Question

Phosphine (PH₃) decomposes into phosphorus and molecular hydrogen:
4PH₃(g) → P₄(g) + 6H₂(g)
Experiments show that this is a first-order reaction, with a rate constant of 0.0173 s^-1 at 650°C. Identify each of the following statements about this reaction as true or false. (Use the drop-down menu and select "True" or "False" for each. You must get all 4 correct.)
True/False  The mechanism for this reaction must involve two or more elementary steps.
True/False  The activation energy for the reaction cannot be determined without additional data.
True/False  The rate constant would be smaller than 0.0173 s^-1 at 500°C.
True/False  The rate-determining step for the reaction could involve a bimolecular collision between two PH₃ molecules.

Answer 1

A) The probability of four PH3 molecules coming together at once is far too low for this to be an elementary reaction. TRUE
B) TRUE. We have two unknowns in the Arrhenius equation, A and ΔE, so we cannot solve for either one.
C.)Rate constants decreases with decreasing temperature, with very few exceptions. This is therefore TRUE

Using the Arrhenius equation. Although it is not easy to see the relationship between the rate constant and the absolute temperature from the equation, if we break it down into steps perhaps it will help. However in the Arrhenius equation Ea/RT has a negative value, therefore as T increases Ea/RT gets LESS negative.
D) False, The The rate-determining step for the reaction could involve a bimolecular collision between two PH₃ molecules .

A trimolecular reaction requires the collision of three particles at the same place and time. This type of reaction is very uncommon because all three reactants must simultaneously collide with each other, with sufficient energy and correct orientation, to produce a reaction but when it become tetramolecular the chances of collison become negligible.