Consider the overall reaction: 2 X2Y + Z2 ⇌ 2 X2YZ which has an experimentally determined rate law of: rate= k[X2Y][Z2]. Which of the following are possible mechanisms for the reaction? Group of answer choices Step 1: 2 X2Y + Z2 → 2X2YZ (slow) Step 1: X2Y + Z2 ⇌ X2YZ + Z (fast) Step 2: X2Y + Z → X2YZ (slow) Step 1: X2Y + Z2→ X2YZ2 (slow) Step 2: X2YZ2 + X2Y → 2 X2YZ (fast) Step 1: 2 X2Y ⇌ X4Y2 (fast) Step 2: X4Y2 + Z2 → 2 X2YZ (slow) Step 1: Z2 → Z + Z (slow) Step 2: X2Y + Z → X2YZ (fast) Step 3: X2Y + Z → X2YZ (fast) None of the above

Rate law : It is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.

As we are given the overall reaction,

[tex]2X_2Y+Z_2\rightarrow 2X_2YZ[/tex]

The given expression of rate law for this reaction is,

[tex]Rate=k[X_2Y][Z_2][/tex]

Now we have to determine the possible mechanisms for the reaction.

The rate law expression for overall reaction should be in terms of [tex]X_2Y[/tex] and [tex]Z_2[/tex].

As we know that the slow step is the rate determining step.

Option 1 :

Step 1 : [tex]2X_2Y+Z_2\rightarrow 2X_2YZ[/tex] (slow)

The expression of rate law for this reaction will be,

[tex]Rate=k[X_2Y]^2[Z_2][/tex]

Option 2 :

Step 1 : [tex]X_2Y+Z_2\rightarrow X_2YZ+Z[/tex] (fast)

Step 2 : [tex]X_2Y+Z\rightarrow X_2YZ[/tex] (slow)

The rate law from the slow step 2 is,

[tex]Rate=K'[X_2Y][Z][/tex] .............(1)

Now applying steady state approximation for [tex]Z[/tex], we get:

[tex]\frac{d[Z]}{dt}=K"[X_2Y][Z_2][/tex] .........(2)

Now put equation 2 in 1, we get:

[tex]Rate=K'K"[X_2Y]^2[Z_2][/tex]

[tex]K'K"=K[/tex]

The rate law expression will be:

[tex]Rate=K[X_2Y]^2[Z_2][/tex]

Option 3 :

Step 1 : [tex]X_2Y+Z_2\rightarrow X_2YZ_2[/tex] (slow)

Step 2 : [tex]X_2YZ_2+X_2Y\rightarrow 2X_2YZ[/tex] (fast)

The expression of rate law for this reaction will be,

[tex]Rate=k[X_2Y][Z_2][/tex]

Option 4 :

Step 1 : [tex]2X_2Y\rightarrow X_4Y_2[/tex] (fast)

Step 2 : [tex]X_4Y_2+Z_2\rightarrow 2X_2YZ[/tex] (slow)

The rate law from the slow step 2 is,

[tex]Rate=K'[X_4Y_2][Z_2][/tex] .............(1)

Now applying steady state approximation for [tex]X_4Y_2[/tex], we get:

[tex]\frac{d[X_4Y_2]}{dt}=K"[X_2Y]^2[/tex] .........(2)

Now put equation 2 in 1, we get:

[tex]Rate=K'K"[X_2Y]^2[Z_2][/tex]

[tex]K'K"=K[/tex]

The rate law expression will be:

[tex]Rate=K[X_2Y]^2[Z_2][/tex]

Option 5 :

Step 1 : [tex]Z_2\rightarrow Z+Z[/tex] (slow)

Step 2 : [tex]X_2Y+Z\rightarrow X_2YZ[/tex] (fast)

Step 3 : [tex]X_2Y+Z\rightarrow X_2YZ[/tex] (fast)

The rate law expression will be:

[tex]Rate=K[Z_2][/tex]

From the given options we conclude that the only option 3 is the correct possible mechanisms for the given reaction.

Hence, the correct possible mechanisms for the reaction is:

Step 1 : [tex]X_2Y+Z_2\rightarrow X_2YZ_2[/tex] (slow)

Step 2 : [tex]X_2YZ_2+X_2Y\rightarrow 2X_2YZ[/tex] (fast)