Explanation:

When a metal carbonate is heated, it decomposes to form metal oxide and carbon dioxide.

The chemical equation is:

Metal Carbonate → Metal Oxide + Carbon Dioxide

Let the metal carbonate be MCO3, then the equation will be:

MCO3 → MO + CO2

Now, we are given that on heating, the metal carbonate is reduced to 60% of its original weight. This means that the metal oxide formed has a weight of 40% of the original weight of the metal carbonate.

Let the original weight of the metal carbonate be x grams, then the weight of the metal oxide formed will be 0.4x grams.

The equivalent weight of a metal is the atomic weight divided by the valency. Let the valency of the metal be n.

Then, the equivalent weight of the metal is:

Equivalent weight = Atomic weight / n

Let the atomic weight of the metal be A.

Now, we can use the law of conservation of mass to relate the weights of the metal carbonate and the metal oxide formed.

The total weight of the metal carbonate is x grams, and the total weight of the metal oxide and carbon dioxide formed is 0.4x + y grams, where y is the weight of carbon dioxide formed.

According to the law of conservation of mass:

Weight of metal carbonate = Weight of metal oxide + Weight of carbon dioxide

x = 0.4x + y

y = 0.6x

This means that the weight of carbon dioxide formed is 60% of the original weight of the metal carbonate.

Now, we can use the concept of equivalent weight to relate the weights of the metal carbonate and the metal oxide formed.

The equivalent weight of the metal carbonate is:

Equivalent weight of MCO3 = Atomic weight of M / (n × 2)

This is because the valency of carbonate ion is -2 and there are two carbonate ions in one molecule of metal carbonate.

Similarly, the equivalent weight of the metal oxide is:

Equivalent weight of MO = Atomic weight of M / n

Now, we can use the fact that the weight of metal oxide formed is 40% of the original weight of the metal carbonate to write:

(Equivalent weight of MCO3) × x = (Equivalent weight of MO) × 0.4x

(A / (n × 2)) × x = (A / n) × 0.4x

n = 5

Therefore, the valency of the metal is 5.

The equivalent weight of the metal is:

Equivalent weight = Atomic weight / n

Equivalent weight = A / 5

Option (a) 5 is the correct answer.