Question

If the concentration is expressed moles/litre, the unit of rate constant for a first-order reaction is (a) mole litre \(^{-1} \mathrm{~s}^{-1}\) (b) mole litre \(^{-1}\) (c) \(s^{-1}\) (d) \(\mathrm{mole}^{-1}\)

Short answer

The unit of rate constant for a first-order reaction when the concentration is expressed in moles/litre is \(s^{-1}\), which corresponds to option (c).

Step-by-step solution

Understand the units of rate of reaction

The rate of a reaction is usually measured in terms of how fast the concentration of reactants decreases or the concentration of products increases. If the concentration is expressed in moles/litre and time is in seconds, then the units of rate of reaction is moles litre \(^{-1} \mathrm{~s}^{-1}\).

Apply the concept of order of reaction

In a first-order reaction, the rate of reaction is directly proportional to the concentration of a single reactant. The rate constant (k) is the proportionality constant. It's expressed mathematically as: rate = k [A], where [A] is the concentration of the reactant A. Rearranging the above equation to calculate the units of k gives: k = rate/[A].

Determine the unit of rate constant for a first-order reaction

Substitute the units for the rate of reaction and the concentration of the reactant into the equation for k: k = (moles litre \(^{-1} \mathrm{~s}^{-1}\))/(moles litre \(^{-1}\)). The mole litre \(^{-1}\) on both the numerator and the denominator cancels out, giving the unit for the rate constant of a first order reaction as \(s^{-1}\).

Key concepts

Rate of Reaction

The rate of a chemical reaction tells us how quickly the reactants are transforming into products. To find the rate, we measure how fast the concentration of a substance changes over time. If the concentration is given in moles per liter ( moles/L ) and time is measured in seconds ( s ), then the unit for the rate of reaction becomes moles per liter per second (moles L^-1 s^-1) . It's important because it provides a clear picture of the speed at which a reaction occurs.

• The higher the rate, the faster the reaction progresses.
• This measurement helps us understand how changing conditions might affect the reaction.

Rate Constant

In the context of a first-order reaction, the rate constant ( k ) serves as a crucial factor that connects the rate of reaction with the concentration of the reactant. It's essentially the proportionality constant in the rate law, allowing us to express the rate mathematically:
rate = k [A] .
This equation indicates that the reaction rate depends directly on the concentration, represented by [A] , and a specific constant ( k ) unique to the reaction.

• The value of k provides insights into the reaction's characteristics, such as speed, under given conditions.
• Understanding k helps predict the reaction behavior when scaling up processes.

Units of Rate Constant

For a clear understanding of the rate constant, we need to consider its units, which vary depending on the order of the reaction. In the case of a first-order reaction:
The general form of the rate equation simplifies to,
k = (rate)/[A] .
Here we use the units:

• Rate = moles L^-1 s^-1
• Concentration [A] = moles L^-1

Canceling the moles L^-1 from both the numerator and denominator leaves us with just s^-1 . Thus, the units of the rate constant, k , for a first-order reaction are per second or s^-1.

Reaction Kinetics

Reaction kinetics is the field of chemistry that examines the rates of chemical reactions and the factors influencing them. By studying kinetics, we gain insight into the complex behaviors of reactions, which can aid in the development of efficient processes. Some essential aspects include:

• The determination of the order of a reaction, which tells us the reaction's dependence on the concentration of reactants.
• The understanding of the mechanisms, explaining the sequence of steps at the molecular level.
• The role of temperature, catalysts, and other environmental conditions in influencing reaction rates.

Knowing these allows chemists to control reactions in industrial processes, leading to optimized production methods and reduced costs.