Question

The basic formulation has not changed since then: 40% potassium nitrate, 30% carbon, and 30% sulfur by weight. The products of the reaction that provide the explosive force when the powder is ignited are three gases: carbon monoxide, carbon dioxide, and nitrogen. An additional product is potassium sulfite. Consider a sample of 100g of black powder.

a. Which reagent is limiting?

B. How much of each of the reagents in excess is left over after the explosion takes place?

Answer 1

The amount of potassium nitrate (KNO₃) in the black powder = 40 g = 40 g/101.1 g.mol^-1 = 0.39565 mol

The amount of carbon (C) in the black powder = 30 g = 30 g/12 g.mol^-1 = 2.5 mol

The amount of sulfur (S) in the black powder = 30 g = 30 g/32 g.mol^-1 = 0.9375 mol

The balanced reaction can be written as follows.

2KNO₃ + 4C + S 2CO + 2CO₂ + N₂ + K₂S

The mole ratio, KNO₃:C = 2:4 = 1:2

The mole ratio, KNO₃:S = 2:1

i.e. The no. of moles of KNO₃ consumed = 0.39565 mol

The no. of moles of 'C' consumed = 2*0.39565 = 0.7913 mol

The no. of moles of 'S' consumed = 1/2 * 0.39565 mol = 0.19782 mol

Therefore, KNO₃ is the limiting reagent because it is completely consumed in the reaction.

The amount of 'C' left over after the explosion takes place = (2.5-0.7913) mol * 12 g/mol = 20.504 g

The amount of 'S' left over after the explosion takes place = (0.9375-0.19782) mol * 2 g/mol = 23.670 g