Answer:

Introduction:
The molecular formula of chloride of a metal M is MCl3. We need to determine the formula of its carbonate.

Explanation:

To determine the formula of the carbonate, we need to understand the valency of the metal (M) and the carbonate ion (CO3^2-).

Valency of Metal M:
Since the chloride of metal M is MCl3, we can determine the valency of M by balancing the charges of the metal and chloride ions. The chloride ion has a charge of -1. Therefore, to balance the charges, the metal M must have a valency of +3.

Valency of Carbonate ion (CO3^2-):
The carbonate ion (CO3^2-) has a charge of -2. To balance the charges, we need two positive charges. Therefore, the valency of carbonate is 2.

Formula of the Carbonate:
Based on the valency of the metal M and the carbonate ion, the formula of the carbonate can be determined.

Since the valency of M is +3 and the valency of CO3^2- is 2, we need to find the least common multiple (LCM) of these two numbers. The LCM of 3 and 2 is 6.

To balance the charges, we need two carbonate ions (2 x CO3^2-), which will give a total charge of -4 (-2 x 2). Therefore, we need three metal ions (3 x M^3+) to balance the charges, which will give a total charge of +9 (+3 x 3).

Hence, the formula of the carbonate of the metal M is M2(CO3)3, which is option B.

Summary:
The molecular formula of the chloride of a metal M is MCl3. Based on the valency of the metal M (+3) and the carbonate ion (CO3^2-) (2), the formula of the carbonate is M2(CO3)3, which is option B.