Stoichiometry: 3.414 - Limiting reagents in gas reaction

This concept of reacting volumes may be easily applied to calculate excess and limiting reagents in gaseous reactions.

Syllabus reference

Reactivity 2.1.3 - The limiting reactant determines the theoretical yield.

Identify the limiting and excess reactants from given data.

Guidance

Distinguish between the theoretical yield and the experimental yield.

Tools and links

Tool 1, Inquiry 1, 2, 3 - What errors may cause the experimental yield to be i) higher and ii) lower than the theoretical yield?

Limiting gas volume

Limiting gas volume

By inspection of the volumes reacting, it is a simple matter to determine the limiting reagent and which is in excess.

N₂	+	3H₂	→	2NH₃
1 volume		3 volumes		2 volumes
Experimental data
300 cm³		300 cm³		???
excess		limiting reagent	→	200cm³ ammonia

In the table above, the amounts of nitrogen and hydrogen provided initially are 300 cm³ of each.

But from the stoichoimetry of the equation we can see that 300cm³ of nitrogen gas would require 3 x that volume of hydrogen gas for complete reaction. The nitrogen is therefore in excess and only 100cm³ of the nitrogen can react with hydrogen.

The reaction proportions then are 100 cm³ nitrogen reacting with 300 cm³ hydrogen to produce 200 cm³ of ammonia.

Note: If only 100cm³ nitrogen reacts there is also 200 cm³ nitrogen left over at the end of the reaction.

Example: Calculate (i) the volume of carbon dioxide produced when 300 cm³ of methane burns in 1000 cm³ oxygen and (ii) the final volume of the reaction mixture.

The equation for the reaction:

CH₄(g) + 2O₂(g) CO₂(g) + 2H₂O(l)

The ratio of gas volumes is 1 volume of methane reacts with 2 volumes of oxygen producing 1 volume of carbon dioxide (and liquid water, no volume)

There is 300 cm³ methane - this needs 2 x 300 cm³ = 600 cm³ oxygen to burn completely and produce 1 x 300 cm³ carbon dioxide = 300cm³ carbon dioxide

During the course of the reaction 300 cm³ methane and 600 cm³ of oxygen is used up from an initial total of 300 cm³ of methane and 1000 cm³ oxygen.

There is 400 cm³ of oxygen in excess therefore the final mixture contains 300 cm³ carbon dioxide + 400 cm³ of oxygen = 700 cm³ of gas

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