Question

2.4 kg of carbon is made to react with 1.35 kg of aluminium to form $A{l}_4{C}_3.$ The maximum amount of aluminium carbide formed is:

• A. 5.44 kg
• B. 3.75 kg
• C. 1.05 kg
• D. 1.80 kg

Answer 1

The correct option is D 1.80 kg

The given balanced chemical equation is:
$4Al+3C\to A{l}_4{C}_3$
molar mass of carbon = 12 g/mol
$\therefore 2.4$ kg of carbon = 2400 g of carbon = 200 mol of carbon
Molar mass of aluminium = 27 g/mol
$\therefore$ 1.35 kg aluminium = 1350 g of aluminium = 50 mol of aluminium
3 moles of carbon reacts with 4 moles of aluminium
So, 200 mol carbon will react with
$=\frac{4}{3}\times 200$ mol of aluminium
= 266.67 mol of aluminium
Aluminium is the limiting reagent here.
So, moles of $A{l}_4{C}_3$ produced $=\frac{1}{4}\times 50$ mol = 12.5 mol
Again, molar mass of $A{l}_4{C}_3=(4\times 27+12\times 3)$ g/mol
= 144 g/mol
$\therefore$ So, mass of $A{l}_4{C}_3$ produced $=144\times 12.5g=1800$ g = 1.8 kg