CE 10167 - CE Principles (Chemical Reaction Engineering)

Question 1

How can the conversion of a limiting reactant be calculated/written?

Answer 1

X = moles ‘A’ reacted/ moles ‘A’ fed

Where X is conversion (no units)

Question 2

How can conversion of substance ‘A’ in a reaction be written?

Answer 2

X = ( N (Ao) - N (A) ) / N (Ao)

Where: X is conversion N (Ao) is initial moles of substance A

N(A) is the final moles / output moles of substance A. This can be written for flow rate and concentration too.

Question 3

What does the yield of a reaction show?

Answer 3

Yield, Y, shows how much of a desired product was formed.

Question 4

What is selectivity (of a reaction)?

Answer 4

How much desired product was formed in ratio to the undesired product.

Question 5

What are reaction kinetics?

Answer 5

The measurement of how quickly reactions (in reactors) occur, and how long reactants should remain in the reactor.

Question 6

What is space time (aka holding time or mean residence time)?

Answer 6

The time necessary to process one reactor’s volume of fluid based on a particular set of entrance conditions.

Question 7

How is space time calculated?

Answer 7

τ = V / v 0 (= s) Where: τ is space time V is reactor volume v 0 is volumetric flow rate

Question 8

What is space velocity?

Answer 8

The reciprocal of space time. SV = 1/τ = v0/V (=s^-1) However, since the flow rates of the fluids are generally very large in industrial systems, space velocity is used in terms of hours.

Question 9

How can rate of consumption of species A be calculated?

Answer 9

-rA = moles of A consumed / (volume * time) -rA = ΔN(A) / (V*Δt) [Since n = cV] rA = -(ΔC (A) / Δt) This is an average rate obtained by taking the change in concentration over a time period, which is an approximation of the average reaction rate in that time interval.

Question 10

What formulae are used to calculate the average and instantaneous rates of reaction?

Answer 10

Average rate is obtained by taking the change in concentration over a time period: rate A = -(ΔC (A) / Δt) Instantaneous rate of reaction is defined as the change in concentration of an infinitely small time interval, which expressed as the limit or derivative expression: rate A = - lim Δt→0 (ΔC (A) / Δt)

Question 11

How is the instantaneous rate of reaction calculated?

Answer 11

Instantaneous rate of reaction is defined as the change in concentration of an infinitely small time interval, which expressed as the limit or derivative expression: rate A = - lim Δt→0 (ΔC (A) / Δt) Taking the limit as Δt approaches to zero, gives the differential: r(A) = -dC(A)/dt Using moles instead of ‘A’, r(A) = -(1/V)(dN (A)/dt) [1/V * rate of moles used]

Question 12

What’s rate of reaction?

Answer 12

The speed at which a chemical reaction proceeds in terms of disappearance of a reactant (how quickly they are used up) or as the rate of appearance of a product (how quickly they are formed) per unit time.

Question 13

What is the rate law?

Answer 13

The Rate Law describes the relationship between reactant rates and reactant concentrations (or pressures) in terms of a mathematical equation which then describes the progress of the reaction.

Question 14

What is the mathematical formula: ‘power law’ for describing the rate law?

Answer 14

-rA = k CᵐA CⁿB (r = k[A][B]) Where: - C is concentration of species - k is reaction rate constant - m and n are reaction orders

Question 15

What factors affect the rate of reaction?

Answer 15

Temperature Order of Reaction 
Concentration 
 Pressure 
Catalyst

Question 16

How does temperature affect the rate of a reaction?

Answer 16

There is an exponential relationship between temperature and rate constant. k = Ae^(-E/RT) Therefore, as temp’ increases, rate increases.

Question 17

How do reaction orders affect reaction rate?

Answer 17

Zero order - constant rate. Rate is independent of conc’. First order: rate is proportional to conc’. Second order: rate is proportional to square of the conc’ of a reactant.

Question 18

How can a zero order reaction be determined graphically?

Answer 18

A concentration-time graph will show a straight line with a negative gradient. Conc’ falls at a steady rate with time. (This wouldn’t work with 1st and 2nd order reactions, which have curved conc’-time graphs)

Question 19

How can a first order reaction be determined graphically?

Answer 19

Plot the graph of ln(C₀/C) against time. [C is conc’] If it produces a straight line with positive gradient, it is first order. (Gradient = k)

Question 20

How can a second order reaction be determined graphically?

Answer 20

Plot the graph of 1/C against time. [C is conc’] If it produces a straight line with positive gradient (and non-zero origin), it is second order. (Gradient = k)

Question 21

What are batch reactors?

Answer 21

Reaction vessels varying in size from <1L to 15,000L

Question 22

What are Fed-batch reactors?

Answer 22

Reaction vessels where reactants enter and remain in the system until the reaction is complete. However, gases produced during the reaction can be removed, or additional reactants can be added throughout the reaction. It doesn’t reach steady state.

Question 23

What are the applications of batch reactors?

Answer 23

Wide variety of uses. Mainly used for liquid phase reactions requiring long period of time. Used when a small amount of product is wanted; thus it’s preferred during product testing phases.

