The first and second ionisation enthalpies of a metal are 496 and 4560 kJ mol –1 , respectively. How many moles of HCl and H₂SO₄, respectively, will be needed to react completely with 1 mole of the metal hydroxide ?

Solution

Chemistry ma’am · 4 steps

Look at the jump from IE1 to IE2: it tells you this is a +1 metal, so its hydroxide is MOH.

1. Read the jump. The second ionisation enthalpy, 4560 kJ mol⁻¹, is about nine times the first, 496 kJ mol⁻¹. After one electron leaves, the next one must come out of a stable noble-gas core, so the metal shows only the +1 state. These values belong to sodium.
2. Write the hydroxide. A +1 metal forms MOH, which has one OH⁻ per formula unit. One mole of it needs one mole of H⁺.

   MOH + HCl → MCl + H₂O 2MOH + H₂SO₄ → M₂SO₄ + 2H₂O

3. Count the acid. HCl gives one H⁺, so 1 mol is needed. H₂SO₄ gives two H⁺, so only 0.5 mol is needed.
4. So. 1 mol of HCl and 0.5 mol of H₂SO₄, which is option (b).

The idea to keep. A huge jump between two successive ionisation enthalpies marks the valency: the jump after IE1 means +1. Then match moles of H⁺ to moles of OH⁻.

Answer from the NTA final answer key. Solution by PrepWiser.