Short Answer 
The reaction involves the decomposition of calcium carbonate into calcium oxide and carbon dioxide, with 1.04 moles of CO‚CC at equilibrium. The temperature is converted from 898¬∞C to 1171 K for use in the ideal gas law, validating that the system maintains 1.00 atm pressure and the calculated gas conditions.
Step 1: Understanding the Chemical Reaction
The reaction involves the decomposition of calcium carbonate (CaCO‚ÄöCE) into calcium oxide (CaO) and carbon dioxide (CO‚ÄöCC) when heated. The balanced equation for this reaction is:
- CaCO‚ÄöCE(s) ‚Äöaa CaO(s) + CO‚ÄöCC(g)
At equilibrium, the system has a specific amount of carbon dioxide present, which is crucial for understanding the reaction dynamics. Here, we know that 1.04 moles of CO‚ÄöCC are present during equilibrium.
Step 2: Calculating the Temperature in Kelvin
To perform calculations involving gases, it is essential to convert the temperature from degrees Celsius to Kelvin. The conversion formula is:
- K = °C + 273.15
In this case, the given temperature is 898°C, which converts to:
- K = 898 + 273.15 = 1171 K
This temperature is used in the ideal gas law for further calculations.
Step 3: Utilizing the Ideal Gas Law
The ideal gas law is used to relate the pressure, volume, temperature, and number of moles of a gas. The formula is:
- P ‚àöo V = n ‚àöo R ‚àöo T
In this scenario, we can plug in the values:
- P = 1.00 atm
- V = 100 L
- R = 0.081 (L·atm)/(K·mol)
- T = 1171 K
After calculating with the ideal gas equation, we confirm that the system indeed has 1.04 moles of CO‚ÄöCC, maintaining a constant pressure of 1.00 atm at equilibrium.