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engineering
introduction to chemical engineering thermodynamics

Questions and Answers of Introduction To Chemical Engineering Thermodynamics

Estimate the fugacity of a gaseous mixture consisting of \(30 \%\) component 1 and \(70 \%\) component 2 by mole, given that at \(100^{\circ} \mathrm{C}\) and \(50 \mathrm{bar}\), the fugacity
What are activity and activity coefficient? How does activity coefficient relate to excess property?
Calculate the fugacity of a mixture of \(60 \mathrm{~mol}\) per cent carbon dioxide and \(40 \mathrm{~mol}\) per cent argon at \(600 \mathrm{~K}\) and \(60 \mathrm{bar}\), assuming that the mixture
Estimate the fugacity of a ternary gas mixture consisting of \(30 \mathrm{~mol}\) per cent of hydrogen (component 1), \(25 \mathrm{~mol}\) per cent of nitrogen (component 2), and \(45 \mathrm{~mol}\)
Deduce the Gibbs-Duhem relation for a multicomponent system.
What is the change in entropy when \(0.7 \mathrm{~m}^{3}\) of \(\mathrm{CO}_{2}\) and \(0.3 \mathrm{~m}^{3}\) of \(\mathrm{N}_{2}\), each at 1 bar and \(25^{\circ} \mathrm{C}\), blend to form a gas
The saturation pressure of liquid water at \(372.12 \mathrm{~K}\) is \(100 \mathrm{kPa}\). Estimate the fugacity of liquid water at \(372.12 \mathrm{~K}\) and \(300 \mathrm{kPa}\), given that the
Derive an expression for the fugacity of a component in a mixture.
One mole of helium at \(100^{\circ} \mathrm{C}\) is mixed with \(0.5 \mathrm{~mol}\) of neon at \(0^{\circ} \mathrm{C}\). Calculate \(\Delta S_{\text {mix }}\) for this mixture if the mixing is
Calculate the fugacity of liquid butadiene at \(313 \mathrm{~K}\) and 10 bar. The saturation pressure of butadiene at \(313 \mathrm{~K}\) is 4.2 bar. The molar volume and saturated fugacity of liquid
What do you mean by fugacity of solid and liquids?
Estimate the entropy change of mixing when \(0.75 \mathrm{~m}^{3}\) of hydrogen and \(0.25 \mathrm{~m}^{3}\) of nitrogen at \(1 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\) are mixed to prepare a
A gas obeys the equation of state \(P(V-b)=R T\). For this gas, \(b=0.0391\) \(\mathrm{dm}^{3} / \mathrm{mol}\). Calculate the fugacity and fugacity coefficient for the gas at \(1000^{\circ}
What is the significance of the Poynting pressure correction factor?
Calculate \(\Delta S_{\text {mixing }}\) for the formation of one mol of a mixture on mixing nitrogen and oxygen in the volume ratio of \(4: 1\).
Estimate the fugacity of liquid acetone at \(110^{\circ} \mathrm{C}\) and 275 bar. At \(110^{\circ} \mathrm{C}\) the vapour pressure of acetone is \(4.360 \mathrm{bar}\) and the molar volume of
In the light of Gibbs theorem, discuss the importance of the ideal gas mixture model.
Calculate \(\Delta G_{\text {mixing }}\) and \(\Delta S_{\text {mixing }}\) per litre of mixture containing \(15 \%\) nitrogen, \(55 \%\) hydrogen and \(30 \%\) ammonia at S.T.P.
Estimate the entropy change of mixing when \(2.8 \mathrm{~L}\) of oxygen and \(19.6 \mathrm{~L}\) of hydrogen at \(1 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\) are mixed to prepare a gaseous
What do you mean by property change of mixing? Derive an expression for the free energy change due to mixing in a solution.
The molar volume of a binary liquid mixture at \(T\) and \(P\) is given by\[ V=120 x_{1}+70 x_{2}+\left(15 x_{1}+8 x_{2}\right) x_{1} x_{2} \](a) Find the expressions for the partial molar volume of
Derive an expression for the free energy change of mixing when two ideal gases of \(n_{1}\) and \(n_{2}\) moles respectively are mixed isothermally but at different pressures.
Define the term 'excess property'. Give an informatory note on the excess free energy of a component in a mixture.
At \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}, 0.7\) moles of helium were mixed with 0.3 moles of argon. Calculate the free energy and enthalpy change of mixing. Assume that the gases behave
Explain the 'ideal solution model' with the help of the Lewis-Randall rule.
State Raoult's law. Show that it is a simplified form of the Lewis-Randall rule.
