Chemical Engineering Test

1. Thermodynamics

A research conducted by the University of Montenegro consisted in a process that was carried out
with a nonpolar substance in vapor phase. The process was a change in state of the nonpolar
substance from state 1 (270°C and 10 bar) to state 2 (320°C and 22 bar). Find the change in its
̂ [ kJ ] and molar entropy ∆𝑆̂ [ kJ ] for the process.
molar enthalpy ∆𝐻 mol mol.K

Since there is a lack of thermodynamic information such as tables or charts for this substance, the
researchers have suggested to use the residual properties from the virial equations of state. It is
known that the virial equation of state truncated in its second term is satisfactory to describe the
substance. The appropriate form is
𝐵𝑃
𝑍 =1+
𝑅𝑇
In this context, the second virial coefficient 𝐵 for a pure nonpolar substance can be found using
𝑅𝑇c (0)
𝐵= (𝐵 + 𝜔𝐵 (1) )
𝑃c

Where 𝐵(0) and 𝐵(1) are given by the correlations

0.422 0.172
𝐵(0) = 0.083 − 𝐵(1) = 0.139 −
𝑇r1.6 𝑇r4.2

Some additional information was provided by the researchers

kJ
𝑇c = 420 K 𝑃c = 7 bar 𝜔 = 0.2 𝐶𝑃 = 0.2001
mol. K
2. Phase equilibria

Consider the binary system substance(1)/substance(2) in vapor-liquid equilibrium (VLE). At VLE

conditions for this system, the vapor phase can be considered ideal while the liquid phase has
deviations from Raoult’s law. The temperature is fixed at 25°C and vapor pressures for substance 1
and 2 at such temperature are 𝑃1sat = 70 kPa and 𝑃2sat = 60 kPa respectively. Find the azeotrope
composition and pressure if it’s known that the Wilson model of local composition represents the
liquid-phase activity coefficients adequately.

Useful data to find the binary interaction parameters of Wilson model:

cm3 cm3
Molar volumes at 25°C of pure liquids 1 and 2 respectively 𝑉1𝐿 = 63 and 𝑉2𝐿 = 27 .
mol mol
𝑎12 𝑎21
Energies of interaction = 375 K and = 675 K.
𝑅 𝑅
3. Material and energy balances (nonreactive process)

The fresh juice of some fruits typically consists of aqueous solution with a content of solids especially
sugars. With the objective to reduce the cost of transport, the juice is concentrated before being
translated. Concentration processes are carried out using special evaporators operating below
atmospheric pressure in order to keep the organoleptic properties of the juice. To minimize the loss
of such properties, a fraction of the juice is overconcentrated and then is mixed with an amount of
fresh juice splitted out before entering the evaporator. This is an example of a system with bypass
stream.
kg
An important processing plant must produce 170 of juice with 30% wt. in solids. The evaporator
h
used operates in such a way that the concentrated juice leaves it with a solids content of 45% wt.
and its mass flow rate corresponds to 16.5% of the mass flow rate entering the evaporator.

Find the amount (mass flow rate) of fresh juice that must be fed to the process and the percentage
of fresh juice that needs to be bypassed from the evaporator to be mixed with the concentrated
juice.
4. Thermodynamics of reacting systems
kJ kJ
̂ro [ ] (at 25°C and 1 atm) and the heat of reaction ∆𝐻
Find the standard heat of reaction ∆𝐻 ̂r [ ]
mol mol
at 270°C for the decomposition reaction

4A(g) → 7B(g) + 3C(g)

Following data may be required:

Standard heats of formation (25°C and 1 atm)

kJ
̂f,o
∆𝐻 A(g) = −185
mol
kJ
̂f,o
∆𝐻 B(l) = 23
mol
kJ
̂f,o
∆𝐻 C(g) =3
mol

Latent heat of vaporization for substance B

kJ
̂vap,B = 97
∆𝐻
mol
Heat capacities at constant pressure (Temperature must be used in °C)
kJ
𝐶𝑝,A(g) = (12 ∗ 10−3 ) + (26 ∗ 10−5 )𝑇 + (2 ∗ 10−8 )𝑇 2
mol °C
kJ
𝐶𝑝,B(g) = (95 ∗ 10−3 ) + (38 ∗ 10−5 )𝑇 + (−28 ∗ 10−8 )𝑇 2 + (80 ∗ 10−12 )𝑇 3
mol °C
kJ
𝐶𝑝,C(g) = (29 ∗ 10−3 ) + (17 ∗ 10−5 )𝑇 + (12 ∗ 10−8 )𝑇 2 + (−15 ∗ 10−12 )𝑇 3
mol °C
5. Material and energy balances (reactive process)

