Question

The reaction shown here is experimentally observed to be second order in X and first order in y.

X + Y ->XY

a.) Does the reaction occur in a single step in which X and Y collide?

b.) Is this two-step mechanism valid?

K1

2X<--> X_{2 fast}

K2

X₂+Y--> XY+X slow

K₃

Answer 1

a)

not likely, if this was the case, it will be 1st order with respect to X and Y both

the ide of 2nd order of X, implies a two step at least mechanism

b)

note that slow step --> determining step

Rate slow = k * [X2][Y]

no tehta

Rate fast = k*[X]^2

[X2] =  k*[X]^2

substitute in

Rate slow = k * [X2][Y]

Rate overall = k * [k*[X]^2][Y]

Rate overall = K * [X]^2[Y]

this is consistent with rate

then

2X <-> X2

X2 + Y --> XY + X

add all

2X + X2 + Y --> X2 + XY + X

X + Y = XY

which is also consistent with the mas sbalance

then, the mechanism is valid