Introduction to Rate Law
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AP Chemistry › Introduction to Rate Law
For a reaction with the general rate law, Rate = $$kA^mB^n$$, what do the exponents $$m$$ and $$n$$ represent?
The reaction orders with respect to reactants A and B, which must be determined experimentally.
The equilibrium constants for the individual elementary steps that involve reactants A and B.
The stoichiometric coefficients of reactants A and B from the overall balanced chemical equation.
The molar masses of reactants A and B, which are used to calculate collision frequencies.
Explanation
The correct answer is A. The exponents $$m$$ and $$n$$ in a rate law are the orders of the reaction with respect to each reactant. These orders indicate how the rate is affected by the concentration of that reactant and must be determined through experimental data, not from the stoichiometry of the overall reaction.
Based on this information, what is the order of the reaction with respect to reactant A?
Zero order
Second order
First order
Third order
Explanation
The correct answer is B. The rate law is Rate = $$k[A]^x$$. When [A] is doubled, the new rate is $$k(2[A])^x = 2^x(k[A]^x)$$. The problem states that the rate doubles, so $$2^x = 2$$, which means $$x = 1$$. The reaction is first order with respect to A.
For a reaction that is found to be third order overall, which of the following are the correct units for the rate constant, k?
$$L \text{mol}^{-1} \text{s}^{-1}$$
$$\text{mol L}^{-1} \text{s}^{-1}$$
$$\text{s}^{-1}$$
$$L^2 \text{mol}^{-2} \text{s}^{-1}$$
Explanation
The units of k can be derived from the general rate law. For a third-order reaction, Rate = $$k[concentration]^3$$. Rearranging for k gives $$k = \text{Rate} / [concentration]^3$$. Substituting units: $$(\text{mol L}^{-1} \text{s}^{-1}) / (\text{mol L}^{-1})^3 = (\text{mol L}^{-1} \text{s}^{-1}) / (\text{mol}^3 \text{L}^{-3}) = L^2 \text{mol}^{-2} \text{s}^{-1}$$.
A chemical reaction is described by the rate law: Rate = $$kXY^2$$. If the concentration of X is tripled and the concentration of Y is doubled, the initial reaction rate will increase by a factor of
6
9
12
18
Explanation
The correct answer is C. The change in rate is determined by the product of the concentration changes raised to their respective orders. The change will be $$(3)^1 \times(2)^2 = 3 \times 4 = 12$$. The rate increases by a factor of 12.
The value of the rate constant, k, for a specific chemical reaction is primarily dependent on which of the following factors?
The pressure of gaseous reactants.
The temperature of the reaction system.
The time elapsed since the start of the reaction.
The initial concentration of the reactants.
Explanation
The rate constant, k, is constant for a given reaction at a fixed temperature. Its value changes significantly with temperature, as described by the Arrhenius equation. The presence of a catalyst also changes k, but temperature is the primary factor listed. Concentrations and time do not affect the value of k.
The balanced equation for the synthesis of ammonia is $$N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$$. A student proposes that the rate law for this reaction is Rate = $$kN_2H_2^3$$. This proposed rate law is
possibly correct, but it cannot be confirmed without evidence from experimental data.
definitely incorrect, because reaction orders cannot be greater than two for any reactant.
definitely incorrect, because the concentration of the product, NH₃, must be included in the rate law.
definitely correct, because the exponents in the rate law must match the stoichiometric coefficients.
Explanation
The correct answer is C. Rate laws must be determined experimentally. They depend on the reaction mechanism, not the overall stoichiometry. While it is possible for the orders to match the coefficients (if the reaction is an elementary step), this cannot be assumed. Choice A is a common misconception. Choice B is false, as orders can be integers, fractions, or zero. Choice D is incorrect as product concentrations do not appear in the forward rate law.
What is the correct rate law for this reaction based on the data?
Rate = $$k[X][Y]$$
Rate = $$k[X][Y]^2$$
Rate = $$k[X]^2[Y]$$
Rate = $$k[X]^2$$
Explanation
To find the order for X, compare Experiments 1 and 2 where [Y] is constant. [X] doubles ($$0.20/0.10 = 2$$), and the rate quadruples ($$0.0200/0.0050 = 4$$). Since $$2^2 = 4$$, the reaction is second order in X. To find the order for Y, compare Experiments 2 and 3 where [X] is constant. [Y] doubles ($$0.20/0.10 = 2$$), and the rate is unchanged ($$0.0200/0.0200 = 1$$). Since $$2^0 = 1$$, the reaction is zero order in Y. The rate law is Rate = $$k[X]^2[Y]^0$$ or Rate = $$k[X]^2$$.
For a general reaction, the exponents in the rate law expression, Rate = $$kA^mB^n$$, are known as the reaction orders. These exponents are determined by which method?
They are calculated from the molar masses of the reactants A and B.
They are equal to the stoichiometric coefficients in the balanced chemical equation.
They must be determined by analyzing experimental rate data.
They are derived from the overall enthalpy change of the reaction.
Explanation
The orders of a reaction (the exponents m and n) are not necessarily related to the stoichiometric coefficients. They can only be determined by conducting experiments that measure how the reaction rate changes as the concentrations of the reactants are varied. This is a fundamental principle of chemical kinetics.
An experiment is performed with $$X = 0.40 M$$ and $$Y = 0.40 M$$. A second experiment is performed with $$X = 0.40 M$$ and $$Y = 0.80 M$$. How will the initial rate of the second experiment compare to the first?
The initial rate will be the same.
The initial rate will be doubled.
The initial rate will be halved.
The initial rate will be quadrupled.
Explanation
The rate law, Rate = $$k[X]^2$$, shows that the reaction is second order in X and zero order in Y. Since the rate does not depend on the concentration of Y, doubling [Y] while keeping [X] constant will have no effect on the initial rate. Therefore, the rate will be the same in both experiments.
Which statement accurately describes the relationship between the balanced chemical equation and the experimentally determined rate law for this reaction?
The reaction order with respect to $$ClO_2$$ is 1, which is different from its stoichiometric coefficient of 2, demonstrating that orders must be found experimentally.
The stoichiometric coefficient for $$F_2$$ is 1, which is why its reaction order is 1; this direct correlation always holds.
The rate law exponents must always be different from the coefficients to account for the reaction mechanism.
The reaction orders for both reactants are identical to their stoichiometric coefficients, as is expected for all reactions.
Explanation
This example highlights the key principle that reaction orders are not necessarily equal to the stoichiometric coefficients. Here, the order for $$F_2$$ happens to match its coefficient (both are 1), but the order for $$ClO_2$$ is 1 while its coefficient is 2. This shows that rate laws must be determined from experimental data, not from the balanced equation.