Problem 88 - Chemistry: The Central Science in SI Units, Global Edition

Question

The degradation of \(\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{~F}\) (an HFC) by OH radicals in the troposphere is first order in each reactant and has a rate constant of \(k=2.1 \times 10^{8} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) at \(10^{\circ} \mathrm{C}\). If the tropospheric concentrations of \(\mathrm{OH}\) and \(\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{~F}\) are \(1.0 \times 10^{12}\) and \(7.5 \times 10^{14}\) molecules \(/ \mathrm{m}^{3}\), respectively, what is the rate of reaction at this temperature in \(M /\) s?

Step-by-Step Solution

Answer

The rate of reaction at 10°C is approximately \(4.36 \times 10^{-33} M/s\).

Step 1: Convert the concentration from molecules/m³ to Molarity

First, we need to convert the concentration from molecules/m³ to moles/liter (M). We'll use Avogadro's number, 6.022 x 10²³ molecules/mol. \(OH\: concentration\: (M) = \frac{1.0 \times 10^{12}\: molecules/m^3}{6.022 \times 10^{23}\: molecules/mol × 10^3\: liters/m^3} = 1.66 \times 10^{-13} M\) \(CF_3CH_2F\: concentration\: (M) = \frac{7.5 \times 10^{14}\: molecules/m^3}{6.022 \times 10^{23} \: molecules/mol × 10^3\: liters/m^3} = 1.25 \times 10^{-11} M\)

Step 2: Calculate the rate of reaction using the rate law

We are given that the decay is first order with respect to both reactants. This means that the rate law is equal to the product of the rate constant and the concentration of each reactant. Rate of reaction = k [\(OH\)] \([CF_3CH_2F]\) Now we can plug in the values we have for \(k\), [\(OH\)] and [\(CF_3CH_2F\)] to calculate the rate of reaction: Rate of reaction = \((2.1 \times 10^{8} M^{-1} s^{-1})(1.66 \times 10^{-13} M)(1.25 \times 10^{-11} M)\)

Step 3: Calculate the rate of reaction in M/s

Multiply the given values to find the rate of reaction: Rate of reaction = \(4.36 \times 10^{-33} M/s\) The rate of reaction at 10°C is approximately \(4.36 \times 10^{-33} M/s\).

Key Concepts

First-order kinetics

In chemical reaction terms, first-order kinetics refers to reactions where the rate of reaction is directly proportional to the concentration of one reactant. This concept is simple but critical for students to understand, especially when dealing with reactions like the degradation of hydrofluorocarbons (HFCs) in the atmosphere. Let’s break it down:

• The rate of a first-order reaction can be described by the equation: \[ \text{Rate} = k[A] \] where \( k \) is the rate constant, and \([A]\) is the concentration of the reactant.
• In first-order reactions, because the rate depends on a single reactant’s concentration, a doubling of that reactant’s amount effectively doubles the reaction rate. Keeping this in mind helps predict how changes in concentration affect the reaction speed.
• Understanding first-order kinetics is fundamental when discussing various reactions, including many atmospheric processes that involve radicals such as the OH radical.

Breaking complex reactions into simpler, understandable kinetics makes analyzing reactions in environments like the troposphere much more accessible.

HFC degradation

Hydrofluorocarbons (HFCs) are a class of chemicals used primarily as refrigerants and aerosol propellants. While they are powerful greenhouse gases, their degradation in the troposphere is intriguing. The specific reaction we’re considering is the breakdown of \(\text{CF}_3\text{CH}_2\text{F}\) by OH radicals. Here's what you need to know about this process:

• HFCs do not react spontaneously; they require a catalyst like OH radicals to begin degradation.
• The degradation of HFCs is important because it leads to shorter atmospheric lifetimes and potentially less environmental impact if managed well.
• This degradation process is categorized as a first-order reaction, signifying that the reaction speed depends linearly on the concentration of OH radicals and HFCs.

Recognizing the significance of HFC degradation is vital due to its implications on global warming and atmospheric chemistry, underscoring the need for environmentally friendly alternatives.

Tropospheric chemistry

The troposphere is the lowest layer of Earth's atmosphere, extending up to about 10 km above sea level. In this layer, complex chemistry shapes our environment and climate tightly connected to everyday life. Tropospheric chemistry involves a vast array of reactions:

• The interactions within the troposphere heavily rely on radicals, such as OH, which play a pivotal role in atmospheric chemical reactions, including the degradation of pollutants like HFCs.
• Several chemical reactions in the troposphere are influenced by sunlight, temperature, and the presence of various compounds, impacting air quality and climate.
• Understanding tropospheric chemistry is crucial for scientists aiming to predict weather patterns, improve air quality, and devise new strategies for reducing environmental pollutants.

Overall, tropospheric chemistry allows us to develop insights into the broader impacts of chemical reactions on climate and environmental health, showing why studying reactions like HFC degradation in this layer are foundational.