What volume of carbon(IV) oxide gas, in \text{dm}^3, measured at STP, is produced by the c… — JAMB UTME

What volume of carbon(IV) oxide gas, in $\text{dm}^3$ , measured at STP, is produced by the complete thermal decomposition of $20.0\text{ g}$ of pure calcium trioxocarbonate(IV), $\text{CaCO}_3$ ? [ $\text{Ca} = 40$ , $\text{C} = 12$ , $\text{O} = 16$ ; Molar volume of gas at STP $= 22.4\text{ dm}^3\text{mol}^{-1}$ ]

Answer: 4.48 dm^3

Answer

4.48 dm³

Complete thermal decomposition of 20.0 g of CaCO₃ (molar mass 100 g/mol) generates 0.20 mol of CO₂ gas according to the equation CaCO₃(s) -> CaO(s) + CO₂(g). Since 1 mol of gas at STP occupies 22.4 dm³, 0.20 mol occupies 4.48 dm³.

Step-by-Step Solution

Determine the molar mass and number of moles of calcium trioxocarbonate(IV).

Molar mass of CaCO₃ = 100 g/mol; Moles of CaCO₃ = 20.0 g / 100 g/mol = 0.20 mol

Converting given mass to moles is required to apply stoichiometric ratios.

Apply the balanced reaction mole ratio to find moles of carbon(IV) oxide produced.

Moles of CO₂ = 0.20 mol

The equation CaCO₃(s) -> CaO(s) + CO₂(g) shows a 1:1 molar ratio between CaCO₃ and CO₂.

Multiply moles of CO₂ by molar gas volume at STP.

Volume of CO₂ = 0.20 mol × 22.4 dm³/mol = 4.48 dm³

At STP, 1 mole of any ideal gas occupies 22.4 dm³.

Key Concept

Thermal decomposition of trioxocarbonate(IV) salts and gas volume calculations at STP

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