What is the percentage composition of carbon in Ca(HCO3)$_{2}$ ? [ Ca = 40.0, 0= 16.0, C = 12.0, H= 1.0]

Analyze the question: We need the percentage by mass of carbon in calcium hydrogen carbonate, Ca(HCO₃)₂.

Concept: Percentage composition of an element = (total mass of the element in one formula unit ÷ molar mass of the compound) × 100

Step 1: Count the atoms in Ca(HCO₃)₂ The bracket is multiplied by 2:

• Ca = 1
• H = 2
• C = 2
• O = 6

Step 2: Calculate the molar mass

• Ca: 1 × 40 = 40
• H: 2 × 1 = 2
• C: 2 × 12 = 24
• O: 6 × 16 = 96

Molar mass = 40 + 2 + 24 + 96 = 162 g/mol

Step 3: Calculate the percentage of carbon % C = (24 ÷ 162) × 100 = 14.81%

Answer: 14.8%, which is option B.

Tip: In formulas with brackets, such as Ca(HCO₃)₂, multiply every atom inside the bracket by the subscript outside. Forgetting this is the most common mistake. Here, using only one carbon (12 ÷ 138) would give the wrong answer of 8.7%, which isn't an option, but in other questions the wrong answer might be an option, so be careful.