Calculate and indicate what mass of lime the mass fraction of calcite in which is equal to 90%

Calculate and indicate what mass of lime the mass fraction of calcite in which is equal to 90% must be used to extract 10.92 g of benzene.

We write down the equation for the reactions of obtaining benzene.
1.CaCO3 + 4C = CaC2 + 3CO.
2.CaC2 + 2H2O = Ca (OH) 2 + C2H2.
3.3C2H2 = C6H6.
We find the amount of benzene substance.
n = m / M.
M (C6H6) = 12 * 6 + 1 * 6 = 72 + 6 = 78 g / mol.
n (C6H6) = 10.92 / 78 = 0.14 mol.
Next, we find the amount of substance ethine.
X mol C2H2 – 0.14 mol C6H6
3 mol С2Н2 – 1 mol С6Н6
X = 3 * 0.14: 1 = 0.42 mol.
Next, we find the amount of substance CaC2.
X mol of CaC2 – 0.42 mol of C2H2
1 mol CaC2 – 1 mol C2H2
X = 1 * 0.42: 1 = 0.42 mol.
Next, we find the amount of calcium carbonate substance.
X mol of CaCO3 – 0.42 mol of CaC2
1 mol CaCO3 – 1 mol CaC2
X = 1 * 042: 1 = 0.42 mol CaCO3
Find the mass of calcium carbonate.
M (CaCO3) = 100 g / mol.
m = 100 * 0.42 = 42 g.
m = 42: 0.9 = 46.67 g.
Answer: m = 46.67 g.