Answer:
12.22 g
Step-by-step explanation:
The reaction is
CaCO₃(s)⇄ CaO (s) + CO₂ (g)
The constant of equilibrium based on pressure (Kp) depends only on the gas substances, so in this case, it will depend on CO₂.
Kp = pCO₂ = 0.220
For the Le Chatêlier principle, a change in the pressure will shift the equilibrium to equilibrate the effect. Kp only changes with the temperature, so all the CO₂ added will form CaCO₃.
The stoichiometry is 1 mol of CaCO₃ for 1 mol of CO₂, and the number of moles of CO₂ can be calculated by the ideal gas equation:
PV = nRT
where P is the pressure, V is the volume, n the number of moles, R the gas constant ( R = 0.082 atm.L/mol.K), and T the temperature.
So, the number of moles of CO₂ in equilibrium is:
0.220x10 = nx0.082x385
31.57n = 2.20
n = 0.0697 mol
Which is the number of moles of CaCO₃ that reacts, so in the equilibrium, there is 0.1 - 0.0697 = 0.0303 mol of CaCO₃.
The number of moles of CO₂ added is:
0.290x10 = nx0.082=385
31.57n = 2.90
n = 0.09186 mol
This will totally form 0.09186 mol of CaCO₃, and it will have, in the final:
n = 0.0303 + 0.09186 = 0.1222 mol
The molar masses are: Ca = 40 g/mol, C = 12 g/mol, O = 16 g/mol
CaCO₃ = 40 + 12 + 3x16 = 100 g/mol
The mass is the moles multiplied by the molar mass:
m = 0.1222 x 100
m = 12.22 g