AdBlue, a solution of urea (NH₂CONH₂) in water, is used in the exhaust systems of some diesel-powered vehicles to remove NO₂ from the hot exhaust flow by making use of the following reaction - Leaving Cert Chemistry - Question c - 2021

To calculate the mass of one mole of urea (NH₂CONH₂), we sum the atomic masses of its constituent elements:

• Nitrogen (N): 14.01 g/mol (2 N = 28.02 g/mol)
• Hydrogen (H): 1.01 g/mol (4 H = 4.04 g/mol)
• Carbon (C): 12.01 g/mol (1 C = 12.01 g/mol)
• Oxygen (O): 16.00 g/mol (1 O = 16.00 g/mol)

The molar mass calculation is:

$ext{Molar mass of NH}_2 ext{CONH}_2 = 28.02 + 4.04 + 12.01 + 16.00 = 60.07 ext{ g/mol}$

To find the number of moles of urea in 1,620 g, we use the formula:

ext{Number of moles} = rac{ ext{mass (g)}}{ ext{molar mass (g/mol)}}

Substituting the values we found:

ext{Number of moles} = rac{1620 ext{ g}}{60.07 ext{ g/mol}} ≈ 26.95 ext{ moles}

From the balanced chemical equation, we see that 4 moles of urea react with 6 moles of NO₂:

ightarrow 7 ext{ N}_2 + 8 ext{ H}_2 ext{O} + 4 ext{ CO}_2$$ Therefore, the ratio of urea to NO₂ is: $$rac{6 ext{ moles NO}_2}{4 ext{ moles NH}_2 ext{CONH}_2} = rac{3}{2}$$ Thus, 1 mole of urea reacts with 1.5 moles of NO₂.

At standard temperature and pressure (s.t.p.), one mole of a gas occupies 22.4 liters. Therefore, to find the volume of NO₂ produced from 1 mole of urea:

$ext{Volume of NO}_2 = 1.5 ext{ moles} imes 22.4 ext{ L/mol} = 33.6 ext{ L}$

Thus, 1.5 moles of NO₂ occupies 33.6 liters at s.t.p.