How to calculate the mass of magnesium and chromium oxide required to obtain 26 kg of chromium?

Given:

m (Cr) = 26 kg

To find:

m (Mg) -?

m (Cr2O3) -?

Decision:

3Mg + Cr2O3 = 2Cr + 3MgO, – we solve the problem, relying on the composed reaction equation:

1) Find the amount of chromium formed during the reaction:

n (Cr) = m: M = 26 kg: 52 kg / kmol = 0.5 kmol, – since we are operating on large numbers, we will convert moles to kilomoles.

2) Find the mass of magnesium by the first logical expression:

if 3 kmol of Mg gives 2 kmol of Cr,

then x kmol Mg will give 0.5 kmol Cr,

then x = 0.5 * 3: 2 = 0.75 kmol.

m (Mg) = n * M = 0.75 kmol * 24 kg / kmol = 18 kg

3) Find the mass of chromium oxide by the second logical expression:

if 1 kmol of Cr2O3 gives 2 kmol of Cr,

then x kmol Cr2O3 will give 0.5 kmol Cr,

then x = 0.25 kmol.

m (Cr2O3) = n * M = 0.25 kmol * 152 kg / kmol = 38 kg

Answer: m (Mg) = 18 kg; m (Cr2O3) = 38 kg.