The degradation of CF3CH2F (an HFC) by OH radicals in the troposphere is first order in each reactant and has a rate constant of k = 1.6x10^8 M-1s-1 at 4 °C. If the tropospheric concentrations of OH and CF3CH2F are 8.1x10^5 and 6.3x10^8 molecules/cm3, respectively, what is the reaction rate at this temperature in M/s?

Verified step by step guidance

Convert the concentrations of OH and CF3CH2F from molecules/cm³ to molarity (M). Use the conversion factor: 1 mole = 6.022 x 10^23 molecules and 1 cm³ = 1 x 10^-3 L.

Calculate the molarity of OH by dividing the number of molecules by Avogadro's number and then converting cm³ to L.

Calculate the molarity of CF3CH2F using the same method as for OH.

Use the rate law for a second-order reaction: Rate = k[OH][CF3CH2F], where k is the rate constant and [OH] and [CF3CH2F] are the molar concentrations.

Substitute the values of k, [OH], and [CF3CH2F] into the rate equation to find the reaction rate in M/s.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

First-Order Reactions

First-order reactions are those where the rate of reaction is directly proportional to the concentration of one reactant. In this case, the degradation of CF3CH2F by OH radicals is first order in both reactants, meaning that the rate can be expressed as rate = k[OH][CF3CH2F], where k is the rate constant. Understanding this relationship is crucial for calculating the reaction rate.

Rate Constant (k)

The rate constant (k) is a proportionality factor that relates the reaction rate to the concentrations of the reactants in a chemical reaction. It is specific to a given reaction at a particular temperature. In this question, the rate constant is given as 1.6x10^8 M-1s-1, which indicates how quickly the reaction occurs under the specified conditions.

Concentration Units and Conversion

Concentration is often expressed in molarity (M), which is moles of solute per liter of solution. However, in this question, concentrations are provided in molecules per cubic centimeter (molecules/cm3). To calculate the reaction rate in M/s, it is necessary to convert these concentrations into molarity, using Avogadro's number (6.022x10^23 molecules/mol) to facilitate the conversion.

Recommended video:

Guided course

01:56

Conversion Factors

Related Practice

Textbook Question

The following data were collected for the desturction of O₃ by H (O₃ + H → O₂ + OH) at very low concentrations (b) Calculate the rate constant

Textbook Question

The Henry's law constant for CO2 in water at 25 °C is 3.1x10^-2 M atm-1. (a) What is the soubility of CO2 in water at this temperature if the soltuion is in contact with air at normal atmospheric pressure?

views

Textbook Question

The precipitation of Al(OH)₃ (K_sp) = 1.3⨉10^-33) is sometimes used ot purify water. (a) Estimate the pH at which precipitation of Al(OH)₃ will begin if 5.0 lb of Al₂(SO₄)₃ is added to 2000 gal of water

Textbook Question

The valuable polymer polyurethane is made by a condensa- tion reaction of alcohols (ROH) with compounds that con- tain an isocyanate group (RNCO). Two reactions that can generate a urethane monomer are shown here: (i)

(ii)

(c) If you wanted to promote the formation of the isocyanate intermediate in each reaction, what could you do, using Le Châtelier's principle?