NDA (II) 2016 General Ability Test · Question 66 of 150

Correct — B, two volumes of ammonia. The balanced equation for the synthesis is N2 + 3H2 giving 2NH3 — one molecule of nitrogen and three of hydrogen produce two molecules of ammonia. For gases measured at the same temperature and pressure that molecular ratio is also a volume ratio, because equal volumes of any gases under the same conditions hold equal numbers of molecules. So one volume of nitrogen with three volumes of hydrogen yields two volumes of ammonia, and the ratio 1 : 3 : 2 is exactly the simple whole-number relationship that Gay-Lussac's law of combining volumes predicts. Notice what this means physically: four volumes of gas go in and only two come out. Mass is conserved in the reaction, but volume is not, because the same atoms have been repacked into fewer molecules.

• (a)one volume of ammonia — This would mean one molecule of ammonia forming from one nitrogen and three hydrogen molecules, which leaves a nitrogen atom and three hydrogen atoms unaccounted for. Atoms cannot vanish, so the equation would not balance.
• (c)three volumes of ammonia — Three molecules of NH3 would need three nitrogen atoms, but only two are available from one N2 molecule. The number three here comes from the hydrogen coefficient and has simply been carried across to the wrong side.
• (d)one and a half volumes of ammonia — Gay-Lussac's law says the volumes of reacting and product gases stand in simple whole-number ratios, so a fractional volume is ruled out on principle as well as by the balanced equation.

Gay-Lussac's law of combining volumes states that when gases react, the volumes they consume and produce bear a simple whole-number ratio to one another, provided all are measured at the same temperature and pressure. Avogadro's law explains why: equal volumes contain equal numbers of molecules, so a volume ratio is a molecule ratio. Together they let you read a balanced chemical equation directly as a statement about gas volumes.

The safe method is to write the balanced equation first and only then translate coefficients into volumes. Balancing N2 + 3H2 gives 2NH3, and the coefficients 1, 3 and 2 become the volumes. A common instinct is to expect volume to be conserved, as mass is, and to look for an answer that adds up to four. It does not work that way for gases, because volume tracks the number of molecules and this reaction packs four molecules into two. Industrially this same reaction is the Haber-Bosch process, run at a pressure of a few hundred atmospheres and around 400 to 500 degrees Celsius over an iron catalyst, and the drop in volume is precisely why high pressure pushes the yield up.

• The balanced equation is N2 + 3H2 giving 2NH3, so the volume ratio is 1 : 3 : 2.
• Gay-Lussac's law of combining volumes holds only when all gases are measured at the same temperature and pressure.
• Avogadro's law supplies the reason a volume ratio is also a molecule ratio.
• Four volumes of reacting gas give two volumes of product, so gas volume is not conserved even though mass is.
• Industrial ammonia is made by the Haber-Bosch process, at high pressure and around 400 to 500 degrees Celsius over an iron catalyst.

• Expecting the total gas volume to stay the same across a reaction, as mass does.
• Reaching for a fractional answer when the law itself guarantees a whole-number ratio.

NDA GAT tests gas stoichiometry both as a named law and as a small volume calculation like this one, so be able to move between the equation and the volumes in either direction.

• practice — not a real PYQ

  Two volumes of hydrogen combine with one volume of oxygen to give

  • (a)one volume of water vapour
  • (b)two volumes of water vapour
  • (c)three volumes of water vapour
  • (d)half a volume of water vapour

  Answer(b) two volumes of water vapour — the balanced equation 2H2 + O2 giving 2H2O fixes the ratio at 2 : 1 : 2.

• practice — not a real PYQ

  The industrial synthesis of ammonia from nitrogen and hydrogen is known as the

  • (a)Ostwald process
  • (b)Contact process
  • (c)Haber-Bosch process
  • (d)Solvay process

  Answer(c) Haber-Bosch process — run at high pressure over an iron catalyst.