If the molar mass of X(HCO3)$_{2}$ is 162 g mol$^{-1}$, determine the relative atomic mass of X. [H = 1.0, C = 12.0, 0 = 16.0]

Analyze the question: We're given the molar mass of a compound, X(HCO₃)₂, and asked to find the atomic mass of X by subtracting the mass of everything else.

Concept: Molar mass of a compound = sum of the atomic masses of all atoms in its formula. The subscript 2 outside the bracket means everything inside the bracket is doubled.

Solution:

Mass of one HCO₃ group:

• H = 1
• C = 12
• O₃ = 3 × 16 = 48
• Total = 1 + 12 + 48 = 61

Mass of two HCO₃ groups = 2 × 61 = 122

Now: X + 122 = 162 X = 162 − 122 = 40

This matches calcium, Ca = 40, so the compound is calcium hydrogencarbonate, Ca(HCO₃)₂, which is a familiar compound (it causes temporary hardness of water).

Answer: A. 40

Tip: Do not pick option C (61) just because it is the mass of one HCO₃ group. Always multiply the bracketed group by the subscript outside it. Also, when the answer matches a known element's mass (Ca = 40), that is a good confirmation.