Question

As with any combustion reaction, the products of combusting a hydrocarbon fuel (CxHy) with oxygen (O2) are carbon dioxide (CO2) and water (H2O).

A mass of 16.89 g for an unknown fuel was combusted in a reaction vessel containing an unknown amount of oxygen. At the end of the reaction, there still remained 16.85 g of the fuel as well as 0.0654 g of water and 0.1198 g of carbon dioxide. The oxygen was completely consumed during the reaction.

How many molecules of oxygen gas were initially present in the reaction vessel?

Express the number of molecules to three significant digits

Answer 1

Note:- the reaction will contain the same amount of oxygen gas as the amount of oxygen gas found in water and carbon dioxide.

Given data,

Mass of H2O = 0.0654g

Mass of CO2 = 0.1198g

We know that, Molar mass of ...

(1) O = 15.9990g/mol

(2) H2O = 18.0153g/mol

(3) CO2 = 44.0100g/mol

(4) O2 = 31.9980g/mol

Step(1) Calculation amount of oxygen present in Water.

From the stoichiometry of formula of water.

1mol H2O contained 1 mol oxygen

Or

18.0153 g (i,e, mass of 1mol water) water contained 15.9990g (i,e mass of 1mol oxygen) oxygen.

So

1.0 g water contained (15.9990/18.0153)g oxygen

Hence,

0.0654g water contained (15.9990/18.0153)×0.0654g oxygen

Mass of oxygen in 0.0654g water = (15.9990/18.0153)×0.0654

Mass of oxygen in 0.0654g water = 0.0581g

Step(2) calculation amount of Oxygen present in carbon dioxide .

From the stoichiometry of chemical Formula of carbon dioxide.

1mol CO2 contained 2 mol oxygen.

Or

44.0100g (i,e mass of 1mol CO2) contained 2×(15.9990)g (i,e mass of 2 mol oxygen) oxygen.

Or

44.0100 g CO2 contained 31.9980g Oxygen

So,

1.0 g CO2 contained (31.9980/44.0100) g oxygen

Hence,

0.1198g CO2 contained (31.9980/44.0100)×0.1198 g oxygen.

Mass of Oxygen in 0.1198 g CO2 = (31.9980/44.0100)×0.1198g

Mass of Oxygen in 0.1198g CO2 = 0.0871g

Step(3) Calculation total amount of Oxygen.

Total amount of Oxygen = mass of oxygen in 0.0654g water + mass of Oxygen in 0.1198g Carbon dioxide.

Total amount of Oxygen = 0.0581g + 0.0871

Total amount of Oxygen = 0.1452g

Step (4) Calculation For number of mole of Oxygen molecule (O2)

number of Oxygen molecule = (mass of Oxygen/molar mass of oxygen molecule)

number of Oxygen molecule = (0.1452g/31.9980g/mol)

number of Oxygen molecule = 4.538×10^-3mol