Consider the decomposition reaction in vapor phase from problem 4

4A(g) → 7B(g) + 3C(g)

Pure gas A at 25°C is fed to a reactor. Measurements done by plant engineers indicate that the
fractional conversion of A (moles of A that reacted/moles of A fed) is about 27%. The products and
the amount of A that didn’t react leave the reactor at 270°C.
kJ
Find the amount of heat 𝑄̂ [mol] that must be added to the reactor in such a way that the process
occurs continuously. Steady state can be assumed and any changes in kinetic and potential energy
can be neglected.
6. Transport phenomena (momentum transfer)

Consider a Newtonian and incompressible fluid of constant viscosity 𝜇 in laminar flow regime. It
flows in the narrow space between two parallel plates separated by a distance 𝛿 as shown in the
figure. The upper plate slides with a constant velocity 𝑣up while the lower plate remains fixed.
∆𝑃
Consider a constant pressure gradient between the inlet and outlet flows. Under these conditions
𝐿
the flow is known as generalized Couette flow.

Find an expression for the velocity profile of the fluid between the plates under steady state
conditions. (Note the y-axis was defined upwards from the center of the space between the plates,
keep this in mind when applying the boundary conditions)
7. Heat transfer
W
A vapor is flowing through a circular pipe of a material with a thermal conductivity of 92 . The
mK
length of the pipe is 5 m, inner radius is 4 in and 0.5 in thickness. The temperature of the vapor
W
inside the pipe is 270 °C and some measurements made previously indicate the value 300 for
m2 K
internal convective heat transfer coefficient. The pipe is in a process plant where the ambient air
temperature is 25 °C and remains constant. At these conditions the external convective heat
W
transfer coefficient is 20 .
m2 K

kW
Find the heat flux (heat flow per unit area) in [ m2 ] at the external surface of the pipe when steady
state condition is reached. Any heat transfer by radiation can be neglected.
8. Transport phenomena (pressure drop in a packed bed/column)

For an absorption process a packed column with 1.5 cm diameter spheres is used to promote the
contact between liquid and gaseous phases. The packing offers a void fraction (porosity) of 0.35 at
operating conditions. The velocity of the gas was measured using a special device and its value was
m g
1.26 s . Also, a laboratory analysis recorded the gas density at 0.0018 cm3 and the viscosity at 2.3 ∗
10−5 Pa. s.

If the pressure of the entering gas is 4 atm, then find the outlet pressure if the length of the column
is 3.2 m.

9. Mass transfer

The process engineer of a processing plant on the outskirts of the city wants to separate
substance(1) from substance(2) using continuous distillation. The engineer’s idea is to obtain a
distillate containing 95% mol of substance(1) and a bottom product with 95% mol of substance(2).

The available column feed is saturated liquid with 60% mol of substance(1). Lab technicians
reported that relative volatility of binary system substance(1)/substance(2) can be considered
constant with a value of 4.7.

Determine the minimum number of ideal stages 𝑁min and reflux ratio 𝑅 if the operational optimum
corresponds to 1.33 times the minimum reflux ratio, in other words 𝑅 = 1.33𝑅min .
10. Chemical reaction engineering

An exothermic reaction occurs in a reactor provided with a cooling system in a corrosive materials
processing plant. The process engineer developed the following model for the reactor after using
material and energy balances. Here, 𝑀 is conversion while 𝑇 is the reactor temperature
𝑑𝑀
= 𝑘(1 − 𝑀)
𝑑𝑡
𝑑𝑇 4𝑈 1
= 𝑘(1 − 𝑀) [Δ𝑇ad − (𝑇 − 𝑇cool )]
𝑑𝑡 𝑑 𝑇 𝜌𝐶𝑃 𝑘(1 − 𝑀)

Where the kinetic constant 𝑘 is given by the Arrenhius equation

𝐸
𝑘 = 𝑘0 exp [− ]
𝑅𝑇
Initial reactor temperature is 300 K, also initial conversion can be considered zero since at the initial
moment the reaction has not started.

Find the conversion one minute after starting the reaction and the maximum temperature reached
by the reactor if the temperature of the fluid used in the cooling system is 𝑇cool = 330 K.

The following information was reported by the engineer on the reactor’s user manual

Δ𝑇ad = 123 K
4𝑈
= 0.3 s−1
𝑑 𝑇 𝜌𝐶𝑃

𝑘0 = 2 ∗ 1012 s−1
𝐸
= 10700 K
𝑅