A vessel, divided into two parts by a partition, contains \(4 \mathrm{~mol}\) of nitrogen gas at \(75^{\circ} \mathrm{C}\) and \(30 \mathrm{bar}\) on one side and \(2.5 \mathrm{~mol}\) of argon gas
A \(20 \mathrm{~L}\) vessel is divided into two compartments with the help of a removable partition. The first compartment contains \(12 \mathrm{~L}\) of hydrogen and the second compartment contains
Explain Henry's law and show that Raoult's law is a special case of Henry's law.
The excess Gibbs free energy of a binary liquid at \(T\) and \(P\) is given by\[ \frac{G^{\mathrm{E}}}{R T}=\left(-2.6 x_{1}-1.8 x_{2}\right) x_{1} x_{2} \](a) Find expressions for \(\gamma_{1}\) and
The excess enthalpy of a binary solution mixture is given by\[ H^{\mathrm{E}}=x_{1} x_{2}\left(40 x_{1}+20 x_{2}\right) \mathrm{J} / \mathrm{mol} \]Determine the expressions for
The excess free energy of a binary solution mixture is given by\[ \frac{G^{\mathrm{E}}}{R T}=-3 x_{1} x_{2}\left(0.4 x_{1}+0.5 x_{2}\right) \mathrm{J} / \mathrm{mol} \]Find the expressions for
The excess free energy of a binary solution mixture is given by\[ \frac{G^{\mathrm{E}}}{R T}=x_{1} x_{2}\left[A+B\left(x_{1}-x_{2}\right)\right] \mathrm{J} / \mathrm{mol} \]Find the expressions for
Show that in a binary solution, if the solute obeys Henry's law, the solvent obeys the Lewis-Randall rule.
The activity coefficients of two components of a solution are given by\(\ln \gamma_{1}=A x_{2}^{2}+B x_{2}^{2}\left(3 x_{1}-x_{2}\right)\) and \(\ln \gamma_{2}=A x_{1}^{2}+B x_{1}^{2}\left(x_{1}-3
Show that\[ M^{\mathrm{E}}=M^{\mathrm{R}}-\sum x_{i} M_{i}^{\mathrm{R}} \]
For a ternary system, the influence of composition on property \(M\) can be represented by \[ M=x_{1} M_{1}+x_{2} M_{2}+x_{3} M_{3}+C x_{1} x_{2} x_{3} \] where \(M_{1}, M_{2}\) and \(M_{3}\) are the
For the benzene-chloroform system, \(H^{\mathrm{E}}\) at \(25^{\circ} \mathrm{C}\) can be expressed as\[ H^{\mathrm{E}}=x_{1}
The volume of a mixture of two organic liquids 1 and 2 is given by\[ V=110-17 x_{1}-2.5 x_{1}^{2} \]where \(V\) is the volume in \(\mathrm{m}^{3} / \mathrm{mol}\) at \(1 \mathrm{bar}\) and \(300
The fugacity of component 1 in a binary liquid mixture consisting of components 1 and 2 at \(298 \mathrm{~K}\) and 20 bar is given by \(\bar{f}_{1}=50 x_{1}-80 x_{1}^{2}+40 x_{1}^{3}\), where
The molar volumes of a binary solution at \(25^{\circ} \mathrm{C}\) are measured as follows:Using the method of tangential intercept, calculate the partial molar volumes of components 1 and 2 at
Estimate the fugacity of a ternary gas mixture consisting of \(25 \mathrm{~mol}\) per cent hydrogen (component 1), \(35 \mathrm{~mol}\) per cent of nitrogen (component 2), and \(40 \mathrm{~mol}\)
The saturation pressure of liquid water at \(393.38 \mathrm{~K}\) is \(200 \mathrm{kPa}\). Estimate the fugacity of liquid water at \(372.12 \mathrm{~K}\) and \(300 \mathrm{kPa}\). We are given that
At \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}, 0.7 \mathrm{~mol}\) of methane were mixed with \(0.3 \mathrm{~mol}\) of oxygen. Calculate the free energy and enthalpy change of mixing. Assume
Ammonia gas obeys the equation of state \(A(V-b)=R T\). For this gas, \(b=0.037 \mathrm{dm}^{3} / \mathrm{mol}\). Calculate the fugacity and \(\phi=1.08\) for the gas at \(0^{\circ} \mathrm{C}\) and
Show that\[ \gamma_{i}=\frac{\bar{\phi}_{i}}{\phi_{i}} \]
Carbon dioxide occupies a tank at \(100^{\circ} \mathrm{C}\). If the volume of the tank is \(0.5 \mathrm{~m}^{3}\) and the pressure is \(500 \mathrm{kPa}\), determine the mass of the gas in the tank.
