Question

Iodide and hypochlorite ion react in aqueous solution according to the reaction below: \(\mathrm{I}^{-}+\mathrm{OCl}^{-} \rightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}\) If the concentration of \(\mathrm{OH}^{-}\)in the solution is doubled, the rate of the reaction is halved. What is the order of the reaction with respect to \(\mathrm{OH}^{-}\)? a. \(+2\) b. \(+1\) c. \(-2\) d. \(-1\)

Short answer

The reaction order with respect to \( \mathrm{OH}^{-} \) is \(-1\).

Step-by-step solution

Understanding the problem

Read the problem carefully to understand what we are being asked. We need to find the order of the reaction with respect to the hydroxide ion, \\( \mathrm{OH}^{-} \). The rate of reaction changes when the concentration of \\( \mathrm{OH}^{-} \) is doubled, indicating that \\( \mathrm{OH}^{-} \) affects the reaction rate.

Analyzing the information

We know that doubling the concentration of \\( \mathrm{OH}^{-} \) leads to halving the reaction rate. This implies a negative reaction order with respect to \\( \mathrm{OH}^{-} \). The order of the reaction determines how concentration changes affect the rate. A negative order means increasing the concentration decreases the rate.

Relating concentration change to rate change

If the concentration of \\( \mathrm{OH}^{-} \) is doubled \((2^{\Delta n})\) and the rate is halved \((0.5\times)\), we relate the change in rate to the change in concentration by equating them using the order \( \Delta n \). This gives the equation: \\[ 2^{\Delta n} = \frac{1}{2} \]

Solving for the reaction order \( \Delta n \)

To solve \\( 2^{\Delta n} = \frac{1}{2} \), we take the logarithm base 2 of both sides: \\( \Delta n = \log_2{\left(\frac{1}{2}\right)} \). This results in: \\( \Delta n = -1 \). Hence, the order of the reaction with respect to \\( \mathrm{OH}^{-} \) is \(-1\).

Key concepts

Negative Reaction Order

In chemical kinetics, the concept of reaction order plays a crucial role in understanding how the concentration of reactants affects the rate of reaction. A negative reaction order is an interesting scenario where increasing the concentration of a reactant leads to a decrease in the reaction rate. This might seem counterintuitive because we often associate increased concentration with a faster reaction.
When examining a reaction, the order with respect to a specific reactant can be determined from experimental data. In this situation, the order of the reaction is negative for hydroxide ions, \( \mathrm{OH}^{-} \). Doubling the concentration results in halving the rate of the reaction. This indicates a negative order because the changes in concentration and rate move in opposite directions.

For a reaction like \( \mathrm{I}^{-} + \mathrm{OCl}^{-} \rightarrow \mathrm{OI}^{-} + \mathrm{Cl}^{-} \), having a negative order of \( -1 \) with respect to \( \mathrm{OH}^{-} \) suggests that the reaction mechanism involves a complex participation of \( \mathrm{OH}^{-} \), such as impacting the equilibrium state or the stability of intermediates.

Rate of Reaction

The rate of reaction is a measure of how quickly reactants are transformed into products in a chemical reaction. It is typically expressed as a change in concentration of a reactant or product per unit time. Understanding the rate of reaction helps scientists predict how changing conditions like temperature or concentration affect the speed of a reaction, allowing better control over chemical processes.
While a positive reaction order implies that an increase in concentration leads to a faster reaction, the inverse is true for a negative reaction order. In our specific problem, when the concentration of \( \mathrm{OH}^{-} \) is doubled, the rate of the reaction with \( \mathrm{I}^{-} \) and \( \mathrm{OCl}^{-} \) ions is reduced.
This inverse relationship is a result of the negative order, indicating that the presence of extra \( \mathrm{OH}^{-} \) ions may hinder the reaction's progress, possibly by disrupting a specific step in the reaction pathway or altering the energy landscape.

Concentration Effects

Concentration plays a significant role in chemical reactions as it determines how frequently reactant molecules collide successfully to form products. However, the effect of concentration on reaction rate is not always straightforward. In the case of our problem, changing the concentration of \( \mathrm{OH}^{-} \) ions leads to a different reaction rate due to its negative order.
A key factor to consider is that changes in concentration can affect reaction kinetics through various mechanisms:

• Collisions: More reactants often mean more collisions, but when it comes to negative reaction orders, these collisions might lead to destabilizing the transition state or inhibiting the reaction.
• Equilibrium shifts: In some reactions, an excess of a particular reactant can shift chemical equilibria, thus slowing down specific pathways.
• Intermediates: Increased concentrations may lead to the formation of intermediates that are less reactive or even obstructive to the pathway towards the desired products.

Understanding the exact effect of concentration changes requires detailed study of the reaction mechanism, but recognizing these general principles helps in decoding the often complex nature of chemical reactions.