Answer:
CaCO₃ = 85.18%
BaCO₃ = 14.82%
Explanation:
The acid will react with the salts, the partial reactions are:
CaCO₃ + 2HCl → CaCl₂ + CO₂ + H₂O
BaCO₃ + 2HCl → BaCl₂ + CO₂ + H₂O
So, the total amount of CaCO₃ BaCO₃ will form the CO₂.
Using the ideal gas law to calculate the number of moles of CO₂:
PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.082 atm*L/mol*K), and T is the temperature (50ºC + 273 = 323 K).
0.904*1.39 = n*0.082*323
26.486n = 1.25656
n = 0.05 mol
So, the number of moles of the mixture is 0.05 mol.
The molar masses of the components are:
CaCO₃ = 40 g/mol of Ca + 12 g/mol of C + 3*16 g/mol of O = 100 g/mol
BaCO₃ = 137.3 g/mol of Ba + 12 g/mol of C + 3*16 g/mol of O = 197.3 g/mol
Let's call x the number of moles of CaCO₃ and y the number of moles of BaCO₃, so:
100x + 197.3y = 5.4
x + y = 0.05 mol
y = 0.05 - x
100x + 197.3*(0.05 - x) = 5.4
100x - 197.3x = 5.4 - 9.865
97.3x = 4.465
x = 0.046 mol of CaCO₃
y = 0.004 mol of BaCO₃
So, the masses are:
CaCO₃ = 100* 0.046 = 4.60 g
BaCO₃ = 137.3*0.004 = 0.80 g
The percentages in the mixture are:
CaCO₃ = (4.60/5.40)*100% = 85.18%
BaCO₃ = (0.80/5.40)*100% = 14.82%