Give an informatory note on saturation temperature and saturation pressure.
Nitrogen at 15 bar is used to fill a container of \(0.25 \mathrm{~m}^{3}\). The filling process is very slow and the contents of the tank attain the room temperature of \(295 \mathrm{~K}\). How much
If a cylinder of volume \(0.1 \mathrm{~m}^{3}\) is filled with \(1.373 \mathrm{~kg}\) of ammonia at \(1.95 \mathrm{MPa}\), determine the temperature at which ammonia exists in the cylinder. Assume
A tank of \(1 \mathrm{~m}^{3}\) volume is filled with \(5 \mathrm{~kg}\) ammonia at \(300 \mathrm{~K}\). Determine the pressure exerted by ammonia using the Redlich-Kwong equation.
Calculate the acentric factor for ethanol. The vapour pressure of ethanol can be estimated from the following equation:\[ \log _{10} P^{\text {Sat }}=8.1122-\frac{1592.864}{t+226.184} \]where
For liquid acetone at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{bar}\),\[ \beta=1.487 \times 10^{-3} /{ }^{\circ} \mathrm{C} \quad \alpha=62 \times 10^{-6} / \mathrm{bar} \quad V=1.287
Determine the molar volume of ammonia vapour and ammonia liquid at \(321.55 \mathrm{~K}\) and 1.95 \(\mathrm{MPa}\). Ammonia is assumed to follow van der Waals equation of state.
Any equation that relates to the pressure, temperature and volume is called an equation of state. Justify the statement.
The Dieterici equation of state is given by\[ P(V-b) \exp \left(\frac{a}{R T V}\right)=R T \]where \(a\) and \(b\) are constants. Develop the relations to determine the constants \(a\) and \(b\) in
Calculate the volume occupied by isopropanol vapour at \(200^{\circ} \mathrm{C}\) and 10 bar by using(a) Ideal gas equation of state(b) Virial equation of state(c) Virial equation of state\[
At \(17^{\circ} \mathrm{C}\), at constant pressure, the heat of combustion of amorphous carbon is 96960 cal and that of \(\mathrm{CO}\) to \(\mathrm{CO}_{2}\) is \(67960 \mathrm{cal}\). Determine the
The heat of combustion of liquid ethanol into \(\mathrm{CO}_{2}\) and liquid water is \(327 \mathrm{kcal}\) at constant pressure. The temperature is maintained at \(327^{\circ} \mathrm{C}\).
The standard enthalpy change of combustion of acetylene is \(-1300.48 \mathrm{~kJ}\) at \(298 \mathrm{~K}\) with \(\mathrm{H}_{2} \mathrm{O}\) in the liquid state. Calculate the standard enthalpy of
Which instrument is used to determine the heat of combustion of a fuel?
A piston-cylinder device contains \(1.2 \mathrm{~kg}\) of saturated water vapour at \(180^{\circ} \mathrm{C}\). Heat is transferred to steam. As a result, steam expands reversibly to a final pressure
In a chemical process plant, water at 67°C is pumped from a storage tank at the rate of 20,000 kg/hr. The motor for the pump expenses work at the rate of 1.5 hp. The water passes through a heat
Prove that \(C_{P}>C_{V}\), where the notations have their usual meanings.
One mol of nitrogen at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) is allowed to expand reversibly to a volume of \(50 \mathrm{dm}^{3}\). If the gas is assumed to be ideal, calculate the final
Derive an expression for the work done if an ideal gas undergoes an adiabatic change.
\(5 \mathrm{~kg}\) of \(\mathrm{N}_{2}\) is heated from an initial state of \(37^{\circ} \mathrm{C}\) and \(101.33 \mathrm{kPa}\) until its temperature reaches \(237^{\circ} \mathrm{C}\). Calculate
A horizontal piston-cylinder assembly is placed in a constant temperature bath. The piston slides in the cylinder with negligible friction, and the external force holds it in place against an initial
\(\mathrm{N}_{2}\) is contained in a cylinder of \(30 \mathrm{~L}\) capacity at \(75 \mathrm{~atm}\) and \(30^{\circ} \mathrm{C}\). Suddenly a valve is opened to release \(\mathrm{N}_{2}\) into the
A rigid vessel containing \(5 \mathrm{~mol}\) of \(\mathrm{He}\) gas at \(25^{\circ} \mathrm{C}\) is heated to \(225^{\circ} \mathrm{C}\). Calculate the heat requirements for the process, given that
A spherical balloon of \(1 \mathrm{~m}\) diameter contains a gas at \(150 \mathrm{kPa}\). The gas inside the balloon is heated until the pressure reaches \(600 \mathrm{kPa}\). During heating the
\(5 \mathrm{kmol}\) of Ar gas confined in a cylinder undergoes a change from an initial condition of \(20 \mathrm{bar}\) and \(350 \mathrm{~K}\) to a final condition of \(2 \mathrm{bar}\) and \(350
A thermally insulated cylinder having a frictionless piston contains \(\mathrm{N}_{2}\) gas. The piston is held in place by latches in such a way that it divides the cylinder into two equal halves.
