Animated Solution for Chemistry - Ionic Equilibrium: For the following Assertion and Reason, the correct option is Assertion (A) When Cu (II) and sulphide ions are mixed, they react together extremely quickly to give a solid. Reason (R) The equilibrium constant of ${\text{Cu}}^{2+}(\text{aq})+{\text{S}}^{2-}(\text{aq})\rightleftharpoons \text{CuS}(\text{s})$ is high because the solubility product is low.

Kinetics vs. Thermodynamics

When tackling Assertion-Reason questions in JEE, one of the most common traps set by examiners is mixing up two fundamentally different domains of chemistry: Kinetics and Thermodynamics. This problem is a perfect example of that trap. Let's break it down step by step.

The Speed of Ionic Reactions

The Assertion states that when ${\text{Cu}}^{2+}$ and ${\text{S}}^{2-}$ ions are mixed, they react extremely quickly to form a solid precipitate of $\text{CuS}$.

Is this true? Absolutely.

Imagine a beaker where these ions are swimming around. Because they are oppositely charged, they experience a massive electrostatic attraction towards each other. Unlike organic reactions where strong covalent bonds must be broken before new ones can form, ionic precipitation reactions require almost zero activation energy. The ions simply crash into each other and stick, forming a solid lattice almost instantaneously.

Therefore, the Assertion is a perfectly true statement based on the principles of Chemical Kinetics.

The Math of Equilibrium

Now, let's shift our focus to the Reason. It claims that the equilibrium constant ($K_{eq}$) for the reaction ${\text{Cu}}^{2+}(\text{aq})+{\text{S}}^{2-}(\text{aq})\rightleftharpoons \text{CuS}(\text{s})$ is high because its solubility product ($K_{sp}$) is low.

Let's write down the math. The equilibrium constant for this forward reaction is:

Notice that we do not include the solid $\text{CuS}$ in the numerator because the active mass of a pure solid is taken as unity.

Now, recall the definition of the solubility product, $K_{sp}$. It is defined for the reverse dissolution reaction:

If we compare the two equations, a beautiful relationship emerges:

Copper sulphide ($\text{CuS}$) is notoriously insoluble in water. This means its $K_{sp}$ is an incredibly tiny number. Because $K_{eq}$ is the reciprocal of $K_{sp}$, dividing one by a very tiny number gives a very massive number. Thus, $K_{eq}$ is indeed very high.

Therefore, the Reason is also a perfectly true statement based on the principles of Chemical Thermodynamics.

Why the Reason Fails

We have established that both statements are true. But does the Reason explain the Assertion?

This is where the trap snaps shut. The Assertion is talking about Rate (how fast the reaction happens). The Reason is talking about Equilibrium (how far the reaction goes before stopping).

A high equilibrium constant only tells us that the reaction is thermodynamically favorable and will proceed almost to completion. It tells us absolutely nothing about the speed. For example, the conversion of diamond into graphite has a high equilibrium constant, but it takes millions of years!

The real reason the reaction is fast is the lack of activation energy in ionic bonding, not the high equilibrium constant. Therefore, while both statements are true, the Reason is not the correct explanation for the Assertion.