Question

Ancient Romans built often out of bricks and mortar. A key ingredient in their mortar was quicklime (calcium oxide), which they produced by roasting limestone (calcium carbonate). 1. Write a balanced chemical equation, including physical state symbols, for the decomposition of solid calcium carbonate (CaCO3) into solid calcium oxide and gaseous carbon dioxide. CaCO3s→CaOs+CO2g 2. Suppose 48.0L of carbon dioxide gas are produced by this reaction, at a temperature of 260.0°C and pressure of exactly 1atm. Calculate the mass of calcium carbonate that must have reacted. Round your answer to 3 significant digits.

Answer 1

110 g

Step-by-step explanation:

Step 1: Write the balanced equation for the decomposition of calcium carbonate

CaCO₃(s) ⇒ CaO(s) + CO₂(g)

Step 2: Convert 260.0 °C to Kelvin

We will use the following expression.

K = °C + 273.15 = 260.0 + 273.15 = 533.2 K

Step 3: Calculate the moles of CO₂ produced

We will use the ideal gas equation.

P × V = n × R × T

n = P × V/R × T = 1 atm × 48.0 L/0.0821 atm.L/mol.K × 533.2 K = 1.10 mol

Step 4: Calculate the moles of CaCO₃ that reacted to produce 1.10 moles of CO₂

The molar ratio of CaCO₃ to CO₂ is 1:1. The moles of CaCO₃ that reacted are 1/1 × 1.10 mol = 1.10 mol.

Step 5: Calculate the mass corresponding to 1.10 moles of CaCO₃

The molar mass of CaCO₃ is 100.09 g/mol.

1.10 mol × 100.09 g/mol = 110 g