Question 24

What are the advantages and disadvantages of batch reactors?

Answer 24

Adv: - High conversions can be obtained by leaving reactants in reactor for longer times - Batch reactor jackets allow the system to change heating or cooling power at constant jacket heat flux. - Can make many products consecutively - Easy to clean - Good for producing small quantities Disadv: - High cost of labour per unit production - Hard to maintain - Long downtime for cleaning = less production

Question 25

What are continuous flow reactors?

Answer 25

Reaction vessels where the reactant is continuously flowing in and products are flowing out. (Examples include tubular flow reactor and CSTR). They continuously flow at steady state.

Question 26

What are tubular flow reactors:

Answer 26

A type of continuous flow reactor where reactants continuously flow at steady state e.g. plug flow reactors. As the reactant travels along the tube, conc’ of reactant decreases.

Question 27

What are the advantages and disadvantages of tubular reactors?

Answer 27

Advs: - Used large scale - High conversion per unit volume - Good heat transfer - Low operating cost Disadv: - May have thermal gradients - Poor temp’ control - Channelling may occur - Shutdown and cleaning is expensive

Question 28

What’s a CSTR, Continuous Stirred Tank Reactor?

Answer 28

A type of continuous flow reactor. reactants flow in and products flow out, and the system is continuously stirred throughout. They’re open systems and steady state. A steady state must be reached where the flow rate into the reactor equals the flow rate out and the conditions in the reactor do not change with time, otherwise the tank would empty or overflow. CSTRs are very well mixed, so the contents have relatively uniform properties such as temperature, density, etc. throughout the operation.

Question 29

What are the advantages and disadvantages of CSTR?

Answer 29

Adv: - Easy to maintain temp’ - Cheap to build - Has large heat capacity Interior of reactor is easily accessed Disadv: - Conversion of reactant to product per volume of reactor is small compared to other flow reactors

Question 30

How can reactors be classified?

Answer 30

Mode of operation e.g. batch, semi-batch, continuous End use e.g. chemical, biological, electrochemical or nuclear Catalyst (or phase) based e.g. homogenous (single phase) or heterogenous (multi-phase)

Question 31

What is the overall material balance on a system?

Answer 31

Mass flow in - mass flow out = accumulation

Question 32

What is the material balance for a certain species, A, on a system?

Answer 32

(Molar flow of species A in)-(Molar flow of species A out) + or - (rate of species A produced/consumed) = (Rate of accumulation of species A in time t)

Question 33

What’s the symbol for molar flowrate?

Answer 33

F_A

Question 34

What are the assumptions in deriving a design equation for a batch reactor?

Answer 34

Closed system Perfectly mixed / uniform composition Conditions can vary over time

Question 35

What are the rate constant equations for batch reactors for zero, first and second order reactions? (Should be derived from rate/-dC/dt and not memorised)

Answer 35

Zero: k = 1/t (C₀ - C) First: k = 1/t ln(C₀/C) Second: k = 1/t (1/C - 1/C₀)

Question 36

How is the design equation for a CSTR reactor formulated?

Answer 36

Molar inflow - Molar outflow + rate of species produced - rate of species consumed = rate of accumulation. However, steady state therefore no accumulation. F in -F out - (-rV) = 0 V = (F in - F out) / (-rA) In terms of conversion, X: V = XF in / (-rA) F in = v₀CA₀ -rA = kCA₀ (1 - X) V = (Xv₀CA₀) / (kCA₀ (1 - X))

Question 37

What’s the Levenspiel plot?

Answer 37

A plot to determine the required volume of a chemical reactor using the experimental data on the reaction taking place in the reactor. It is a plot of the inverse of the reaction rate (y axis) as a function of conversion (x axis). The area is therefore equal to V/F A₀. Knowing F A₀ means that reactor volume can be estimated.

Question 38

What is the Levenspiel plot used for?

Answer 38

It is a plot of the inverse of the reaction rate (y axis) as a function of conversion (x axis), used to determine the required volume of a chemical reactor using the experimental data on the reaction taking place in the reactor. The area is therefore equal to V/F A₀. Knowing F A₀ means that reactor volume can be estimated.

Question 39

How is a design equation for a PFR (plug flow reactor) determined?

Answer 39

(The reactor is divided into sub-volumes and a mass balance is carried out on the sub-volume rather than the whole volume, ΔV) Therefore: [molar flow of A into ΔV] - [molar flow of A out of ΔV] +/- [rate of formation/consumption in ΔV] = [Rate of accumulation in ΔV during Δt] Fₐ₍ᵥ₎ - Fₐ₍ᵥ₊Δᵥ₎ - (-rₐΔV) = 0 Rearrange to find -rₐ and take the limit as ΔV approaches 0. The design equation becomes: -dFₐ/dV = -rₐ Integrate both sides: V = ∫ dFₐ/rₐ from Fₐ to Fₐ,₀ Writing in terms of conversion, (Fₐ = Fₐ,₀ - Fₐ,₀X) so Fₐ,₀*dX/dV = rₐ Now, integrating from X = 0 to X = X: V = Fₐ,₀*∫dX/-rₐ