Chapter 9: Problem 18
For a reaction; \(3 A \longrightarrow\) Products, it is found that the rate of reaction becomes nine times if concentration of \(A\) is increased three times, calculate order of reaction.
Short Answer
Expert verified
The order of the reaction with respect to reactant A is 2, indicating it's a second order reaction.
Step by step solution
01
Understanding the Rate Law
The rate of a reaction can be expressed by its rate law, which shows how the rate is dependent on the concentrations of reactants. For a general reaction, the rate law is written as: rate = k[A]^n, where [A] is the concentration of reactant A, k is the rate constant, and n is the order with respect to A.
02
Identifying the Change in Rate
From the given information, when the concentration of A is increased by a factor of 3, the rate of the reaction becomes nine times faster. This can be mathematically expressed as: rate2 = 9 * rate1, where rate1 is the initial rate and rate2 is the new rate after increasing the concentration of A.
03
Setting Up the Rate Equation with Given Data
Let's use the rate law and the provided information to set up an equation that relates the initial and new rates. If [A1] is the initial concentration, then the rate1 is k[A1]^n. When the concentration of A is tripled, the new concentration is 3[A1], so the rate2 can be written as k[3A1]^n.
04
Substituting and Simplifying the Equation
Substituting the values into the rate equation yields: 9 * k[A1]^n = k(3[A1])^n. Simplifying gives us 9 * k[A1]^n = k(3^n)[A1]^n.
05
Isolating the Order of Reaction (n)
By dividing both sides by k[A1]^n, we get 9 = 3^n. To find n, we need to solve this equation.
06
Calculating the Order of Reaction
Take the logarithm of both sides, and we get log(9) = n*log(3). Since log(3^2) = log(9), we get 2*log(3) = n*log(3). By isolating n, we find that n = 2, which means the reaction is second order with respect to reactant A.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Rate Law
Understanding rate law is crucial for grasping the basics of chemical kinetics. It's an equation that relates the rate of a chemical reaction to the concentration of its reactants. In the simplest form, the rate law can be represented as 'rate = k[A]n', where 'rate' is the speed at which the reaction occurs, 'k' is the rate constant unique to each reaction, 'A' is the concentration of reactant 'A', and 'n' represents the order of the reaction with respect to 'A'.
The rate constant 'k' is a measure of how quickly a reaction proceeds, and it's influenced by factors like temperature and the presence of catalysts. The reaction order 'n' is an exponent that denotes how the rate is affected by the concentration of the reactant. If 'n' is 1, the reaction is first-order, and the rate will directly double if you double the concentration. Higher orders result in a more complex relationship. For instance, in a second-order reaction, doubling the concentration of the reactant will quadruple the rate.
Through rate laws, chemists can predict how different conditions will affect the speed of chemical reactions, which is paramount for both industrial applications and academic research.
The rate constant 'k' is a measure of how quickly a reaction proceeds, and it's influenced by factors like temperature and the presence of catalysts. The reaction order 'n' is an exponent that denotes how the rate is affected by the concentration of the reactant. If 'n' is 1, the reaction is first-order, and the rate will directly double if you double the concentration. Higher orders result in a more complex relationship. For instance, in a second-order reaction, doubling the concentration of the reactant will quadruple the rate.
Through rate laws, chemists can predict how different conditions will affect the speed of chemical reactions, which is paramount for both industrial applications and academic research.
Reaction Kinetics
Reaction kinetics is the field of chemistry that studies the speed or rate of chemical reactions and the mechanisms by which they occur. Key factors influencing the rate of a chemical reaction include reactant concentrations, temperature, and the presence of a catalyst.
The kinetic analysis of a reaction helps determine the rate law, which is discovered by experimentally measuring how the changes in concentration affect the reaction rate. By modifying the concentrations of reactants in a systematic way and measuring the resulting change in reaction rate, chemists can deduce the order of the reaction and the rate constant.
The kinetic analysis of a reaction helps determine the rate law, which is discovered by experimentally measuring how the changes in concentration affect the reaction rate. By modifying the concentrations of reactants in a systematic way and measuring the resulting change in reaction rate, chemists can deduce the order of the reaction and the rate constant.
Importance of Temperature
Temperature is another vital piece of the puzzle. Generally, increasing the temperature will speed up a reaction because the reactants gain kinetic energy, leading to more frequent and energetic collisions. This is quantitatively explained by the Arrhenius Equation, which links the rate constant 'k' to the temperature.Role of Catalysts
Moreover, catalysts are substances that increase the reaction rate without getting consumed in the process. They work by providing an alternative reaction pathway with a lower activation energy, which significantly speeds up the rate at which the reaction equilibrium is reached.Concentration Dependence
The concentration of reactants plays a fundamental role in determining the rate of a chemical reaction. As we’ve seen with the rate law, the rate is often dependent on the concentration of the reactants raised to a power, which is the reaction order.
The exercise provided is a perfect illustration of concentration dependence. When the concentration of the reactant 'A' was increased threefold, the reaction rate increased nine times, indicating a relationship not just proportional but to the square, which suggests a second-order reaction.
This dependency is why chemists often run experiments at different concentrations to identify the rate law and order of reaction. In practical terms, understanding concentration dependence is essential. For instance, in pharmaceuticals, it is pivotal to know how quickly a drug will react, which depends on the concentration of its active ingredient. This knowledge is crucial for dosing and ensuring the drug's efficacy without causing adverse effects due to too rapid metabolism. The simple adjustment in reactant concentration can lead to significant changes in reaction time, which is important for controlling industrial processes, laboratory experiments, and the stability of products.
The exercise provided is a perfect illustration of concentration dependence. When the concentration of the reactant 'A' was increased threefold, the reaction rate increased nine times, indicating a relationship not just proportional but to the square, which suggests a second-order reaction.
This dependency is why chemists often run experiments at different concentrations to identify the rate law and order of reaction. In practical terms, understanding concentration dependence is essential. For instance, in pharmaceuticals, it is pivotal to know how quickly a drug will react, which depends on the concentration of its active ingredient. This knowledge is crucial for dosing and ensuring the drug's efficacy without causing adverse effects due to too rapid metabolism. The simple adjustment in reactant concentration can lead to significant changes in reaction time, which is important for controlling industrial processes, laboratory experiments, and the stability of products.