A steel container with a volume of 500.0 mL is evacuated, and 25.0 g of CaCO₃ is added. The container and contents are then heated to 1500 K, causing the CaCO₃ to decompose completely, according to the equation CaCO₃(s) → CaO(s) + CO₂(g). (b) Now make a more accurate calculation of the pressure inside the container. Take into account the volume of solid CaO (density = 3.34 g/mL) in the container, and use the van der Waals equation to calculate the pressure. The van der Waals constants for CO₂(g) are a = 3.59 (L²-atm)/mol² and b = 0.0427 L/mol.

Verified step by step guidance

1. Calculate the number of moles of CaCO₃ that decomposed. Use the molar mass of CaCO₃ (100.09 g/mol) to convert the mass of CaCO₃ to moles.
2. Determine the volume occupied by the solid CaO produced. Use the mass of CaO formed (equal to the mass of CaCO₃ decomposed, assuming complete decomposition) and the density of CaO (3.34 g/mL) to calculate the volume.
3. Subtract the volume occupied by CaO from the total volume of the container to find the volume available for the CO₂ gas.
4. Use the ideal gas law initially to estimate the number of moles of CO₂ produced, assuming the decomposition reaction produces 1 mole of CO₂ for every mole of CaCO₃ decomposed.
5. Apply the van der Waals equation, P = \frac{nRT}{V-nb} - \frac{an^2}{V^2}, where P is the pressure, n is the number of moles of CO₂, R is the gas constant (0.0821 L-atm/K-mol), T is the temperature (1500 K), V is the volume available for the gas, a and b are the van der Waals constants for CO₂ (3.59 (L²-atm)/mol² and 0.0427 L/mol respectively).

Key Concepts

Decomposition Reaction

A decomposition reaction is a type of chemical reaction where a single compound breaks down into two or more simpler products. In this case, calcium carbonate (CaCO3) decomposes into calcium oxide (CaO) and carbon dioxide (CO2) when heated. Understanding this reaction is crucial for determining the amount of gas produced, which directly affects the pressure in the container.

Ideal Gas Law and van der Waals Equation

The Ideal Gas Law (PV=nRT) describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. However, real gases deviate from this behavior under high pressure or low temperature, necessitating the use of the van der Waals equation. This equation accounts for the volume occupied by gas particles and the intermolecular forces, providing a more accurate calculation of pressure in non-ideal conditions.

Density and Volume Calculations

Density is defined as mass per unit volume and is essential for calculating the volume occupied by solids in a mixture. In this scenario, the density of solid CaO is given, allowing us to determine its volume in the container. This volume must be subtracted from the total volume of the container to find the effective volume available for the gas, which is critical for accurate pressure calculations using the van der Waals equation.