How much CO₂ is produced on heating of 1 kg of carbon ?
- (a)11/3 kg
- (b)3/11 kg
- (c)4/3 kg
- (d)3/4 kg
Correct — A, 11/3 kg. Carbon burns in oxygen by the equation C + O₂ → CO₂, one mole of carbon giving one mole of carbon dioxide. Taking the atomic mass of carbon as 12 and of oxygen as 16, 12 grams of carbon yield 12 + 32 = 44 grams of carbon dioxide. The mass ratio is therefore 44 to 12, which reduces to 11 to 3. Scaling up, 1 kilogram of carbon yields 44/12 kilograms, that is 11/3 kilograms, or about 3.67 kilograms of carbon dioxide. The product weighs more than the carbon burnt because the oxygen from the air has been added to it, and that extra mass is the two-thirds that came out of the atmosphere.
- (b)3/11 kg — This is the ratio inverted. It would mean the carbon dioxide weighed less than the carbon that made it, which is impossible when oxygen has been added to the carbon.
- (c)4/3 kg — This is 16 over 12, the ratio you get by pairing carbon with a single oxygen atom instead of the molecule of oxygen, or by weighing only the oxygen added. It ignores half the oxygen in CO₂.
- (d)3/4 kg — The inverse of option (c), and again smaller than 1 kilogram. Any answer below one can be ruled out by inspection, since the product must be heavier than the carbon alone.
A balanced chemical equation is also a statement about masses. Once you know the formula masses, the coefficients tell you what mass of each substance reacts and what mass forms. For the complete combustion of carbon the equation is C + O₂ → CO₂, so the mass ratio is 12 to 32 to 44. Nothing is created: the 44 grams of product is the 12 grams of carbon plus the 32 grams of oxygen, which is the law of conservation of mass in arithmetic form.
The quickest route in the examination hall is to skip moles altogether and work with the formula masses directly, because the question asks only for a ratio. Divide 44 by 12, get 11 over 3, and stop. Two sanity checks save time: the answer must exceed 1 kilogram, which eliminates two options at a glance; and the two surviving fractions are reciprocals of one another, so choose the one greater than 1. The same relation is what lets an engineer convert tonnes of coal burnt into tonnes of carbon dioxide emitted, the arithmetic behind every emissions figure quoted for a thermal power station.
- C + O₂ → CO₂, with formula masses 12, 32 and 44, so the mass ratio of carbon to carbon dioxide is 12 to 44, that is 3 to 11.
- One kilogram of carbon burnt completely gives 44/12 = 11/3 kilograms, about 3.67 kilograms, of carbon dioxide.
- The product is heavier than the carbon because the oxygen consumed comes from the air; mass is conserved across reactants and products.
- Incomplete combustion in a poor air supply gives carbon monoxide instead, by 2C + O₂ → 2CO, which is why unventilated coal fires are dangerous.
- The same arithmetic converts fuel burnt into carbon dioxide emitted, which is how emission figures for thermal power are calculated.
The whole item is one division, 44 by 12, and the sanity check disposes of half the options.
- Using the atomic mass of oxygen instead of the molecular mass of O₂, which gives 4 over 3.
- Inverting the ratio and reporting a product lighter than the reactant.
- Forgetting that the added mass comes from atmospheric oxygen, so the product must always outweigh the fuel.
NDA sets a short mass or mole calculation from a familiar reaction, usually solvable by one division if the formula masses are known.
Which one of the following has different number of molecules ? (All are kept at normal temperature and pressure)
- (a) 3 gram of Hydrogen
- (b) 48 gram of Oxygen
- (c) 42 gram of Nitrogen
- (d) 2 gram of Carbon
Answer(d) 2 gram of Carbon
Rests on the same conversion between mass and formula mass that this question needs, and rewards the same habit of dividing by the atomic or molecular mass first.
What is the formula mass of anhydrous sodium carbonate? (Given that the atomic masses of sodium, carbon and oxygen are 23 u, 12 u and 16 u respectively)
- (a) 286 u
- (b) 106 u
- (c) 83 u
- (d) 53 u
Answer(b) 106 u
The same arithmetic one step earlier, building a formula mass from atomic masses before any ratio can be taken.
- practice — not a real PYQ
On complete combustion, 24 g of carbon will produce how much carbon dioxide ?
- (a)44 g
- (b)66 g
- (c)88 g
- (d)12 g
Answer(c) 88 g — 12 g of carbon gives 44 g of carbon dioxide, so twice the carbon gives twice the product.
- practice — not a real PYQ
When carbon burns in a limited supply of air, the gas chiefly formed is
- (a)carbon dioxide
- (b)carbon monoxide
- (c)methane
- (d)hydrogen
Answer(b) carbon monoxide — incomplete combustion follows 2C + O₂ → 2CO, which is why unventilated coal fires are dangerous.