Determine the molar volume of a gas at \(137^{\circ} \mathrm{C}\) and a pressure of 12 bar. Assume the gas behaves ideally.
Determine the molar volume of a gas at \(37^{\circ} \mathrm{C}\) and a pressure of \(2 \mathrm{bar}\). Assume that the gas behaves ideally.
What is pure substance? Give some examples to justify the concept.
A spherical balloon with a diameter of \(6 \mathrm{~m}\) is filled with helium at \(20^{\circ} \mathrm{C}\) and \(200 \mathrm{kPa}\). Determine the mole number and the mass of the helium in the
\(3.28 .0 \mathrm{~m}^{3}\) of air is enclosed by a frictionless piston at in a cylinder at \(300 \mathrm{kPa}\). The gas undergoes a compression process with no change in temperature and its volume
What do you mean by the different phases of a pure substance?
\(12.0 \mathrm{~m}^{3}\) of air is enclosed by a frictionless piston at in a cylinder at \(325 \mathrm{kPa}\). The gas undergoes a compression process with no change in temperature and its volume
A vessel contains \(6 \mathrm{~m}^{3}\) of air at a pressure of \(500 \mathrm{kPa}\). If one-fifth of the air be removed by an air pump, what will be the pressure of the remaining air, the
What is the difference between compressed liquid and saturated liquid?
A steel cylinder containing air has a closely fitted piston and a set of stops as shown in Fig. 3.7. The piston is loaded with certain weights. The air inside the cylinder is initially at
Explain the significance of critical point and triple point.
For a gas, \(T_{\mathrm{C}}=304.2 \mathrm{~K}\) and \(P_{\mathrm{C}}=72.8 \mathrm{~atm}\). Calculate the van der Waals constant for the gas.
Calculate the molar volume of methane at \(773 \mathrm{~K}\) and 15 bar using the following methods:(a) Ideal gas equation of state(b) van der Waals equation of state, with \(a=0.2303 \mathrm{Nm}^{4}
Draw a \(T-V\) diagram and indicate the saturated liquid and saturated vapour lines.
Prove that where\[ \left(\frac{\partial \beta}{\partial P}\right)_{T}=-\left(\frac{\partial \alpha}{\partial T}\right)_{P} \]\(\alpha=\) Isothermal compressibility\(\beta=\) Volume expansivity.
Find the second, third and fourth virial coefficients of the van der Waals equation of state.
Draw a \(P-T\) diagram and show the sublimation and vaporization curves.
Calculate the molar volume of ammonia at \(350 \mathrm{~K}\) and 100 bar using van der Waals equation of state, given that \(a=0.4233 \mathrm{Nm}^{4} / \mathrm{mol}^{2}\) and \(b=3.73 \times 10^{-5}
Determine the molar volume of \(n\)-butane at \(500 \mathrm{~K}\) and \(8 \mathrm{MPa}\) by making use of(a) the ideal gas law and(b) the virial equation of state. The virial coefficients of
What is the importance of latent heat of fusion and vaporization?
Determine the specific volume of \(\mathrm{N}_{2}\) gas at \(10 \mathrm{MPa}\) and \(150 \mathrm{~K}\) based on(a) ideal gas equation and(b) generalized compressibility factor.
Prove that where\[ C_{P}-C_{V}=\frac{T V \beta^{2}}{\alpha} \]\(\alpha=\) Isothermal compressibility\(\beta=\) Volume expansivity.
Establish the ideal gas equation of state from Charles' law, Boyle's law and Avogadro's law. Enumerate the limitation of the ideal gas law.
What is the necessity of cubic equation of state?
Calculate the mass of ethane contained in a \(0.3 \mathrm{~m}^{3}\) cylinder at \(60^{\circ} \mathrm{C}\) and 130 bar using the virial equation of state \(Z=1+\frac{B P}{R T}\) for gases, and compare
How does the van der Waals equation of state play an important role in improving the ideal gas law?
Calculate the pressure of \(\mathrm{CO}_{2}\) occupying a volume of \(0.425 \mathrm{~m}^{3}\) at \(327 \mathrm{~K}\) by using the following equation of state:(a) Ideal gas equation of state(b) Van

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