The hypothetical reaction 2 A+2 B ⟶C+3 D was studied by measuring the initial rate of appearan

Step 1: First, we need to find the order of the reaction with respect to substance A. To do this

The hypothetical reaction 2 A+2 B ⟶C+3 D was studied by...

The hypothetical reaction $$ 2 \mathrm{~A}+2 \mathrm{~B} \longrightarrow \mathrm{C}+3 \mathrm{D} $$ was studied by measuring the initial rate of appearance of $\mathrm{C}$. These data were obtained: (a) What is the order of the reaction with respect to substance $A$ ? (b) What is the order with respect to $B$ ? (c) What is the overall order? (d) What is the rate law? (e) Calculate the rate constant. (f) If at a given instant $A$ is disappearing at a rate of $0.034 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$, what is the rate of appearance of C? What is the rate of appearance of $D$ ?

The hypothetical reaction
$$
2 \mathrm{~A}+2 \mathrm{~B} \longrightarrow \mathrm{C}+3 \mathrm{D}
$$
was studied by measuring the initial rate of appearance of $\mathrm{C}$. These data were obtained:
(a) What is the order of the reaction with respect to substance $A$ ?
(b) What is the order with respect to $B$ ?
(c) What is the overall order?
(d) What is the rate law?
(e) Calculate the rate constant.
(f) If at a given instant $A$ is disappearing at a rate of $0.034 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$, what is the rate of appearance of C? What is the rate of appearance of $D$ ?

Key Concepts

Reaction Stoichiometry and Rate Relationships

Reaction stoichiometry gives the mole ratios in which reactants are consumed and products are formed. This stoichiometric information is used to relate the rates of disappearance of reactants to the rates of appearance of products. Even if the rate law is determined experimentally, the stoichiometric coefficients allow the calculation of individual species’ rates provided one rate (either reactants or products) is known.

Rate Constant

The rate constant, typically denoted as k, is a proportionality factor in the rate law that is characteristic of a specific reaction at a given temperature. It provides a quantitative measure of the reaction's speed and is determined by substituting experimental data into the rate law equations after the reaction orders have been established.

Rate Law

The rate law is an equation that expresses the rate of a chemical reaction in terms of the concentrations of its reactants and a rate constant. It is typically determined through experimental data and does not necessarily reflect the stoichiometry of the overall balanced chemical equation. The exponents in the rate law represent the reaction order with respect to each reactant.

Reaction Order

The reaction order describes the power to which a reactant’s concentration is raised in the rate law and indicates how sensitively the rate depends on that concentration. Individual orders with respect to each reactant are determined experimentally, and the overall order is the sum of these individual orders.

Initial Rate Method

The initial rate method involves measuring the initial reaction rate under different starting concentrations of reactants. By comparing how the rate changes with varying concentrations, one can deduce the order of reaction with respect to each reactant and subsequently determine the rate constant.

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