The experiment is repeated at 500˚C. How would the following change (qualitatively) at the new temperature (explain your answer)?

Question

This reaction was originally done at a temperature of 250K, but now it is being done at 500K.

4PH3 (g) ➞ P4 (g) + 6H2 (g)

a. The half-life of phosphine.

b. The rate law for phosphine decomposition.

c. The value of the rate constant.

Justify each answer!

Answer 1

The experiment is being repeated at a much higher temperature of 500 K, which will cause several changes in the reaction.

a. The half-life of phosphine: The half-life of a reaction is directly proportional to the activation energy of the reaction. At a higher temperature, the activation energy of the reaction decreases, and the half-life of the reaction decreases as well. Therefore, the half-life of phosphine will decrease at 500 K compared to 250 K.

b. The rate law for phosphine decomposition: The rate law of a reaction describes the relationship between the rate of the reaction and the concentrations of the reactants. The rate law for phosphine decomposition may change at a higher temperature due to changes in the reaction mechanism. Therefore, it is difficult to predict how the rate law will change qualitatively without further information.

c. The value of the rate constant: The rate constant is affected by the temperature-dependent Arrhenius equation, which states that k = Ae^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature. As the temperature increases, the rate constant increases due to the exponential term in the equation. Therefore, the value of the rate constant for the decomposition of phosphine will increase at 500 K compared to 250 K.

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