Reference no: EM133025055

Mass And Energy Balance

FUNDAMENTAL PRINCIPLES

Question 1. (a) State what the following terms represent and give an example of where each may be used:
(i) w/w
(ii) w/v
(iii) v/v(iv) mole fraction
(v) mass fraction.
(b) What is the difference between the units 'kmol' and 'mol'?
(c) (i) Name the three main ideal gas laws and give the mathematical way of expressing each.
(ii) How are they combined in a single equation?
(iii) Use the ideal gas laws to calculate the mass of 25 m³ of a mixture of 21% v/v oxygen (O₂) and 79% nitrogen (N₂) which is at a temperature of 65°C and pressure of 2 bar.

Question 2. For each of the following compounds:
(i) aluminium chloride - AlCl₃
(ii) iron (III) sulphate (ferric sulphate) - Fe₂(SO₄)₃
(iii) cobalt nitrate - Co(NO₃)₂
(iv) sodium phosphate - Na₃PO₄

(v) amino-butane - C₄H₉NH₂

calculate, using values obtained from the Periodic Table given in Lesson 1: (a) the number of moles of that compound present in a mass of 200 g
(b) the amount in grams per litre (g l-1) contained in a 2 M solution of the compound.

Question 3. (a) Classify the following changes as either physical or chemical:
(i) the melting of ice
(ii) the purification of sugar by dissolving and re-crystallising
(iii) the removal of an acid gas by dissolving it in an alkali solution
(iv) the removal of water and gas from crude oil by settling and then separating the oil by distillation into various fractions (v) converting water into hydrogen and oxygen by electrolysis.
(b) Balance the following chemical equations, if necessary:
(i) MnO₂( )s + HCl(aq) → MnCl₂(aq) + HO₂ (l) + Cl₂( )g
(ii) Zn OH( )2(aq) + H SO₂ 4(aq) → ZnSO₄(aq) + HO₂ (l)
(iii) CHNH₂ 5 2( )l + O₂(g) → CO₂(g) + HO₂ (l) + N₂(g)
(iv) Al(s) + ZnO(s) → Al O₂ 3(s) + Zn(s)
(v) CaO( )s + H O₂ (l) → Ca OH( )2(s)
(c) For each of the following balanced equations, calculate the amounts of each reactant required to produce 100 kg of the product underlined (assume 100% conversion).
(i) H₂(g) + S(l) → H S₂ (g)

(ii) 3NaOH(aq) + H PO3 4(aq) → Na PO3 4(aq) + 3H O2 (l)

(iii) 2C H₂ 6( )g + 7O2(g) → 4CO₂(g) + 6H O₂ (g)

Question 4. Explain the terms:
(a) limiting reactant
(b) excess reactant
(c) tie substances
(d) % conversion
(e) equilibrium
(f) recycle
(g) purge
(h) by-pass.

Question 5. Sulphur trioxide is formed by the reaction between sulphur dioxide and air (more correctly oxygen) in a catalytic reactor, according to the unbalanced equation

SO₂(g) + O₂(g) →catalyst SO₃(g)

The reaction conditions give a 50% conversion when stoichiometric quantities of the reactants are used.
(a) Balance the equation.
(b) Calculate the composition (on a mole fraction basis) of the final mixture leaving the reactor.
Data: air consists of 21% v/v oxygen and 79% v/v nitrogen.

EXAMPLES OF ENERGY BALANCE

Question 1. In the production of soya bean oil, the oil is extracted from the original beans using hexane as solvent. The soya beans contain 12% w/w oil, the rest being insoluble bean waste. 500 kg min^-1 of soya beans are to be extracted. The bean waste leaving the process (known as raffinate) contains 0.5% w/w oil and 2% w/w hexane. The extract is 22% w/w oil and the rest is hexane. No bean waste leaves with the extract.

The extract is then passed to a distillation column which separates the mix into pure hexane, which is recycled back to the extractor for reuse, and 98.5% oil as final product. Hexane losses are made up by continuous make up from the hexane storage system.
(a) Draw a block diagram of the process incorporating all theinformation given in the question.
(b) Calculate (in kg min^-1):
(i) the amount of extract leaving the extractor
(ii) the amount of hexane required in the extraction stage
(iii) the amount of both streams leaving the distillation stage
(iv) the amount of hexane make-up required to ensure the process is steady state.
Check your answer by carrying out an additional balance not already used in your calculation.

Question 2. 180 kmol h^-1 of a three component mixture is made up of 60 mol % 'A', 25 mol % 'B' and 15 mol % 'C'. Component 'A' is the most volatile and 'C' the least volatile. The mixture is to be separated by continuous distillation in two columns so that 80% of 'C' in the feed is removed as bottom product in the first column as a 90 mol % solution with B.

The top product from the first column will be separated in the second column to give a top product here of 95 mol % 'A' and a bottom product of 85 mol % 'B'.

Determine the flows from the two columns and the mol % 'A' in bottom product from column 2.
(Assume there is to be no 'A' in the bottom product of column 1 and no 'C' in the top product of column 2.)

Question 3. The product from a reactor contains 60% w/w A, 25% w/w B and 15% w/w C. The final saleable product is required to contain 90% A.
The mixture can be purified in a distillation column but under the conditions possible in the column the product produced is 100% A with the bottom product containing no A. It is possible to mix the reactor products and distillation product.
Calculate:
(i) the amount of reactor product that could by-pass the distillation system to give the maximum amount of saleable product at minimum cost
(ii) the amount and composition of 'waste' material.

