Final answer:
To calculate the volume of CO2 produced when heating limestone, we need to use the ideal gas law. First, we calculate the number of moles of CO2 by converting the given mass of CaCO3. Then, we use the ideal gas law equation PV = nRT to find the volume of CO2. The volume of CO2 produced is 828 L.
Step-by-step explanation:
In the given problem, a sample of limestone (calcium carbonate, CaCO3) is heated at 950 K until it is completely converted to calcium oxide (CaO) and CO2. The given information states that 8.47 kg of solid Ca(OH)2 is formed by addition of water.
The first step requires us to calculate the volume of CO2 produced. We need to use the ideal gas law to solve this problem. According to the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. We have the pressure (0.976 atm), temperature (950 K), and we can calculate the number of moles of CO2 from the given mass of CaCO3.
First, we need to convert the mass of CaCO3 to the number of moles using its molar mass. The molar mass of CaCO3 is 100.09 g/mol. So, the number of moles of CaCO3 is (8.47 kg * 1000 g/kg) / 100.09 g/mol = 84.61 mol.
From the balanced equation CaCO3(s) -> CaO(s) + CO2(g), we can see that 1 mole of CaCO3 produces 1 mole of CO2. Therefore, the number of moles of CO2 produced is also 84.61 mol.
Now, we can use the ideal gas law to find the volume of CO2 produced. Rearranging the ideal gas law equation, we get V = (nRT) / P. Plugging in the values, V = (84.61 mol * 0.0821 atm·L/mol·K * 950 K) / 0.976 atm = 828 L.
Therefore, the volume of CO2 produced in the first step is 828 L.