 #### Concept explainers

Question Chapter 4, Problem 4.66P
Interpretation Introduction

## (a)Interpretation:The formula for KeT is to be derived and Ke450 K=0.0548 atm−2 is to be shown.Concept introduction:The Arrhenius equation for the equilibrium rate constant as a function of the absolute temperature is:KeT=A0exp−EaRTK ...... (1)Here, Ea is the activation energy of the reaction, R is the universal gas constant with the value 8.314 J/mol·K and A0 is an Arrhenius constant.The equation of a straight line on semi-log plot is, lny=mx+lnb.Given two points x1,y1 and x2,y2, the slope m for this equation is calculated as:m=lny2−lny1x2−x1 ...... (2)The value of intercept can be calculated using this slope and any one of the given points.

Interpretation Introduction

### (b)Interpretation:The expressions for nA,nB, and nC and then for yA,yB, and yC in terms of nA0,nB0,nC0 and ξ is to be written. Also, an expression involving only nA0,nB0,nC0,P,T, and ξe is to be derived.Concept introduction:For a single reaction system, the extent of reaction for each of the components present in the products can be estimated by the equation:ni=nio+viξ ...... (5)Here, ni is the final moles of the component i, nio is the initial moles of the component i, vi is the stoichiometric coefficient of the component i in the reaction and ξ is the extent of the reaction. vi is taken as negative for reactants and positive for products.Mole fraction yi of any component is given by:yi=ni∑ni ...... (6)Here, ni is the moles of component i and ∑ni is the total moles of all the components present in the mixture.

Interpretation Introduction

### (c)Interpretation:The molar composition of the product stream and fractional conversion of CO is to be calculated.Concept introduction:The formula for the fractional conversion f is:f=moles reactedmoles fed ...... (13)

Interpretation Introduction

### (d)Interpretation:Any physical constraints on ξe associated with nA0=nB0=1 mol is to be determined. Also, fractional conversion of CO and total gram moles of methanol produced in the modified process is to be calculated.Concept introduction:The formula for the fractional conversion f is:f=moles reactedmoles fed ...... (13)

Interpretation Introduction

### (e)Interpretation:The calculations done in part (d) are to be repeated for nB0=2 mol. Also, the subsequent increase in the fractional conversion of CO is to be explained.Concept introduction:The formula for the fractional conversion f is:f=moles reactedmoles fed ...... (13)

Interpretation Introduction

### (f)Interpretation:The equations for yA,yB,yC, and fA is to be written in terms of yA0,yB0,P and T in an excel spreadsheet and checked for the values given in part (c). Also, the effect of increase in the moles of CH3OH in the feed, temperature and pressure on fA is to be determined.Concept introduction:Mole fraction yi of any component is given by:yi=ni∑ni ...... (6)Here, ni is the moles of component i and ∑ni is the total moles of all the components present in the mixture.The formula for the fractional conversion f is:f=moles reactedmoles fed ...... (13) 10:17
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