Question

The direct gas carbonation route of finely ground olivine (Mg2SiO4) occurs under high pressure and elevated temperature conditions according

to the following unbalanced equation:

Mg2SiO4(s) + CO2(g) + H2O(g)  MgCO3(s) + H4SiO4(l)

Use this equation to calculate the mass of magnesium carbonate (in kg) produced when

5.00 metric tons of olivine is combined with 5.00 x 104 Liters of CO2 under the following two

sets of conditions:

1 atm and 25ºC and

25 atm and 25ºC

Which will be better yield?

Answer 1

The balanced chemical equation is shown below.

Mg2 Sio (s) + 2C02(g) + 2H2O(g) + 2MgCO3(s) + HASIO (1)

5.00 metric tons of olivine contains

5.00 metric tons = X- 1000 kg - = 5000 kg 1 metric ton

Convert unit from kg to g

1000 g 5000 kg X- - 5.00 x 100 g 1 kg

Molar mass of olivine

Mg2S104 = 2(24.3) + 28.1+ 4(16) = 140.7 g/mol

Number of moles of olivine

5.00 x 100 g = 35536.6 mol 140.7 g/mol

(1)

Calculate number of moles of carbon dioxide gas at 1 atm and 25 deg C (298 K).

5.00 x 104 L

n = P XV RXT

n = 1 atm x 5.00 x 10'L 0.08206 batm x 298 K

n = 2044.7 mol

Since the number of moles of carbon dioxide is less than the number of moles of olivine, carbon dioxide is the limiting reagent and olivine is the excess reagent.

As per the reaction stoichiometry

Mg2 Sio (s) + 2C02(g) + 2H2O(g) + 2MgCO3(s) + HASIO (1)

2 mol MgCO3 2044.7 mol CO2 X – 3= 2044.7 mol MgCO3 2 mol CO2

Mass of magnesium carbonate produced

= 2044.7 mol x 84.3 g 1 mol = 172365 g

Convert unit from grams to kg

L = 172.4 kg = 172365 9 * 1000 g

(2)

Calculate number of moles of carbon dioxide gas at 25 atm and 25 deg C (298 K).

5.00 x 104 L

n = P XV RXT

n = 25 atm x 5.00 x 10 L 0.08206 batm x 298 K

n = 51116.6 mol

1 mol olivine 51116.6 mol CO2 X – 2 * 2 mol CO2 = 25558 mol olivine

But 35536.6 moles of olivine are present.

Since the number of moles of carbon dioxide is less than the number of moles of olivine, carbon dioxide is the limiting reagent and olivine is the excess reagent.

As per the reaction stoichiometry

Mg2 Sio (s) + 2C02(g) + 2H2O(g) + 2MgCO3(s) + HASIO (1)

2 mol MgCO3 51116.6 mol CO2 = 3 =51116.6 mol MgCO3 2* 2 mol CO2

Mass of magnesium carbonate produced

84.3 g = 51116.6 mol x = 4309132 g 1 mol

Convert unit from grams to kg

1 kg -4309.1 kg = 4309132 9 X 1000

25 atm at 25 deg C will give better yield than 1 atm at 25 deg C. This is in accordance with Le Chatelier's principle. When partial pressure of a reactant is increased, the equilibrium shifts in forward direction so that more and more of product is obtained.