What mass of aluminum can be obtained from 2.5 kg of alumina, the mass fraction of aluminum oxide in which is 90%?

Let’s find the mass of aluminum in the clay.

2.5 kg – 100%,

x – 90%,

x = (2.5 kg × 90%): 100% = 2.25 kg.

Let’s find the amount of substance Al.

n = m: M.

M (Al) = 27 kg / kmol.

n = 2.25 kg: 27 kg / kmol = 0.083 mol.

M (Al2O3) = 2Ar (Al) + 3Ar (O) = 2 × 27 + 3 × 16 = 102 kg / kmol.

W (Al) = (54: 102) × 100% = 52.94%.

m (Al) = (w (Al) × m (Al2O3)): 100% = (52.94% × 2.25 kg): 100% = 1.91 kg.

Second option.

102 kg / kmol – 54 kg (Al),

2.25 kg – x kg (Al).

X = (2.25 × 54 kg): 102 kg / kmol = 1.191 kg.

Answer: 1.191 kg.