Consider the reaction: 8H2S(g)+4O2(g)→8H2O(g)+S8(g) Δ[H2S]/Δt = -0.071 M/s . A.) Find Δ[O2]/Δt Express your answer to two significant figures and include the appropriate units. B.)Find Δ[H2O]/Δt Express your answer to two significant figures and include the appropriate units. C)Find Δ[S8]/Δt Express your answer to two significant figures and include the appropriate units. D)Find the rate of the reaction. Express your answer to two significant figures and include the appropriate units.
The Correct Answer and Explanation is :
To solve this problem, we will use the stoichiometric coefficients of the balanced reaction and the rate of change of the concentration of ( \text{H}_2\text{S} ), ( \Delta[\text{H}_2\text{S}]/\Delta t = -0.071 \, \text{M/s} ), to find the rates of change for the other reactants and products in the reaction.
The balanced chemical equation is:
[
8 \, \text{H}_2\text{S}(g) + 4 \, \text{O}_2(g) \rightarrow 8 \, \text{H}_2\text{O}(g) + \text{S}_8(g)
]
The key to solving these problems is understanding how the rate of change of one substance relates to the others through their stoichiometric coefficients.
A) Find ( \Delta[\text{O}_2]/\Delta t ):
From the balanced equation, we can see that for every 8 molecules of ( \text{H}_2\text{S} ) consumed, 4 molecules of ( \text{O}_2 ) are consumed. This gives the ratio of ( \text{H}_2\text{S} ) to ( \text{O}_2 ) as ( 8 : 4 ), or ( 2 : 1 ). Therefore, the rate of change of ( \text{O}_2 ) is half the rate of change of ( \text{H}_2\text{S} ) but positive because oxygen is being consumed.
[
\Delta[\text{O}_2]/\Delta t = \frac{1}{2} \times (-0.071 \, \text{M/s}) = 0.035 \, \text{M/s}
]
Answer: ( \Delta[\text{O}_2]/\Delta t = 0.035 \, \text{M/s} )
B) Find ( \Delta[\text{H}_2\text{O}]/\Delta t ):
Similarly, from the balanced equation, we see that for every 8 molecules of ( \text{H}_2\text{S} ) consumed, 8 molecules of ( \text{H}_2\text{O} ) are produced, meaning that the rates of change for ( \text{H}_2\text{S} ) and ( \text{H}_2\text{O} ) are the same in magnitude, but the rate for ( \text{H}_2\text{O} ) is positive because it is being produced.
[
\Delta[\text{H}_2\text{O}]/\Delta t = \Delta[\text{H}_2\text{S}]/\Delta t = -0.071 \, \text{M/s}
]
Answer: ( \Delta[\text{H}_2\text{O}]/\Delta t = 0.071 \, \text{M/s} )
C) Find ( \Delta[\text{S}_8]/\Delta t ):
For every 8 molecules of ( \text{H}_2\text{S} ) consumed, 1 molecule of ( \text{S}_8 ) is produced. Therefore, the rate of change of ( \text{S}_8 ) is one-eighth of the rate of change of ( \text{H}_2\text{S} ), and positive because sulfur is being produced.
[
\Delta[\text{S}_8]/\Delta t = \frac{1}{8} \times (-0.071 \, \text{M/s}) = 0.0089 \, \text{M/s}
]
Answer: ( \Delta[\text{S}_8]/\Delta t = 0.0089 \, \text{M/s} )
D) Find the rate of the reaction:
The rate of the reaction is the rate of change of any reactant or product, but we will use ( \text{H}_2\text{S} ) since we have its rate. The rate is typically expressed in terms of the consumption of reactants or the production of products. We will use the absolute value of ( \Delta[\text{H}_2\text{S}]/\Delta t ) to represent the overall rate:
[
\text{Rate of the reaction} = \left| \Delta[\text{H}_2\text{S}]/\Delta t \right| = 0.071 \, \text{M/s}
]
Answer: Rate of the reaction = ( 0.071 \, \text{M/s} )
Summary of Answers:
- A) ( \Delta[\text{O}_2]/\Delta t = 0.035 \, \text{M/s} )
- B) ( \Delta[\text{H}_2\text{O}]/\Delta t = 0.071 \, \text{M/s} )
- C) ( \Delta[\text{S}_8]/\Delta t = 0.0089 \, \text{M/s} )
- D) Rate of the reaction = ( 0.071 \, \text{M/s} )
Explanation:
- The rate of change for each substance in the reaction is determined by their stoichiometric coefficients relative to the substance whose rate is provided, which is ( \text{H}_2\text{S} ).
- The stoichiometry helps to scale the rate of change for other substances.
- The overall rate of the reaction is based on the rate of consumption of reactants or production of products, which is represented by the rate of ( \text{H}_2\text{S} ).