Phosphine (PH 3 ) decomposes into phosphorus and molecular hydrogen: 4PH 3 (g) P
ID: 925885 • Letter: P
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.)
TrueFalse The rate constant would be smaller than 0.0173 s-1 at 590°C.
TrueFalse The reaction PH3 PH2 + H might be the rate-determining step in the mechanism of this reaction.
TrueFalse The mechanism for this reaction must involve two or more elementary steps.
TrueFalse The data given would allow us to determine the activation energy for the reaction.
Explanation / Answer
1) The rate constant would be smaller than 0.0173 s-1 at 590°C
We know that,
K = A exp (-Ea / RT)
where,
K = Rate constant,
Ea = Activation energy
T = Temperature
=> ln K = ln A - (Ea / RT)
As T increases Ea / RT decreases and hence K increases.
Therefore K at 690 degree C > K at 590 degree C
Statement 1 is TRUE
2) The reaction PH3 PH2 + H might be the rate-determining step in the mechanism of this reaction.
PH2 and H formed in the reaction are unstable. Therefore this step would be slow. Hence it might be the RDS.
Statement 2 is True.
3) The mechanism for this reaction must involve two or more elementary steps.
The above mechanism cannot be a 1 step mechanism as 4 PH3 molecules coming together in 1 step is very less probable. Hence, this has to be a 2 or more step reaction.
Statement 3 is TRUE
4) The data given would allow us to determine the activation energy for the reaction.
K = A exp (-Ea / RT)
We have 2 variables (A and Ea) and only one equation. Therefore we cannot find Ea with the given information.
Statement 4 is FALSE