   Chapter 12, Problem 100CWP

Chapter
Section
Textbook Problem

# Consider the hypothetical reaction A2(g) + B2(g) ⟶ 2AB(g), where the rate law is: Δ [ A 2 ] Δ t = k [ A 2 ] [ B 2 ] The value of the rate constant at 302°C is 2.45 × 10−4 L/mol s, and at 508°C the rate constant is 0.891 L/mol·  s. What is the activation energy for this reaction? What is the value of the rate constant for this reaction at 375°C?

Interpretation Introduction

Interpretation: For the given hypothetical reaction, the value of activation energy and at 375°C the value of rate constant is to be calculated

Concept introduction: Rate constant is a proportionality coefficient that relates the rate of any chemical reaction at a specific temperature to the concentration of the reactant or the concentration of the product.

The value of the rate constant is determined with the help of Arrhenius equation.

Arrhenius equation is a mathematical relation between rate constant, activation energy and the temperature.

With the help of activation energy the value of rate constant is determined.

To determine: The value of activation energy;and the value of rate constant at 375°C for the given hypothetical reaction.

Explanation

Explanation

Given

The reaction is given as,

A2(g)+B2(g)2AB(g)

At the temperature 302°C the value of rate constant is 2.45×104L/mols .

At the temperature 508°C the value of rate constant is 0.891L/mols .

The given temperature is 375°C on which the rate constant is to be determined.

The temperature 302°C is assumed to be T1 .

The temperature 508°C is assumed to be T2 .

At the temperature T1 rate constant is known as k1 .

At the temperature T2 rate constant is known as k2 .

The conversion of temperature from degree Celsius do Kelvin is given by the formula,

x°C=(273+x)K

Where,

• x is the temperature in degree Celsius.

Substitute the values of T1 and T2 in the above formula.

For T1, ,

x°C=(273+x)K=273+302=575K

For T2 ,

x°C=(273+x)K=273+508=781K

The activation energy for the reaction is given by the Arrhenius equation,

lnk2k1=EaR[T2T1T1T2]

Where,

• k1,k2 are the rate constants at different temperatures.
• Ea is the activation energy.
• R is the gas constant and it has the value 8.314JK1mol .
• T1,T2 are the temperatures.

Substitute the values of temperatures with their respective rate constants.

lnk2k1=EaR[T2T1T1T2]ln0.8912.450×104=Ea8.314JK1mol1[(781575)K(781×575)K2]8

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