Question

t-Butyl alcohol (TBA) is an important octane enhancer that is used to replace lead additives in gasoline [Ind. Eng. Chem. Res., 27, 2224 (1988)]. TBA was produced by the liquid-phase hydration (W) of isobutene (I) over an Amberlyst-15 catalyst. The system is normally a multiphase mixture of hydrocarbon, water, and solid catalysts. However, the use of cosolvents or excess TBA can achieve reasonable miscibility. The reaction mechanism is believed to be

Answer 1

Complete Question:

t-Butyl alcohol (TBA) is an important octane enhancer that is used to replace lead additives in gasoline [Ind. Eng. Chem. Res., 27, 2224 (1988)]. TBA was produced by the liquid-phase hydration (W) of isobutene (I) over an Amberlyst-15 catalyst. The system is normally a multiphase mixture of hydrocarbon, water, and solid catalysts. However, the use of cosolvents or excess TBA can achieve reasonable miscibility. The reaction mechanism is believed to be

I + S ⇄ I*S

W + S ⇄ W*S

W*S + I*S ⇄ TBA * S * S

TBA * S ⇄ TBA + S

Derive a rate law assuming:

(a) The surface reaction is rate limiting

(b) The adsorption of isobutene is limiting

(c) The reaction follows Eley-rideal Kinetics

I*S+W ⇄ TBA * S

and surface reaction is limiting

(d) Isobutene (I) and water (W) are adsorbed on different sites

I + S₁ ⇄ I*S₁

W + S₂ ⇄ W*S₂

TBA is not on the surface, and the surface reaction is rate-limiting

$[Ans: r'_{TBA}=-r'_1=\frac{k[C_1C_w-C_{TBA/K_C}]}{(1+K_WC_W)(1+K_1C_1)} ]$

(e) What generalizations can you make by comparing rate laws derived from part (a) through (d)?

Answer and explanation:

The mechanism for the production of t-butyl alcohol is as follows:

the reaction and rate law for the adsorption of isobutene over the amberlyst-15 is as follows:

I + S ⇄ I * S                                        $-r_{ADI} = k_I(C_1C_v-\frac{C_{I.S}}{K_I} )$

where $C_V$ is the concentration of vacant site

$K_I$ is the equilibrium constant of the adsorption

$k_I$ is the rate constant for forward

$C_I,C_{I.S}$ are concentration of isobutene and site filled with isobutene

The reaction and rate law for the adsorption of water (W) over the amberlyst-15 catalyst catalyst is as follows

W + S ⇄ W.S                                      $-r_{ADW} = k_W(C_WC_V-\frac{C_{W.S}}{K_W} )$

The reaction and rate law for the surface reaction on the catalyst is as follows

W.S + I.S ⇄ TBA . S + Sn                         $-r_s = k_s(C_{W.S}C_{I.S}-\frac{C_{TBA.S}C_V}{K_s} )$

The reaction and rate law for the desorption of TBA from catalyst is as follows

TBA . S ⇄ TBA + S                             $-r_{D TBA} = k_{DTBA}(C_{TBA.S}-\frac{C_{TBA}C_V}{K_{DTBA}} )$

the attached image below gives the remaining steps