Question 4. 500 kg h^-1 of a 10% w/w solution of a compound X(OH)₂ is to be treated using a 5% excess of 20% w/w solution of sodium carbonate (Na2CO3) to precipitate the X as its carbonate according to the balanced reaction equation:
X OH( )₂(aq) + Na CO₂ 3(aq) → XCO₃( )s + 2NaOH(aq)
All the solid is filtered off but some solution remains with the solid such that the solution forms 4% w/w of the total mass removed.
The filtered liquid product is then neutralised with 2 molar hydrochloric acid according to the reactions:
Na CO₂ 3(aq) +2HCl(aq) → 2NaCl(aq) + H O₂ ( )l + CO₂( )g
NaOH(aq) + HCl(aq) → NaCl(aq) + H O₂ ( )l
Calculate:
(i) the amount (kg h^-1) of sodium carbonate solution required
(ii) the amount (kg h^-1) and composition (% w/w) of the liquid product after filtration
(iii) the amount (kg h^-1) and composition (% w/w) of the solid product after filtration
(iv) the amount of acid (in litres per hour) required for neutralisation.
Data: Relative atomic mass of X = 40, O = 16, H = 1, Na = 23, C = 12, Cl = 35.5.

Question 5. A chemical process is represented by the equation and diagram below:
A + 3B 2C

The feed to the process (F) contains 'A' and 'B' in stoichiometric proportions. It also contains 0.5 mol % of impurity 'I'.
The mixture (X) entering the reactor (i.e. feed and recycle) contains 'A' and 'B' in stoichiometric proportion but the level of impurity must not exceed 4 mol%.

In the reactor, the reaction goes to 60% completion. Pure product (C) is removed completely in the separator. The remainder of the reaction products (i.e. unconverted 'A' and 'B' together with any impurity) is recycled. In order not to exceed the maximum quantity of impurity in the reactor feed, some of the recycle is purged (P), the remainder (R) going back to the reactor.

On the basis of 100 kmol of 'A' plus 'B' entering the reactor at (X), carry out mass balances to find the flows of:
(i) feed (F)
(ii) recycle (R) (iii) purge (P).

ENERGY BALANCE

Attempt ALL questions.

Question 1. (a) Define:
(i) specific heat capacity (ii) molar heat capacity.
(b) Distinguish between:
(i) heat capacity at constant volume and constant pressure
(ii) internal energy and enthalpy
(iii) sensible heat and latent heat.
(c) State the First Law of Thermodynamics as applicable to energybalance.

Question 2. Identify a process you are familiar with from your job (or everyday experience), which involves at least two different gases (you could for example use methane and air in a gas cooker if no other suitable alternative is available). Note the normal temperature (°C) of the gases in use.
(a) Estimate the molar heat capacity at constant pressure (Cp in J mol-1 K-1) for each gas at its normal operating temperature using:
(i) the correlation
Cp = a+ bT+ cT₂ + dT₃ where a, b, c and d are constants to be obtained from a relevant source and T is in K.
(ii) any other method (quote the source of data so it can be checked).
(c) Comment on the difference (if any) between the two answers foreach gas obtained in (a).
(d) Estimate the mean molar heat capacity at constant pressure over therange 273 K to T K and hence calculate the change in enthalpy over that range for each gas.

Question 3. (a) Write the balanced chemical equation for the complete combustion of 1 mole of liquid methanol (CH₃OH) to carbon dioxide (CO₂ (g)) and water (H₂O(g)).
(b) Using the data given, calculate the standard heat of reaction(combustion) when methanol is completely burned in air.
Data:
ΔHf° of HO₂ (g) = - 242 1. kJ mol^-1
ΔHf° of CO₂(g) = - 393 8. kJ mol^-1
ΔHf° of CH OH₃ (l) = - 238 7. kJ mol^-1
(c) Using the answer obtained in (b) and the data given below, calculatethe standard heat of reaction (combustion) of methanol at 300°C.
Data:
Mean specific heat capacities over the range 25°C to 300°C for
CO₂ (g) = 32.0 J mol^-1 K^-1 H₂O(g) = 36.5 J mol^-1 K^-1
O₂(g) = 30.0 J mol^-1 K^-1
CH₃OH(l) = 50.0 J mol^-1 K^-1
(d) (i) Using the answer from (b) calculate a value for the heat of
reaction (combustion) of methanol at constant volume.
Take R = 0.0083 kJ mol^-1 K^-1.
(ii) Give one instance where the heat of reaction at constant volume may be required rather than the one at constant pressure.

Question 4. Fuel oil is to be heated in a heat exchanger using steam under the following conditions:
Inlet temperature of oil = 40°C.
Outlet temperature of oil = 120°C.
Flow rate of oil = 420 kg h^-1.
Mean specific heat capacity of oil = 2.05 kJ kg^-1 K^-1.
Temperature of steam = 165°C (dry saturated).
Temperature of steam condensate = 130°C
8% of the heat is lost to the atmosphere (i.e. process is 92% efficient).
(a) Using steam tables, find:
(i) the specific latent heat of vaporization of steam (hfg) at 165°C in kJ kg^-1
(ii) the difference in enthalpy of liquid water (hf) between 165°C and 130°C in kJ kg^-1.
(c) Calculate the quantity of this steam required per hour to perform this duty.

Attachment:- Mass And Energy Balance.rar