# How can a dilute acid dissociate more than a concentrated one? (Ostwald dilution law)

According to Ostwald's dilution law, the degree of dissociation of an electrolyte is inversely related to the concentration of it.

$$\alpha = \sqrt{\frac{K_a}{C}}$$

This means that a dilute acid can dissociate more than a concentrated one. How is it possible? Please explain the physical meaning of this.

• Come to think of it, this is very natural and by no means limited to chemistry. When there are fewer competitors (whatever is their nature, molecules seeking to dissociate or people standing in a line for a new iPhone), more of them would get what they want. – Ivan Neretin Jan 28 '17 at 6:33

A dilute acid has more solvent molecules to interact with than a concentrated acid, and thereby has more frequent collisions with the solvent. You can think of the dilute acid as "drowning" in the solvent.

A concentrated acid, by contrast, interacts more with other acid molecules, and therefore less with the solvent which dissolves it.

A concentrated acid will typically have more total dissolved molecules than a diluted acid simply because there are more of them, but it will have less as a fraction of total number of acid molecules; i.e. a weaker affinity for dissociation.

In short, $\alpha$ describes affinity for dissociation, not total dissociation. "Better", not "more".

Note that a higher $K_a$ corresponds to a stronger acid, so it makes sense that stronger acids will have a higher affinity for dissociation.

• Also the dissociation of an acid corresponds to its strength, so isn't it a bit confusing that a dilute acid is stronger than a concentrated one. – jyoti proy Jan 28 '17 at 5:58
• Dilution doesn't have any bearing on whether an acid is strong/weak. You can dilute a strong acid, and you can dilute a weak acid. Strong/weak is a property of the chemical substance; dilution is simply related to how much of it you put in the solvent. – khaverim Jan 28 '17 at 6:02
• I want to say about the dilute & concentrated forms of the same acid. – jyoti proy Jan 28 '17 at 6:12
• 1M HCl will dissolve more easily than 2M HCl because the HCl in the first solution has more collisions with solvent molecules, on average. Hence I compared it to "drowning" in the solvent. – khaverim Jan 28 '17 at 6:29