Problem 82 - Introductory Chemistry Atoms First

Question

True or false? (a) The orders \(x\) and \(y\) in a rate law are written directly from the balancing coefficients from the balanced equation for a reaction. (b) The overall order of a reaction is the sum of the individual orders of the reactants. (c) If you start a reaction with just reactants (no product present), then the rate of the reaction will remain constant with time. (d) If you start a reaction with just reactants (no product present), then the rate of the reaction will decrease with time.

Step-by-Step Solution

Answer

(a) False - The orders x and y in a rate law are not necessarily the same as the balancing coefficients from the balanced equation for a reaction. (b) True - The overall order of a reaction is the sum of the individual orders of the reactants. (c) True or False - The rate of reaction may remain constant with time for zero-order reactions, but for reactions of first order or higher, the rate will change with time. (d) True or False - For first-order reactions or higher, the rate of the reaction will decrease with time, but for zero-order reactions, the rate will not decrease with time.

Step 1: a) Balancing coefficients and rate law orders

This statement is false. The orders x and y in a rate law are not necessarily the same as the balancing coefficients from the balanced equation for a reaction. The rate law and its order generally need to be determined experimentally. The balancing coefficients might give an initial guess for the rate law, but they may not always be the correct sums.

Step 2: b) Overall order of a reaction

This statement is true. The overall order of a reaction is the sum of the individual orders of the reactants. If the reaction rate law is given by \(Rate = k[A]^x[B]^y\), the overall order of the reaction would be \((x + y)\), where x and y are the individual orders of reactants A and B respectively.

Step 3: c) Constant rate with just reactants

This statement can be true or false depending on the reaction order. For zero-order reactions, the rate of reaction is independent of the concentration of reactants, and thus the rate remains constant with time. However, for reactions of first order or higher, the rate of reaction depends on the concentration of the reactants and will change with time.

Step 4: d) Decreasing rate with just reactants

This statement can be true or false depending on the reaction order. For first-order reactions or higher, the rate of the reaction will decrease with time as the concentration of reactants decreases. However, for zero-order reactions, the rate of the reaction is independent of the concentration of reactants and will not decrease with time.

Key Concepts

Rate Law

A rate law is a mathematical expression that relates the reaction rate to the concentration of reactants. It usually takes the form \(\text{Rate} = k[A]^x[B]^y\), where \(k\) is the rate constant, and \(x\) and \(y\) are the orders of reaction with respect to reactants \(A\) and \(B\), respectively. It's important to note that the values of \(x\) and \(y\) are not necessarily equal to the stoichiometric coefficients from the balanced chemical equation.
Unlike the balancing coefficients, rate law orders must be determined through experiments. Here's how they are different:

• Rate law orders describe how changes in concentration affect rate.
• They can be fractional and are not tied to stoichiometry directly.

In summary, rate laws are essential for predicting how fast a reaction will occur under certain conditions.

Balancing Coefficients

Balancing coefficients are numbers placed before compounds in a chemical equation to ensure that the number of atoms for each element is the same on both sides of the equation. This process reflects the law of conservation of mass, which states matter cannot be created or destroyed in a chemical reaction.
Balancing coefficients, however, do not provide direct information on the reaction kinetics or how the concentrations of reactants affect the reaction rates. Here’s a quick breakdown:

• Balancing reflects conservation and stoichiometry.
• It ensures atoms match up on both sides of the equation.
• It does not connect directly to the rate law.

Although they are the first step in understanding a chemical reaction, additional information is needed to connect these coefficients to the reaction rate.

Zero-Order Reaction

In a zero-order reaction, the rate of reaction is independent of the concentration of the reactants. This means no matter how much reactant you have, the reaction proceeds at a constant rate. Mathematically, it can be expressed as:
\[ \text{Rate} = k, \]
where \(k\) is the zero-order rate constant. This simplicity can be both a benefit and a limitation.
Characteristics of zero-order reactions include:

• A linear decrease in reactant concentration over time.
• A constant rate up until the reactant is nearly depleted.

Understanding zero-order reactions is crucial in processes where maintaining a steady rate is important, such as certain catalytic processes.

First-Order Reaction

First-order reactions have a rate that is directly proportional to the concentration of one reactant. They can be expressed in the rate law as:
\[ \text{Rate} = k[A], \]
indicating that as the concentration of \(A\) changes, the rate of reaction changes correspondingly.
Some key points about first-order reactions include:

• A characteristic semi-logarithmic plot when plotted \(\ln[A]\) versus time.
• The rate decreases over time as the concentration of \(A\) decreases.

In practical terms, first-order kinetics are applied in radioactive decay and many chemical reactions within cells, providing a predictable pattern of reaction decay over time.