NDA (II) 2016 General Ability Test · Question 142 of 150

Correct — C, three moles. Aluminium sits in group 13 and forms the Al³⁺ ion, while the hydroxide ion carries a single negative charge, so three hydroxide ions are needed to balance one aluminium ion and the formula is Al(OH)₃. Each hydroxide group carries exactly one hydrogen atom, so one formula unit of aluminium hydroxide contains three hydrogen atoms. Scaling up by Avogadro's number changes nothing about the ratio: one mole of aluminium hydroxide contains three moles of hydrogen atoms. The whole question is really a test of whether you can write the formula from the valencies.

• (a)One mole — This would be the answer for a hydroxide of a monovalent metal such as sodium hydroxide, NaOH. Aluminium is trivalent, so it needs three hydroxide groups, not one.
• (b)Two moles — This fits a divalent metal — calcium hydroxide, Ca(OH)₂, or magnesium hydroxide. It is the natural slip for anyone who assumes aluminium behaves like the group 2 metals it sits beside in the table.
• (d)Four moles — There is no neutral hydroxide of aluminium with four hydroxide groups. The species with four is the aluminate ion formed in strong alkali, and it carries a negative charge, so it is not what the name aluminium hydroxide refers to.

A mole is Avogadro's number of particles, about 6.022 × 10²³. When a formula is scaled to moles, the subscripts become mole ratios: one mole of a compound contains as many moles of each atom as the subscript beside it. So one mole of water contains two moles of hydrogen atoms and one mole of oxygen atoms, and one mole of Al(OH)₃ contains one mole of aluminium, three of oxygen and three of hydrogen. Writing the formula correctly is therefore the only real step, and that comes from balancing the charges — a trivalent cation needs three univalent anions.

Two traps are worth naming. First, the question asks for hydrogen atoms, not hydrogen molecules; three moles of hydrogen atoms would correspond to one and a half moles of H₂ gas, and NDA has asked that distinction directly in other years. Second, the hydroxide group must be treated as a single unit with a charge of minus one, which is why the formula is written with brackets and a subscript outside them rather than as AlO₃H₃. Aluminium hydroxide itself is worth remembering as an amphoteric hydroxide — it dissolves in acids and in strong alkalis alike — and as the active ingredient of many antacids.

• The formula of aluminium hydroxide is Al(OH)₃, because aluminium forms a tripositive ion and hydroxide is uninegative.
• One mole is Avogadro's number of particles, about 6.022 × 10²³.
• Subscripts in a formula are mole ratios once the formula is scaled up, so Al(OH)₃ gives 1 : 3 : 3 for aluminium, oxygen and hydrogen.
• Three moles of hydrogen atoms correspond to one and a half moles of hydrogen molecules, since each molecule holds two atoms.
• Aluminium hydroxide is amphoteric, reacting with both acids and strong alkalis, and is used as an antacid.

• Reading 'moles of hydrogen atom' as moles of hydrogen gas; the two differ by a factor of two.
• Assuming aluminium is divalent because of where it sits in the table; it is trivalent.
• Forgetting that the subscript outside the bracket applies to every atom inside it.

NDA sets a straightforward mole-ratio or formula item most years, and it is usually decided by whether you can write the formula from valencies rather than by any calculation.

• practice — not a real PYQ

  How many moles of oxygen atoms are present in one mole of calcium hydroxide?

  • (a)One
  • (b)Two
  • (c)Three
  • (d)Four

  Answer(b) Two — calcium is divalent, so the formula is Ca(OH)₂ and each of the two hydroxide groups contributes one oxygen atom.

• practice — not a real PYQ

  Three moles of hydrogen atoms are equivalent to how many moles of hydrogen gas?

  • (a)1·5 moles
  • (b)3 moles
  • (c)6 moles
  • (d)0·5 mole

  Answer(a) 1·5 moles — hydrogen gas is diatomic, so each molecule accounts for two atoms.