The decomposition of CO2 is first order with respect to the concentration of CO2. 2 CO2(g) ⟶2 CO

step 1 So we're told that with respect to CO2, the, we're told that with respect to CO2, the rate law i

The decomposition of CO2 is first order with respect to the...

The decomposition of $\mathrm{CO}_{2}$ is first order with respect to the concentration of $\mathrm{CO}_{2}.$ $$2 \mathrm{CO}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$ Data on this reaction are provided in the table below. $$\begin{array}{lc}\hline\left[\mathrm{CO}_{2}\right](\mathrm{mol} / \mathrm{L}) & \text { Time }(\mathrm{s}) \\\hline 0.38 & 0 \\0.27 & 12 \\\hline\end{array}$$ (a) Write the rate equation for this reaction. (b) Use the data to determine the value of $k$ (c) What is the half-life of $\mathrm{CO}_{2}$ under these conditions?

The decomposition of $\mathrm{CO}_{2}$ is first order with respect to the concentration of $\mathrm{CO}_{2}.$
$$2 \mathrm{CO}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$
Data on this reaction are provided in the table below.
$$\begin{array}{lc}\hline\left[\mathrm{CO}_{2}\right](\mathrm{mol} / \mathrm{L}) & \text { Time }(\mathrm{s}) \\\hline 0.38 & 0 \\0.27 & 12 \\\hline\end{array}$$
(a) Write the rate equation for this reaction.
(b) Use the data to determine the value of $k$
(c) What is the half-life of $\mathrm{CO}_{2}$ under these conditions?

Key Concepts

Half-Life Concept

The half-life of a reaction is the time required for the concentration of a reactant to be reduced to half of its initial value. For a first order reaction, the half-life is independent of the initial concentration and is given by the formula t½ = 0.693/k. This concept is useful in comparing reaction speeds and in predicting how long a reaction will take to significantly decrease the concentration of a reactant.

Rate Constant Determination

Determining the rate constant (k) involves using experimental data and the integrated rate law. By plotting the natural logarithm of the reactant concentration against time, the slope of the line gives the rate constant k, or by solving the integrated rate law using two known concentration values at specific times, one can directly calculate k.

First Order Kinetics

In chemical kinetics, a first order reaction is one in which the rate is directly proportional to the concentration of one reactant. This means that as the concentration of the reactant decreases, the rate decreases proportionally, and the reaction exhibits an exponential decay in the concentration of the reactant over time.

Rate Law Formulation

The rate law expresses the relationship between the reaction rate and the concentrations of the reactants. For a reaction that is first order with respect to a particular reactant, the rate law is typically written as Rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Integrated Rate Law

The integrated rate law for a first order reaction relates the concentration of the reactant at any time to the initial concentration through the equation ln[A]_t = ln[A]_0 ? kt. This equation is crucial for analyzing concentration vs. time data and allows one to easily compute the rate constant or predict the concentration at a given time.

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