Chem Quiz 5-Ch.13 (#1-11)

13.5 Explain the difference between the average rate of reaction and the instantaneous rate of reaction.

The average rate of the reaction can be calculated for any time interval as: (refer to handout) for the chemical reaction aA +bB → cC + dD. The instantaneous rate of the reaction is the rate at any one point in time, represented by the instantaneous slope of the plot of concentration versus time at that point. We can obtain the instantaneous rate from the slope of the tangent to this curve at the point of interest.

13.11 What does the term half-life mean? Write the expressions for the half-lives of zero-order, first-order, and second-order reactions.

The half-life (t1/2) of a reaction is the time required for the concentration of a reactant to fall to one-half of its initial value. For a zero-order reaction, t(1/2) = [A]₀/2k. For a first-order reaction, t(1/2) = 0.693/k. For a second-order reaction, t(1/2) = 1/k[A]₀.

13.6 Consider a simple reaction in which a reactant A forms products: A --> products. What is the rate law if the reaction is zero order with respect to A? First order? Second order? For each case, explain how a doubling of the concentration of A would affect the rate of reaction.

For a zero-order reaction, Rate = k[A]⁰ = k; doubling the concentration of A does nothing to the reaction rate. For a first-order reaction, Rate = k[A]¹ = k[A]; doubling the concentration of A doubles the reaction rate. For a second-order reaction, Rate = k[A]²; doubling the concentration of A quadruples the reaction rate.

13.10 Write integrated rate laws for zero-order, first-order, and second-order reactions of the form A --> products.

For a zero-order reaction, [A]t = -kt + [A]₀. For a first-order reaction, ln[A]t = -kt + ln[A]₀. For a second-order reaction, 1/[A]t = kt + 1/[A]₀.

13.1 Explain why lizards become sluggish in cold weather. How is this phenomenon related to chemistry?

Lizards' body temperatures depend on their surroundings. When splashed with cold water, a lizard's body gets colder. The drop in body temperature immobilizes the lizard because its movement depends on chemical reactions that occur within its muscles, and the rates of those reactions are highly sensitive to temperature. When the temperature drops, the reactions that produce movement occur more slowly. Therefore, the movement itself slows down. Cold reptiles are lethargic. Therefore, reptiles try to maintain their body temperature in a narrow range by moving between sun and shade.

13.2 Why are reaction rates important (both practically and theoretically)?

The human body's ability to switch a specific reaction on or off at a specific time is achieved largely by controlling the rate of that reaction through the use of enzymes. Chemical kinetics is an important subject to chemists and engineers. The launching of a rocket depends on controlling the rate at which fuel burns: too quickly and the rocket can explode, too slowly and it will not leave the ground. The rate of nuclear decay in a nuclear power plant must be carefully controlled to provide electricity safely and efficiently. Chemists must consider reaction rates when synthesizing compounds. No matter how stable a compound might be, its synthesis is impossible if the rate at which it forms is too slow.

13.9 Explain the difference between the rate law for a reaction and the integrated rate law for a reaction. What relationship does each kind of rate law express?

The rate law shows the relationship between the rate of a reaction and the concentrations of the reactants. The integrated rate law for a chemical reaction is a relationship between the concentration of a reactant and time.

13.3 What units are typically used to express the rate of a reaction?

The rate of a chemical reaction is measured as a change in the amounts of reactants or products (usually in terms of concentration) divided by the change in time. Typical units are molarity per second (M/s), molarity per min (M/min), and molarity per year (M/year), depending on how fast the reaction proceeds.

13.7 How is the order of a reaction generally determined?

The reaction order cannot be determined by the stoichiometry of the reaction. It can only be determined by running controlled experiments where the concentrations of the reactants are varied and the reaction rates are measured and analyzed.

13.4 Why is the reaction rate for reactants defined as the negative of the change in reactant concentration with respect to time, whereas for products it is defined as the change in reactant concentration with respect to time (with a positive sign)?

The reaction rate is defined as the negative of the change in reactant concentration divided by the change in time because reactant concentrations decrease as a reaction proceeds. Therefore, the change in the concentration of a reactant is negative. The negative sign in the definition makes the overall rate positive. The negative sign is the result of the convention that reaction rates are usually reported as positive quantities. Because the product concentrations are increasing, the concentration of a product divided by the change in time is positive.

13.8 For a reaction with multiple reactants, how is the overall order of the reaction defined?

When multiple reactants are present, Rate = k[A]^m[B]ⁿ; where m is the reaction order with respect to A and n is the reaction order with respect to B. The overall order is the sum of the exponents (m+n).