Chapter 60: Problem 5

According to equation 1 , if the activation energy for some reaction, \(Q\), is greater than the activation energy for a different reaction, \(W\), which has the greater rate constant - reaction \(Q\) or reaction \(W\) (assuming that the value of \(A\), the frequency factor, is identical in both reactions)? Explain.

Short Answer

Expert verified

Reaction \(W\) has the greater rate constant because it has a smaller activation energy than reaction \(Q\).

Step by step solution

Understanding the Arrhenius equation

The Arrhenius equation is given by \(k=Ae^{-Ea/RT}\). In this equation, \(k\) is the rate constant, \(Ea\) is the activation energy, \(R\) is the gas constant, \(T\) is the temperature and \(A\) is the frequency factor. Both reactions \(Q\) and \(W\) have the same frequency factor.

Comparing activation energies for reactions Q and W

In the given problem, it is stated that the activation energy for reaction \(Q\) (let's call it \(Ea_Q\)) is greater than the activation energy for reaction \(W\) (let's call it \(Ea_W\)) i.e. \(Ea_Q > Ea_W\).

Determining the effect on the rate constant

According to the Arrhenius equation, the rate constant \(k\) is inversely proportional to the activation energy \(Ea\). This means that a greater activation energy results in a smaller rate constant. Therefore, since the activation energy \(Ea_Q\) of reaction \(Q\) is greater than \(Ea_W\) of reaction \(W\), the rate constant for reaction \(Q\) is smaller than for reaction \(W\).

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Short Answer

Step by step solution

Understanding the Arrhenius equation

Comparing activation energies for reactions Q and W

Determining the effect on the rate constant

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