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A sample of \(\mathrm{H}_{2} \mathrm{S}\) gas is placed in an evacuated, sealed container and heated until the following decomposition reaction occurs at \(1000 \mathrm{K} :\) $$2 \mathrm{H}_{2} \mathrm{S}(g) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \qquad K_{\mathrm{c}}=1.0 \times 10^{-6}$$ If, at a given point in the reaction, the value for the reaction quotient \(Q\) is determined to be \(2.5 \times 10^{-8},\) which of the following is occurring? (A) The concentration of the reactant is decreasing while the concentration of the products is increasing. (B) The concentration of the reactant is increasing while the concentration of the products is decreasing. (C) The system has passed the equilibrium point, and the concentration of all species involved in the reaction will remain constant. (D) The concentrations of all species involved are changing at the same rate.

Step by step solution

01

Understanding the Reaction Quotient and Equilibrium Constant

The reaction quotient (Q) gives the same ratio as the equilibrium constant (\(K_c\)), but Q can be calculated at any time, while \(K_c\) is only true at equilibrium. If Q < \(K_c\), the reaction would shift in the forward direction to reach equilibrium. Conversely, if Q > \(K_c\), the reaction would shift in the reverse direction to reach equilibrium.

02

Comparing Q and \(K_c\)

The given value for Q is \(2.5 \times 10^{-8}\), and the given equilibrium constant \(K_c\) is \(1.0 \times 10^{-6}\). So the condition Q < \(K_c\) is met as \(2.5 \times 10^{-8}\) < \(1.0 \times 10^{-6}\).

03

Deciding the Direction of Reaction

Because Q < \(K_c\), the reaction will need to shift in the forward direction to reach equilibrium. This means that more reactants will be transformed into products, thus the concentration of the reactants will decrease while that of the products will increase.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equilibrium Constant

The equilibrium constant, represented as \(K_c\), is a crucial concept in understanding reactions. It serves as a value that relates the concentrations of products and reactants at chemical equilibrium. Essentially, it provides a snapshot of the ratio between products and reactants when a reaction has reached a state where no further net change in concentration occurs.
\[ K_c = \frac{[\text{products}]}{[\text{reactants}]} \]
As every reaction has its own \(K_c\), knowing this constant helps predict the extent to which a reaction will occur. Smaller \(K_c\) values, for instance, suggest that products are not favored, while larger values indicate more product formation. However, it’s important to remember that \(K_c\) is valid only when the reaction is at equilibrium. This means that \(K_c\) values do not change unless there is a change in temperature.

Chemical Equilibrium

Chemical equilibrium is the stage in a reaction when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of all reactants and products remain constant over time. It's important to note that these concentrations are not necessarily equal, only constant.
During equilibrium, reactions may seem to be still, but they are dynamic and ongoing. Molecules continue to react, forming products and reverting to reactants at balanced rates.

• Equilibrium can be shifted by changing temperature, pressure, or concentration.
• The system will adjust itself to counteract the imposed change, a principle known as Le Chatelier's Principle.

Understanding equilibrium helps in controlling industrial chemical reactions and other processes to optimize yields.

Reaction Shift

Reaction shift refers to the direction a reaction will move to reach equilibrium when disturbed. The reaction quotient \(Q\) plays a vital role in determining this shift. \(Q\) is calculated in the same way as \(K_c\) but represents the ratio of products to reactants at any given point in time, not just at equilibrium.
Given a scenario:

• If \( Q < K_c \), the reaction will shift to the right, meaning that more reactants will convert to products until equilibrium is restored.
• If \( Q > K_c \), the reaction will shift to the left, favoring the conversion of products back into reactants.
• When \( Q = K_c \), the reaction is at equilibrium, and no shift occurs.

In practice, recognizing the direction of a shift helps in predicting how changes in conditions can affect the outcome of a reaction, vital for experimental setups and industrial applications.