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AfilCa [17]
3 years ago
10

The reverse water-gas shift (RWGS) reaction is an equimolar reaction between CO2 and H2 to form CO and H2O. Assume CO2 associati

vely adsorbs to the surface, while H2 dissociatively adsorbs. These adsorption steps are followed by reversible formation of formate (COOH*) and slow dissociation of formate into gaseous CO and adsorbed OH. The adsorbed OH is then removed as gaseous H2O via a hydrogenation step.
a) Using the details of the mechanism listed above, write out the elementary steps for the RWGS reaction.
b) Derive a rate law for the RWGS reaction consistent with the above assumptions and mechanism from (i).
c) Under what conditions is the RWGS reaction first order in CO2?
Engineering
1 answer:
klasskru [66]3 years ago
7 0

Answer:

a) Check explanation for this

b)Rate law is  Rate = \frac{k_{1}k_{4}  }{k_{3}+ 2k_{4}  } [H_{2} ]

c) The rate does not depend on the concentration of CO₂

Explanation:

a) Elementary steps for the RWGS reaction:

  • Dissociative adsorption of the H₂ Molecule

                 H_{2} $\xrightarrow{\text{k1}}$H + H   (Fast process)

  • Reversible Reaction between CO₂ and H

                \[ CO_{2} + H\mathrel{\mathop{\rightleftarrows}^{\mathrm{k2}}_{\mathrm{k3}}}COOH \] (Fast Process)

  • Slow dissociation of COOH into gaseous CO and absorbed OH

                COOH $\xrightarrow{\text{k1}}$ CO + OH (Slow process)

  • Fast hydrogenation of the OH to form H₂O

                   OH + H $\xrightarrow{\text{k5}}$H_{2} O (Fast process)

b) Derivation of the rate law

We need to determine the rate law for H, OH and COOH because these are the intermediates for this reaction.

The steady state approximation is applied to a consecutive reaction with a slow first step and a fast second step (k1≪k2). If the first step is very slow in comparison to the second step, there is no accumulation of intermediate product.

Rate of consumption = Rate of production

For COOH:

Using steady state approximation

\frac{d[COOH]}{dt} = 0

k_{2} [CO_{2} ][H] = k_{3} [COOH] k_{4} [COOH]\\

[COOH] = \frac{k_{2} [CO_{2} ][H]}{k_{3}k_{4}  } \\

For H:

\frac{d[H]}{dt} = 0

k_{1}[H_{2}] = k_{2}[CO_{2} [H]+k_{5} [ OH][H]

[H]= \frac{k_{1}[H_{2}]  }{k_{5}[OH] +k_{2}[CO_{2}]}\\

For OH:

\frac{d[OH]}{dt} = 0

k_{4} [COOH] = k_{5} [OH][H]\\\k[OH] = \frac{k_{4} [COOH]}{k_{5} H}\\

The rate of the overall reaction is determined by the slowest step of the reaction. The slowest process is the dissociation of COOH

Therefore the overall rate of reaction is:

Rate = k_{4} [COOH]\\

Rate = k_{4}  \frac{k_{2} [CO_{2} ][H]}{k_{3}k_{4}  }\\Rate = k_{4}  \frac{k_{2}[CO_{2}]\frac{k_{1}[H_{2}]  }{k_{5}[OH] +k_{2}[CO_{2}]}  }{k_{3}k_{4}}\\Rate = k_{4}  \frac{k_{2}[CO_{2}]\frac{k_{1}[H_{2}]  }{k_{5}\frac{k_{4}COOH }{k_{5}H }  +k_{2}[CO_{2}]}  }{k_{3}k_{4}}

Simplifying the equation above, the rate law becomes

Rate = \frac{k_{1}k_{4}  }{k_{3}+ 2k_{4}  } [H_{2} ]

c) It is obvious from the rate law written above that the rate of the RWBG reaction does not depend on the concentration of CO₂

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Answer:

The solution to this question is 5.153×10⁻⁴(kmol)/(m²·s)

That is the rate of diffusion of ammonia through the layer is

5.153×10⁻⁴(kmol)/(m²·s)

Explanation:

The diffusion through a stagnant layer is given by

N_{A}  = \frac{D_{AB} }{RT} \frac{P_{T} }{z_{2} - z_{1}  } ln(\frac{P_{T} -P_{A2}  }{P_{T} -P_{A1} })

Where

D_{AB} = Diffusion coefficient or diffusivity

z = Thickness in layer of transfer

R = universal gas constant

P_{A1} = Pressure at first boundary

P_{A2} = Pressure at the destination boundary

T = System temperature

P_{T} = System pressure

Where P_{T} = 101.3 kPa P_{A2} =0, P_{A1} =y_{A}, P_{T} = 0.5×101.3 = 50.65 kPa

Δz = z₂ - z₁ = 1 mm = 1 × 10⁻³ m

R =  \frac{kJ}{(kmol)(K)} ,    T = 298 K   and  D_{AB} = 1.18 \frac{cm^{2} }{s} = 1.8×10⁻⁵\frac{m^{2} }{s}

N_{A} = \frac{1.8*10^{-5} }{8.314*295} *\frac{101.3}{1*10^{-3} }* ln(\frac{101.3-0}{101.3-50.65}) = 5.153×10⁻⁴\frac{kmol}{m^{2}s }

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5.153×10⁻⁴(kmol)/(m²·s)

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<h3>What is likely the reason when an A/C compressor will not engage if A/C is turned on?</h3>

The cause that hinders the A/C Compressor from engaging are:

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  • Due to bad clutch coil.
  • Dur to an opening in the wire that links to the clutch coil.
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Note that the pressure switches is known to be one that control the on/off function of any kind of AC compressor and as such, if there is switch failure, it can hinder the AC compressor from functioning at all.

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True

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