NDA (II) 2018 General Ability Test · Question 65 of 146

Correct — B, 106 u. Anhydrous sodium carbonate is Na₂CO₃, so one formula unit contains two sodium atoms, one carbon atom and three oxygen atoms. Adding the masses given in the question: sodium contributes 2 × 23 = 46, carbon contributes 12, and oxygen contributes 3 × 16 = 48. The total is 46 + 12 + 48 = 106 u. The word 'anhydrous' in the stem is doing real work — it tells you to take the formula without any water of crystallisation attached, and the paper has planted the hydrated value among the options for anyone who ignores it.

• (a)286 u — The formula mass of washing soda, the decahydrate Na₂CO₃·10H₂O. Ten water molecules add 10 × 18 = 180 u to the 106 u of the anhydrous salt, giving 286 u. This is the option 'anhydrous' exists to exclude.
• (c)83 u — What you get by counting only one sodium atom — 23 + 12 + 48 = 83. The subscript 2 on sodium has been read as part of the name rather than as a count of atoms.
• (d)53 u — Exactly half of 106. It is sodium carbonate's equivalent mass, which is the formula mass divided by 2 because the carbonate ion carries two units of charge — a real quantity, but not what the question asks for.

Sodium carbonate is an ionic compound, so it has no discrete molecules and the sum of the atomic masses in its formula is called the formula unit mass rather than the molecular mass. The calculation is the same either way: multiply each element's atomic mass by the number of its atoms in the formula and add. Many ionic salts crystallise with a fixed number of water molecules locked into the lattice, called water of crystallisation, and those molecules count towards the mass of the hydrated salt.

Read the qualifier before you calculate. 'Anhydrous' means without water of crystallisation and points to Na₂CO₃ at 106 u; 'washing soda' or 'hydrated' points to Na₂CO₃·10H₂O at 286 u. NDA has set the hydrated formula as its own question in the very same year's first session, so the paper expects you to hold both. Two related numbers are worth memorising outright because they recur — copper sulphate crystallises with five water molecules and gypsum with two, against sodium carbonate's ten.

• Formula unit mass is the sum of the atomic masses of all the atoms in a formula unit, used for ionic compounds.
• Na₂CO₃ = 2(23) + 12 + 3(16) = 46 + 12 + 48 = 106 u.
• Washing soda is Na₂CO₃·10H₂O with a formula mass of 286 u; heating it drives off the water and leaves anhydrous soda ash.
• Copper sulphate crystallises as CuSO₄·5H₂O and gypsum as CaSO₄·2H₂O.
• Sodium carbonate is manufactured by the Solvay or ammonia-soda process and is used in glass and soap making and to soften hard water.

• Ignoring the word 'anhydrous' and calculating for the decahydrate.
• Counting one sodium atom instead of two.
• Confusing sodium carbonate, Na₂CO₃, with sodium bicarbonate, NaHCO₃, which is baking soda.

Formula-mass items give the atomic masses in the stem, so the marks turn entirely on writing the right formula — which means reading the qualifier in the name.

• practice — not a real PYQ

  The formula mass of washing soda, Na₂CO₃·10H₂O, taking H = 1 u, C = 12 u, O = 16 u and Na = 23 u, is

  • (a)106 u
  • (b)124 u
  • (c)286 u
  • (d)322 u

  Answer(c) 286 u — the anhydrous salt is 106 u and the ten water molecules add 10 × 18 = 180 u.

• practice — not a real PYQ

  Water of crystallisation in a salt refers to

  • (a)water used to dissolve the salt
  • (b)a fixed number of water molecules present in one formula unit of the crystal
  • (c)moisture absorbed from the air
  • (d)water produced when the salt is heated in acid

  Answer(b) a fixed number of water molecules present in one formula unit of the crystal — it is part of the crystal structure and counts towards the formula mass.