Answer:
To calculate the mass of chromium produced from a given amount of chromium(III) oxide (Cr2O3), we need to use the balanced chemical equation for the reaction between chromium(III) oxide and aluminum powder.
The balanced chemical equation for the reaction is as follows:
4Al + 3Cr2O3 → 2Cr + 2Al2O3
From the equation, we can see that 3 moles of chromium(III) oxide react with 4 moles of aluminum to produce 2 moles of chromium. Using this information, we can calculate the molar mass of Cr2O3 and then use stoichiometry to determine the mass of chromium produced.
(a) Calculation for 50g of Cr2O3:
1. Calculate the molar mass of Cr2O3:
Molar mass of Cr = 52 g/mol
Molar mass of O = 16 g/mol
Molar mass of Cr2O3 = (2 * Molar mass of Cr) + (3 * Molar mass of O)
= (2 * 52 g/mol) + (3 * 16 g/mol)
= 104 g/mol + 48 g/mol
= 152 g/mol
2. Convert the given mass of Cr2O3 to moles:
Moles of Cr2O3 = Mass / Molar mass
= 50g / 152 g/mol
≈ 0.329 moles
3. Use stoichiometry to calculate the moles of chromium produced:
Moles of Cr = (2/3) * Moles of Cr2O3
= (2/3) * 0.329 moles
≈ 0.219 moles
4. Convert moles of chromium to mass:
Mass of Cr = Moles of Cr * Molar mass of Cr
= 0.219 moles * 52 g/mol
≈ 11.388 g
Therefore, the mass of chromium produced from 50g of Cr2O3 is approximately 11.388 g.
(b) Calculation for 5kg of Cr2O3:
1. Convert the given mass of Cr2O3 to grams:
Mass of Cr2O3 = 5kg * 1000g/kg
= 5000g
2. Convert the mass of Cr2O3 to moles:
Moles of Cr2O3 = Mass / Molar mass
= 5000g / 152 g/mol
≈ 32.895 moles
3. Use stoichiometry to calculate the moles of chromium produced:
Moles of Cr = (2/3) * Moles of Cr2O3
= (2/3) * 32.895 moles
≈ 21.930 moles
4. Convert moles of chromium to mass:
Mass of Cr = Moles of Cr * Molar mass of Cr
= 21.930 moles * 52 g/mol
≈ 1140.360 g
Therefore, the mass of chromium produced from 5kg of Cr2O3 is approximately 1140.360 g.
(c) Calculation for 5 tonnes of Cr2O3:
1. Convert the given mass of Cr2O3 to grams:
Mass of Cr2O3 = 5 tonnes * 1000 kg/tonne * 1000g/kg
= 5,000,000g
2. Convert the mass of Cr2O3 to moles:
Moles of Cr2O3 = Mass / Molar mass
= 5,000,000g / 152 g/mol
≈ 32,894.737 moles
3. Use stoichiometry to calculate the moles of chromium produced:
Moles of Cr = (2/3) * Moles of Cr2O3
= (2/3) * 32,894.737 moles
≈ 21,929.825 moles
4. Convert moles of chromium to mass:
Mass of Cr = Moles of Cr * Molar mass of Cr
= 21,929.825 moles * 52 g/mol
≈ 1,140,360.900 g
Therefore, the mass of chromium produced from 5 tonnes of Cr2O3 is approximately 1,140,360.900 g.
Step-by-step explanation: