Consider the data showing the initial rate of a reaction (A ⟶products) at several different conc

step 1 In this question, we also have the generic reaction of a single reactant A going to products. We

Consider the data showing the initial rate of a reaction (A...

Consider the data showing the initial rate of a reaction (A $\longrightarrow$ products) at several different concentrations of A. What is the order of the reaction? Write a rate law for the reaction, includ- ing the value of the rate constant, $k$. $$ \begin{array}{cc} {[\mathrm{A}](\mathrm{M})} & \text { Initial Rate }(\mathrm{M} / \mathrm{s}) \\ 0.15 & 0.008 \\ \hline 0.30 & 0.016 \\ \hline 0.60 & 0.032 \\ \hline \end{array} $$

Consider the data showing the initial rate of a reaction (A $\longrightarrow$ products) at several different concentrations of A. What is the
order of the reaction? Write a rate law for the reaction, includ-
ing the value of the rate constant, $k$.
$$
\begin{array}{cc}
{[\mathrm{A}](\mathrm{M})} & \text { Initial Rate }(\mathrm{M} / \mathrm{s}) \\
0.15 & 0.008 \\
\hline 0.30 & 0.016 \\
\hline 0.60 & 0.032 \\
\hline
\end{array}
$$

Key Concepts

Method of Initial Rates

The method of initial rates is a technique in chemical kinetics used to determine the reaction order by comparing the initial reaction rates at different starting concentrations of reactants. By analyzing how small changes in concentration affect the initial rate, one can deduce the exponent to which the concentration term is raised in the rate law without interference from reverse reactions or product formation.

Rate Constant

The rate constant, typically denoted as k, is a proportionality factor in the rate law that is characteristic of the particular reaction at a given temperature. It quantifies the speed of the reaction and, when combined with the concentration terms from the rate law, allows for the calculation of the reaction rate. Determining the rate constant is crucial for making predictions about reaction behavior under various conditions.

Reaction Order

Reaction order refers to the exponent of the concentration term in the rate law of a reaction and indicates how the rate depends on the concentration of a reactant. In kinetics, if increasing the concentration of a reactant leads to a proportional increase in the reaction rate, the reaction is typically first order with respect to that reactant. Determining the reaction order is key in understanding the kinetics and mechanism of the reaction.

Rate Law

The rate law is an equation that expresses the reaction rate as a function of the concentration of reactants raised to their respective orders and includes the rate constant. It provides a quantitative relationship that reflects how the concentration changes influence the rate, and the form of the rate law helps in predicting how the reaction will progress under different conditions.

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