When heated, CaCO3 decomposes as follows: CaCO3 (s) = CO2 (g) +CaO (s)
in an experiment, 10.00 g of CaCO3 was placed in a .500 L container, and when it was heated to a constant temperature, 50% of the solid decomposed. What is the value of Kc for this reaction under these conditions?
Kc = (CO2)
If we start with 10.00 g CaCO3 and half of it decomposes, that is 5.00 grams.
5 g CaCO3 = g/molar mass = 5.00/100 = 0.05 moles CaCO3. That will give, from the equation, 0.05 moles CO2 and the concn is moles/L; therefore, (CO2) = 0.05/0.5 L = 0.1 M. Thus Kc = 0.1.
To find the value of Kc for this reaction, we need to know the concentration of each species at equilibrium. However, in this case, we are given the mass of the solid rather than the concentration. Therefore, we need to convert the mass of the solid into moles in order to determine the concentration.
First, we calculate the moles of CaCO3 decomposed:
Molar mass of CaCO3 = 40.08 g/mol (Ca) + 12.01 g/mol (C) + 3(16.00 g/mol) (O) = 100.09 g/mol
Moles of CaCO3 decomposed = (10.00 g / 100.09 g/mol) * 0.50 (since 50% of the solid decomposed)
Next, we determine the change in the number of moles for each species involved in the reaction:
According to the balanced equation: CaCO3 (s) = CO2 (g) + CaO (s)
-1 mole CaCO3 produces +1 mole CO2 and +1 mole CaO
Since the reaction goes to completion, the change in moles of CO2 and CaO will be equal to the moles of CaCO3 decomposed.
Now, we can convert the moles of CO2 into concentration (M) by dividing by the volume of the container:
Concentration of CO2 = Moles of CO2 / Volume of the container (in liters)
After that, we can write the expression for Kc:
Kc = [CO2] / [CaCO3]
By substituting the concentration obtained for CO2 and the initial concentration of CaCO3 (which is the same as the concentration of CaCO3 because only a fraction of it decomposes), we can calculate the value of Kc.
Note: The value of Kc will depend on the specific temperature at which the reaction was carried out.