Examkin

Question

Difficulty: MediumGay-Lussac's Law of Combining Volumes and Avogadro's Law
A mixture of 10 cm310\text{ cm}^3 of hydrogen sulfide (H2SH_2S) gas and 40 cm340\text{ cm}^3 of oxygen gas was sparked to react completely at constant temperature and pressure according to the equation:
2H2S(g)+3O2(g)→2SO2(g)+2H2O(l)2H_2S(g) + 3O_2(g) \rightarrow 2SO_2(g) + 2H_2O(l)
Assuming the water formed condenses into liquid, what is the total volume of the residual gas mixture?
  1. 35 cm335\text{ cm}^3Answer
  2. B
    25 cm325\text{ cm}^3
  3. C
    10 cm310\text{ cm}^3
  4. D
    45 cm345\text{ cm}^3

Answer

The total volume of the residual gas mixture is 35 cm335\text{ cm}^3.
According to Gay-Lussac's law, 2 cm32\text{ cm}^3 of H2SH_2S reacts with 3 cm33\text{ cm}^3 of O2O_2 to form 2 cm32\text{ cm}^3 of SO2SO_2 gas. Thus, 10 cm310\text{ cm}^3 of H2SH_2S consumes 15 cm315\text{ cm}^3 of O2O_2 and yields 10 cm310\text{ cm}^3 of SO2SO_2. The remaining excess O2O_2 is 40 cm3−15 cm3=25 cm340\text{ cm}^3 - 15\text{ cm}^3 = 25\text{ cm}^3. Combining the unreacted oxygen (25 cm325\text{ cm}^3) and produced sulfur(IV) oxide (10 cm310\text{ cm}^3) gives a total residual gas volume of 35 cm335\text{ cm}^3.

Step-by-Step Solution

1
Determine the stoichiometric volume ratios from the balanced chemical equation
2 volumes of H2S(g)H_2S(g) react with 3 volumes of O2(g)O_2(g) to produce 2 volumes of SO2(g)SO_2(g).
According to Gay-Lussac's Law of Combining Volumes, gases react in simple whole-number volume ratios at constant temperature and pressure.
2
Calculate the volume of oxygen required to react with 10 cm310\text{ cm}^3 of H2SH_2S
Volume of O2O_2 used = 10 cm3×32=15 cm310\text{ cm}^3 \times \frac{3}{2} = 15\text{ cm}^3.
Since 10 cm310\text{ cm}^3 of H2SH_2S is available, it is the limiting reactant and requires 15 cm315\text{ cm}^3 of O2O_2.
3
Find the volume of unreacted excess oxygen
Unreacted O2=40 cm3−15 cm3=25 cm3O_2 = 40\text{ cm}^3 - 15\text{ cm}^3 = 25\text{ cm}^3.
Subtracting the reacted oxygen volume from the initial volume gives the excess.
4
Calculate the volume of gaseous SO2SO_2 produced
Volume of SO2=10 cm3×22=10 cm3SO_2 = 10\text{ cm}^3 \times \frac{2}{2} = 10\text{ cm}^3.
The mole ratio of H2SH_2S to SO2SO_2 is 2:22:2, so 10 cm310\text{ cm}^3 of H2SH_2S produces 10 cm310\text{ cm}^3 of SO2SO_2 gas. Water is liquid so its volume is neglected.
5
Calculate total residual gas volume
Total residual volume = 25 cm3 (excess O2)+10 cm3 (produced SO2)=35 cm325\text{ cm}^3 \text{ (excess } O_2) + 10\text{ cm}^3 \text{ (produced } SO_2) = 35\text{ cm}^3.
The residual gas consists of both unreacted excess reactant and gaseous product.

Key Concept

Gay-Lussac's Law of Combining Volumes
Rate this question

Topics

Gay-Lussac's Law of Combining Volumes and Avogadro's Law

More questions from this topic