Hard and soft water

Soft water lathers with soap almost immediately, producing a stable foam with very little soap used up. Hard water does the opposite: the first portions of soap added react with dissolved calcium and magnesium ions to form an insoluble, curdy scum, and only once every last calcium/magnesium ion has been mopped up this way does any true lather begin to form. This is why hard water "wastes" soap — a real, measurable cost in a household or laundry. The cause is always the same two metals, calcium and magnesium, but the anion (negative ion) they are paired with decides how stubborn the hardness is.

• Temporary hardness comes from dissolved bicarbonates, $Ca(HCO_3)_2$ and $Mg(HCO_3)_2$. These are unstable to heat, so a simple boil decomposes them, precipitating the metal out as an insoluble carbonate and driving off carbon dioxide gas — this is exactly the "fur" or scale you see forming inside a kettle.
• Permanent hardness comes from dissolved chlorides and sulphates, such as $CaCl_2$, $MgCl_2$, $CaSO_4$ and $MgSO_4$. These salts are thermally stable, so boiling leaves them fully dissolved and the hardness unchanged.

The decomposition that removes temporary hardness on boiling is:

where: $Ca(HCO_3)_2$ is dissolved calcium bicarbonate, $\Delta$ over the arrow marks heating, $CaCO_3\downarrow$ is the insoluble calcium carbonate precipitate that settles out (kettle fur), and $CO_2\uparrow$ is the gas released. The identical reaction happens for magnesium bicarbonate, giving $MgCO_3$ instead. Only one chemical treatment removes both kinds of hardness at once: adding washing soda, $Na_2CO_3\cdot10H_2O$. Its carbonate ion precipitates calcium or magnesium out of solution regardless of which anion they started attached to:

where: the left-hand salt is any dissolved calcium/magnesium chloride or sulphate causing permanent hardness, $Na_2CO_3$ supplies the precipitating carbonate ion, and the right-hand insoluble carbonate removes the hardness-causing metal from solution, leaving behind only soluble sodium salts that do not react with soap.

There is no numerical formula to derive here — the chapter is deliberately qualitative — but the reasoning behind both removal methods rewards careful thought, and understanding it is worth more marks than memorising the equations alone. The question to answer precisely: why does heat destroy bicarbonate hardness but leave chloride/sulphate hardness completely untouched, while washing soda destroys both?

Step 1. Start from what soap actually reacts with. Ordinary soap is a sodium or potassium salt of a fatty acid. When it meets calcium or magnesium ions in solution, it swaps its sodium/potassium for calcium/magnesium and forms an insoluble calcium/magnesium "soap" — the scum. This reaction happens with calcium or magnesium ions no matter which anion originally carried them into solution; the metal ion is the only thing soap cares about.

Step 2. Removing hardness therefore means removing the calcium/magnesium ions from solution before soap ever meets them — either by making them precipitate as an insoluble solid, or by locking them away so they cannot react. Both prescribed methods work by precipitation.

Step 3. Boiling only precipitates bicarbonates because bicarbonate ions ($HCO_3^-$) are thermally unstable: heat drives them to decompose into carbonate, water and carbon dioxide, and calcium/magnesium carbonate happens to be insoluble, so it drops out of solution. Chloride and sulphate ions, by contrast, are thermally stable — no amount of boiling breaks a $Cl^-$ or $SO_4^{2-}$ ion apart — so the calcium/magnesium stays dissolved and able to react with soap.

Step 4. Washing soda works on both because it does not rely on heat at all — it supplies a fresh, ready-made carbonate ion ($CO_3^{2-}$) directly. That carbonate ion combines with calcium or magnesium ions wherever they came from (bicarbonate, chloride or sulphate) to form the same insoluble carbonate precipitate. Since the mechanism does not depend on what anion the metal started attached to, it removes both types of hardness in one step. This is exactly why washing soda, not boiling, is the general-purpose softening method.

Question: A sample of well water forms scum with soap. When boiled, the scum problem disappears entirely and the water lathers normally afterwards. A second sample from a different well still forms scum even after prolonged boiling. (a) Identify the type of hardness in each sample. (b) Write the equation for what happens to sample one on boiling, taking calcium bicarbonate as the hardness-causing salt. (c) Suggest how to soften sample two, writing a balanced equation, taking magnesium sulphate as the hardness-causing salt.

Step 1. Sample one is fully cured by boiling alone, so its hardness must be temporary hardness, caused by dissolved calcium/magnesium bicarbonate. Sample two survives prolonged boiling unchanged, so it must be permanent hardness, caused by dissolved calcium/magnesium chloride and/or sulphate — bicarbonates would already have decomposed under that much heating.

Step 2. For sample one, heating decomposes the calcium bicarbonate into insoluble calcium carbonate (which settles out as kettle fur), water and carbon dioxide gas:

With the calcium removed from solution, no scum-forming reaction with soap remains possible, so the water lathers normally.

Step 3. Sample two needs a chemical method, since boiling cannot touch chlorides or sulphates. Adding washing soda ($Na_2CO_3\cdot10H_2O$) supplies carbonate ions that precipitate the magnesium out as insoluble magnesium carbonate:

Sample one: temporary hardness, cured by boiling via calcium carbonate precipitation. Sample two: permanent hardness, cured by washing soda via magnesium carbonate precipitation, leaving only soluble sodium sulphate behind.

• Believing boiling cures all hardness — it only decomposes bicarbonates; chlorides and sulphates are heat-stable and stay dissolved no matter how long you boil.
• Thinking washing soda only treats permanent hardness — it precipitates calcium/magnesium ions regardless of their original anion, so it removes temporary hardness too.
• Assuming hard water is unhealthy — it is generally safe, even beneficial, to drink because of the dissolved calcium and magnesium; its problems are practical (soap wastage, scum, boiler scale), not toxicity.
• Mixing up which anion causes which type — bicarbonate means temporary (boil it away); chloride or sulphate means permanent (needs washing soda), and the metal (calcium or magnesium) is irrelevant to that distinction.

Ask the tutor: want to practice writing the bicarbonate-decomposition or washing-soda equations for a different named calcium or magnesium salt?