Question

The rate constant of a reaction is equal to its rate constant at constant temperature when the concentration of the reactants is (a) unity (b) zero (c) two (d) three

Short answer

The rate constant of a reaction remains equal to its rate constant at constant temperature, regardless of the concentration of reactants. Therefore, it's the same when the concentrations are (a) unity (b) zero (c) two (d) three.

Step-by-step solution

Comprehension of Rate Constant

First, it's fundamental to understand what a rate constant is. In a reaction, the rate constant (often denoted by k) is a proportionality constant connecting the rates of reaction to the concentrations of the reactants. In general, a larger k leads to a faster reaction. The value of the rate constant is independent of the concentration of reactants, but it is dependent on temperature.

Analyzing Case (a) - Unity Concentration

When the concentration of reactants is one (unity), it doesn't alter the value of the rate constant. Therefore, the rate constant of the reaction is equal to its rate constant at constant temperature.

Analyzing Case (b) - Zero Concentration

In the case when the concentration of reactants is zero, the rate of reaction itself becomes zero because there are no reactants to react. The rate constant remains unaffected and is not zero.

Analyzing Case (c) - Concentration of Two

Even when the concentration of reactants is two, it doesn't impact the rate constant. Hence, the rate constant remains the same as at constant temperature.

Analyzing Case (d) - Concentration of Three

Equally, when the concentration is three, the rate constant of the reaction stays equal to its rate constant at constant temperature. Again, this is because the rate constant is independent of the concentration of reactants.

Key concepts

Understanding Reaction Rate

The reaction rate is a measure of how fast a chemical reaction occurs. It is usually expressed in terms of the change in concentration of a reactant or product per unit time. Reaction rate can be influenced by various factors, including the nature of the reactants, temperature, and the presence of a catalyst.

To understand the reaction rate further, consider these points:

• The rate of reaction is directly proportional to the concentration of the reactants. This means if the concentration increases, the reaction rate typically increases as well.
• Temperature can affect the reaction rate. Generally, higher temperatures increase the reaction rate because the molecules collide more frequently with greater energy.

The reaction rate is crucial in determining how long a reaction will take to reach completion. By manipulating the conditions of the reaction, such as altering the temperature or concentration, chemists can control the speed of a reaction.

Role of Concentration of Reactants

The concentration of reactants is one of the key factors determining the rate of a reaction. As mentioned before, the reaction rate is often proportional to the concentration of the reactants. This relationship is generally expressed as:\[ ext{Rate} = k imes [ ext{A}]^m imes [ ext{B}]^n \]where \(k\) is the rate constant, \([ ext{A}]\) and \([ ext{B}]\) are the concentrations of reactants A and B, and \(m\) and \(n\) are the orders of the reaction with respect to A and B.

• Increased concentration typically leads to a higher reaction rate, due to more frequent molecular collisions.
• The rate constant \(k\) remains unchanged by changes in concentration, meaning the intrinsic speed of the reaction is not altered.

By understanding how concentration affects the reaction rate, chemists can predict how changes in a reaction's environment will alter its progress. This is particularly important in industrial applications where precise control is needed.

Temperature Dependence of Rate Constant

The rate constant, denoted by \(k\), is significantly influenced by temperature. According to the Arrhenius equation, the rate constant \(k\) can be expressed as:\[ k = Ae^{-E_a/RT} \]where \(A\) is the frequency factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. This equation highlights several important points:

• The rate constant increases with temperature. As temperature rises, molecules gain more energy, which increases the likelihood of effective collisions.
• The activation energy \(E_a\) defines the sensitivity of the reaction to temperature changes. Reactions with lower activation energies are more sensitive to temperature variations.

Understanding the temperature dependence of \(k\) is crucial in both laboratory settings and industrial processes, as it helps in controlling reaction kinetics effectively. By adjusting the temperature, scientists and engineers can either speed up or slow down a reaction, depending on the desired outcome.