Question

Given the reaction: (NH4)2CO3 → NH3 + CO2 + H20
What is the minimum amount of ammonium carbonate, in grams, that reacts to produce 1.0 mole of
ammonia?

Answer 1

Let a, b, c, d be integer coefficients that balance the reaction,

a (NH₄)₂CO₃   →   b NH₃ + c CO₂ + d H₂O

• N : 2a = b

• H : 8a = 3b + 2d

• C : a = c

• O : 3a = 2c + d

Since a = c, it follows that

2a = b   ⇒   2c = b

8a = 3b + 2d   ⇒   8c = 3b + 2d   ⇒   4b = 3b + 2d   ⇒   b = 2d

3a = 2c + d   ⇒   3c = 2c + d   ⇒   c = d

So if we let a = 1, then c = d = 1 and b = 2, and the balanced reaction is

(NH₄)₂CO₃   →   2 NH₃ + CO₂ + H₂O

which says that 2 moles of ammonia are produced for each mole of ammonium carbonate.

If we have enough (NH₄)₂CO₃ to produce 1.0 mol NH₃, then we must have started with 0.50 mol (NH₄)₂CO₃. It has a molar mass of about 96.09 g/mol, so

(0.5 mol (NH₄)₂CO₃) (96.09 g/mol) ≈ 48 g (NH₄)₂CO₃