When crystals of ammonium dichromate (NH₄)₂Cr₂O₇ are heated strongly, they decompose strongly according to the following balanced equation - Leaving Cert Chemistry - Question b - 2014

From the balanced equation, we see that 1 mole of (NH₄)₂Cr₂O₇ produces 1 mole of Cr₂O₃. Therefore, the moles of Cr₂O₃ formed is also 0.05 mol.

The molar mass of Cr₂O₃ is:

• Chromium: $2 \times 52 = 104 \, g$
• Oxygen: $3 \times 16 = 48 \, g$

Total molar mass of Cr₂O₃:

$M = 104 + 48 = 152 \, g/mol$

Thus, the mass of Cr₂O₃ formed is:

$m = n \times M = 0.05 \, mol \times 152 \, g/mol = 7.6 \, g$.

From the balanced equation, 1 mole of (NH₄)₂Cr₂O₇ produces 1 mole of N₂. Therefore, 0.05 mol of ammonium dichromate will produce 0.05 mol of nitrogen gas.

At s.t.p., 1 mole of gas occupies $22.4 \, L$:

The volume of nitrogen gas evolved is:

$V = n \times 22.4 \, L/mol = 0.05 \, mol \times 22.4 \, L/mol = 1.12 \, L = 1,120 \, cm³$.

From the balanced equation, 1 mole of (NH₄)₂Cr₂O₇ produces 4 moles of H₂O. Therefore, 0.05 moles of (NH₄)₂Cr₂O₇ will produce:

$0.05 \, mol \times 4 = 0.20 \, mol$

To find the number of molecules, we use Avogadro's number, $6.02 \times 10^{23} \, molecules/mol$:

$N = 0.20 \, mol \times 6.02 \times 10^{23} \, molecules/mol = 1.2 \times 10^{23} \, molecules.$

Each molecule of water (H₂O) contains 3 atoms (2 hydrogen and 1 oxygen). Thus, the total number of atoms in 1.2 x 10²³ molecules of water is:

$\text{Total atoms} = 1.2 \times 10^{23} \times 3 = 3.6 \times 10^{23} \text{ atoms}.$