12.3 Rate Laws

Doubling the concentration of a reactant increases the rate of a reaction four times. With this knowledge, answer the following questions:

(a) What is the order of the reaction with respect to that reactant?

(b) Tripling the concentration of a different reactant increases the rate of a reaction three times. What is the order of the reaction with respect to that reactant?

How will the rate of reaction change for the process: $\text{CO}( g \left.\right) + \text{NO}_{2} \left(g\right) \rightarrow \text{CO}_{2} \left(g\right) + \text{NO}( g \left.\right)$ if the rate law for the reaction is $\text{rate} = k \left[\text{NO}_{2}\right]^{2} ?$

(a) Decreasing the pressure of NO₂ from 0.50 atm to 0.250 atm.

(b) Increasing the concentration of CO from 0.01 M to 0.03 M.

Regular flights of supersonic aircraft in the stratosphere are of concern because such aircraft produce nitric oxide, NO, as a byproduct in the exhaust of their engines. Nitric oxide reacts with ozone, and it has been suggested that this could contribute to depletion of the ozone layer. The reaction $\text{NO} + \text{O}_{3} \rightarrow \text{NO}_{2} + \text{O}_{2}$ is first order with respect to both NO and O₃ with a rate constant of 2.20 $\times$ 10⁷ L/mol/s. What is…

The rate constant for the radioactive decay of ¹⁴C is 1.21 $\times$ 10⁻⁴ year⁻¹. The products of the decay are nitrogen atoms and electrons (beta particles):
$_{6}^{14} \text{C} \rightarrow _{7}^{14} \text{N} + \text{e}^{-}$
$\text{rate} = k \left[_{6}^{14} \text{C}\right]$

What is the instantaneous rate of production of N atoms in a sample with a carbon-14 content of 6.5 $\times$ 10⁻⁹ M?

Alcohol is removed from the bloodstream by a series of metabolic reactions. The first reaction produces acetaldehyde; then other products are formed. The following data have been determined for the rate at which alcohol is removed from the blood of an average male, although individual rates can vary by 25–30%. Women metabolize alcohol a little more slowly than men:

Determine the rate law, the rat…

Nitrosyl chloride, NOCl, decomposes to NO and Cl₂.
$\text{2NOCl}( g \left.\right) \rightarrow \text{2NO}( g \left.\right) + \text{Cl}_{2} \left(g\right)$

Determine the rate law, the rate constant, and the overall order for this reaction from the following data:

Nitrogen monoxide reacts with chlorine according to the equation:
$\text{2NO}( g \left.\right) + \text{Cl}_{2} \left(g\right) \rightarrow \text{2NOCl}( g \left.\right)$

The following initial rates of reaction have been observed for certain reactant concentrations:

What is the rate law that describes the rate’s dependence on the concentrations of NO and Cl₂? What is the rate constant? What are the orders with respect to each reactant?

For the reaction $A \rightarrow B + C ,$ the following data were obtained at 30 °C:

(a) What is the order of the reaction with respect to [A], and what is the rate law?

(b) What is the rate constant?

The rate constant for the first-order decomposition at 45 °C of dinitrogen pentoxide, N₂O₅, dissolved in chloroform, CHCl₃, is 6.2 $\times$ 10⁻⁴ min⁻¹.
$\text{2N}_{2} \text{O}_{5} \rightarrow \text{4NO}_{2} + \text{O}_{2}$

What is the rate of the reaction when [N₂O₅] = 0.40 M?

The following data have been determined for the reaction:
$\text{I}^{−} + \text{OCl}^{−} \rightarrow \text{IO}^{−} + \text{Cl}^{−}$

Determine the rate law and the rate constant for this reaction.