.
Below 7: acidic. Above 7: basic.
Each step of one unit is a tenfold change. A solution of pH 3 has ten times as many hydronium ions as one of pH 4.
A lower pH means more hydronium ions.
A horizontal pH scale from 0 to 14, red at the acid end, green near 7 and blue at the basic end. Markers show gastric juice near 1.2, lemon juice near 2.2, vinegar near 2.8, milk near 6.8, pure water at 7.0, human blood at 7.4, milk of magnesia near 10 and lime water near 10.5. Below the scale: acidic to the left of 7, neutral at 7, basic to the right.
In the same way, pOH=−log10[OH−] and pKw=−log10Kw=14. Take logarithms of the Kw equation:
pH+pOH=14at298K
Strong acids and bases
A strong acid ionises fully. So its hydronium concentration equals the acid concentration, for an acid with one proton to give.
Worked example. Find the pH of 0.010mol/L HCl.
[H3O+]=0.010=1.0×10−2mol/L.
pH=−log10(1.0×10−2)=2.00.
A strong base gives its hydroxide fully. Find the pOH first, then the pH.
Worked example. Find the pH of 0.0010mol/L NaOH.
[OH−]=1.0×10−3mol/L, so pOH=3.00.
pH=14−3.00=11.00.
Watch the formula. Ba(OH)2 gives two hydroxide ions for each unit. So its [OH−] is twice its concentration.
Practise with new numbers
When the acid is very dilute
The rule [H3O+]=C assumes the acid gives far more hydronium ions than water does. Water itself gives 10−7mol/L. So when an acid is near or below that, the water's ions count too. A very dilute acid can never have a pH above 7. The paid course of this chapter works such cases out in full.
Try it in Python
The program finds the pH and pOH of four strong solutions, and checks that each pair adds up to 14.
Common mistakes
Forgetting the minus sign. pH is minus the logarithm. A logarithm of a small number is negative.
Thinking pH 4 is half as acidic as pH 2. It is a hundred times less acidic. Each unit is a factor of ten.
Using the base concentration as the pH. For a base, find the pOH first.
Missing the second hydroxide.Ba(OH)2 and Ca(OH)2 give two OH− each.
Saying neutral means pH 7 always. Neutral means equal ion concentrations. Only at 298K is that pH 7.
Remember these
Kw=[H3O+][OH−]=1.0×10−14 at 298K, and it rises with temperature.
pH=−log10[H3O+]. Lower pH, more acidic.
pH+pOH=14 at 298K.
Strong acid: [H3O+]=C. Strong base: [OH−]=C times the number of OH−.
One pH unit is a tenfold change.
Check yourself
Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.
What is [OH−] in a solution where [H3O+]=1.0×10−3mol/L?
How many times more hydronium ions does a solution of pH 2 hold than one of pH 5?
What is the pH of a solution with pOH=4.5?
Pure water is warmed. Does its pH rise or fall? Is it still neutral?
Why can a very dilute acid never have a pH above 7?
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. The pH, minus the logarithm of the hydronium concentration, turns these tiny numbers into a scale from about 0 to 14. For a strong acid or base the concentration gives the pH at once.