Question

The rate constant of a reaction depends on (a) temperature (b) pressure (c) extent of reaction (d) initial concentration of the reactant

Short answer

The rate constant of a reaction depends on temperature and, in cases involving gases, pressure; it does not depend on the extent of reaction or the initial concentration of the reactant.

Step-by-step solution

Understanding the Concept of Rate Constant

The rate constant of a reaction is a proportionality constant in the rate equation that provides a relationship between the rate of a chemical reaction and the concentrations of the reactants. It is influenced by certain factors that affect the speed at which a reaction occurs.

Analyzing Each Option

(a) Temperature directly affects the rate constant; as temperature increases, the rate constant generally increases due to higher kinetic energy of molecules.(b) Pressure primarily affects reactions involving gases; an increase in pressure can increase the rate constant for gaseous reactants.(c) The extent of reaction does not affect the rate constant as it is constant for a given reaction at a specific temperature.(d) Initial concentration of the reactant does not affect the rate constant; the rate constant is independent of the concentrations of the reactants.

Comparing Options to Determine Dependency

By comparing the given options, we can see that the rate constant depends on temperature and, for gases, on pressure; it does not depend on the extent of the reaction or the initial concentration of reactants.

Key concepts

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rates of chemical reactions and the mechanisms by which they occur. It provides valuable insights into how different conditions, like temperature and pressure, can affect the speed of a reaction. Key parameters in this field include the rate constant, activation energy, reaction order, and half-life of a reaction. The rate constant, in particular, is a critical factor as it represents the speed at which a reaction proceeds under certain conditions and is used in the rate law equation to quantify the reaction rate.

Reaction Rate

The reaction rate is defined as the speed at which the concentrations of reactants decrease or the concentrations of products increase over time. It can be expressed using the general rate law equation:
\( rate = k[A]^m[B]^n \)
where \( k \) is the rate constant, \( [A] \) and \( [B] \) are the concentrations of the reactants, and \( m \) and \( n \) are the orders of the reaction with respect to each reactant. The units of the rate constant can vary depending on the reaction order. Understanding how the rate constant changes with different conditions is vital for controlling reaction speeds in various industrial and research applications.

Temperature and Reaction Rate

Temperature plays a crucial role in chemical kinetics. According to the Arrhenius equation, the rate constant \( k \) is exponentially related to temperature:
\( k = A e^{(-Ea/RT)} \)
where \( A \) is the pre-exponential factor, \( Ea \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. As the temperature increases, molecules move faster and collide more frequently with sufficient energy to react, resulting in an increased rate constant and thus a faster reaction rate. This is why reactions tend to accelerate with heat and why controlling temperature is essential in chemical processes.

Pressure and Reaction Rate

For reactions involving gaseous reactants, pressure can significantly influence the rate of reaction. According to Le Chatelier's principle, increasing the pressure will favor the movement of the reaction towards the side with fewer gas molecules. As pressure increases, reactant molecules are pushed closer together, which can increase the frequency of collisions and, potentially, the rate of reaction. However, this effect is mostly relevant for reactions where gases are involved, and there's a change in the number of moles of gas during the reaction. For reactions in liquid or solid phase, pressure has a negligible effect on the reaction rate compared to temperature.