A mixture of 15\text{ cm}^3 of ethene (C_2H_4) and 50\text{ cm}^3 of oxygen gas was explod… — JAMB UTME

A mixture of $15\text{ cm}^3$ of ethene ( $C_2H_4$ ) and $50\text{ cm}^3$ of oxygen gas was exploded at constant temperature and pressure. If the resulting mixture was cooled to room temperature, what is the total volume of the residual gas in $\text{cm}^3$ ?

Answer: 35 cm^3

Answer

35 cm³

According to Gay-Lussac's Law,

15\text{ cm}^3

of ethene reacts with

45\text{ cm}^3

of oxygen to produce

30\text{ cm}^3

of carbon(IV) oxide gas. Since

50\text{ cm}^3

of oxygen was initially present,

5\text{ cm}^3

of unreacted oxygen gas remains. Upon cooling to room temperature, water condenses to liquid, leaving a total residual gaseous volume of

5\text{ cm}^3 + 30\text{ cm}^3 = 35\text{ cm}^3

Step-by-Step Solution

Write the balanced equation for the complete combustion of ethene gas.

C_2H_4(g) + 3O_2(g) \rightarrow 2CO_2(g) + 2H_2O(l)

By Gay-Lussac's Law of Combining Volumes, gases react in simple whole-number volume ratios equal to their stoichiometric coefficients at constant temperature and pressure.

Determine the volume of oxygen required and the unreacted excess volume.

Volume of

O_2

consumed =

3 \times 15\text{ cm}^3 = 45\text{ cm}^3

. Remaining unreacted

O_2 = 50\text{ cm}^3 - 45\text{ cm}^3 = 5\text{ cm}^3

Since

15\text{ cm}^3

C_2H_4

requires only

45\text{ cm}^3

O_2

, oxygen is in excess and ethene is the limiting reactant.

Calculate the volume of carbon(IV) oxide gas produced.

Volume of

CO_2

produced =

2 \times 15\text{ cm}^3 = 30\text{ cm}^3

1 volume of

C_2H_4

produces 2 volumes of

CO_2

gas.

Calculate the total volume of the residual gaseous mixture after cooling to room temperature.

Total residual gaseous volume =

5\text{ cm}^3 \text{ (excess } O_2\text{)} + 30\text{ cm}^3 \text{ (produced } CO_2\text{)} = 35\text{ cm}^3

Water formed is in the liquid state at room temperature and contributes negligible volume to the gaseous mixture.

Key Concept

Gay-Lussac's Law of Combining Volumes and Residual Gas Volume Calculations

Estimated Time:1m 30s

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