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The activation energy for the decomposition of benzene diazonium chloride is [tex]99.1 \, \text{kJ/mol}[/tex]. At what temperature will the rate be 10 percent greater than its rate at [tex]25^\circ \text{C}[/tex]?

Answer :

The temperature at which the rate will be 10% greater than its rate at 25°C is approximately 116.7°C.

The Arrhenius equation describes the relationship between the rate constant (k) of a reaction, the activation energy (Ea), and the temperature (T):

k = A * exp(-Ea / (R * T))

To find the temperature at which the rate is 10% greater than its rate at 25°C, we can set up the following equation:

k(T) = 1.1 * k(25°C)

where k(T) is the rate constant at temperature T.

Plugging in the values into the Arrhenius equation:

A * exp(-Ea / (R * T)) = 1.1 * A * exp(-Ea / (R * 298 K))

Simplifying the equation:

exp(-Ea / (R * T)) = 1.1 * exp(-Ea / (R * 298 K))

Taking the natural logarithm of both sides:

-Ea / (R * T) = ln(1.1) - Ea / (R * 298 K)

Simplifying further:

1 / (R * T) = (1 / (R * 298 K)) * (ln(1.1) - Ea / (R * 298 K))

Solving for T:

T = 1 / ((ln(1.1) - Ea / (R * 298 K)) * R)

Substituting the values of Ea = 99.1 kJ mol^(-1) and R = 8.314 J mol^(-1) K^(-1), we can calculate the temperature T, which is approximately 116.7°C.

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