GATE-CH-2003-42-pc-2mark

A sample of natural gas containing 80% methane (CH₄) and the rest nitrogen (N₂) is burnt with 20% excess air. With 80% of the combustibles producing CO₂ and the remainder going to CO the Orsat analysis in volume percent is

• CO₂: 6.26, CO: 1.56, O₂: 3.91, H₂O: 15.66, N₂: 72.60
• CO₂: 7.42, CO: 1.86, O₂: 4.64, N₂: 86.02
• CO₂: 6.39, CO: 1.60, O₂: 3.99, H₂O: 15.96, N₂: 72.06
• CO₂: 7.60, CO: 1.90, O₂: 4.75, N₂: 85.74

GATE-CH-2010-33-pc-2mark

The products of combustion of methane in atmospheric air (21% O₂ and 79% N₂) have the following composition on a dry basis:

Products	Mole %
CO2	10.00
O2	2.37
CO	0.53
N2	87.10

The ratio of the moles of CH₄ to the moles of O₂ in the feed stream is

• 1.05

• 0.60

• 0.51

• 0.45

GATE-CH-2011-32-pc-2mark

The following combustion reactions occur when methane is burnt. \[ \begin{align*} \text{CH}_4 + 2\text{O}_2 &\rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \tag*{(reaction 1)}\\ 2\text{CH}_4 + 3\text{O}_2 &\rightarrow 2\text{CO} + 4\text{H}_2\text{O} \tag*{(reaction 2)} \end{align*} \] 20% excess air is supplied to the combustor. The conversion of methane is 80% and the molar ratio of CO to CO₂ in the flue gas is 1:3. Assume air to have 80 mol % N₂ and rest O₂. The O₂ consumed as a PERCENTAGE of O₂ entering the combustor is 

• 20

• 62.5

• 80

• 83.3

GATE-CH-1990-11-i-pc-6mark

Pure propane (\(\ce {C3H8}\)) is burnt with an excess of air to give the following analysis of combustion products in volume percent:
\(\ce {CO2}\) = 5.0, \(\ce {CO}\) = 3.5, \(\ce {H2O}\) = 11.4, \(\ce {O2}\) = 7.0 and \(\ce {N2}\) = 73.1
Calculate the percentage of excess air used.

• Answer

GATE-CH-1996-11-pc-5mark

A hydrocarbon is burnt with excess air. The Orsat analysis of the flue gas shows 10.81% \(\ce {CO2}\), 3.78% \(\ce {O2}\) and 85.4% \(\ce {N2}\). Calculate: (i) the atoms of H per atom of C in the hydrocarbon, and (ii) the % excess air.
(i) ____________
{#1}

(ii) ____________
{#2}

GATE-CH-2007-80-81-pc-4mark

44 kg of C₃H₈ is burnt with 1160 kg of air (Mol. Wt. = 29) to produce 88 kg of CO₂ and 14 kg of CO 

\[ \text {C$_3$H$_8$} + \text {5O$_2$} = \text {3CO$_2$} + \text {4H$_2$O} \] 

(i) What is the percent excess air used ?

{#1}

(ii) What is the % carbon burnt ?

{#2}

GATE-CH-1990-1-ii-pc-4mark

The following data on heats of combustion at 25\(^\circ \)C are given:

Compound	Heat of combustion at 25\(^\circ\)C
n-Heptane \(\ce{C7H16(g)}\)	\(-4850\) kJ/mol
Ethyl alcohol \(\ce{C2H5OH(g)}\)	\(-1410\) kJ/mol

Heats of formation of \(\ce {CO2(g)}\) and \(\ce {H2O(l)}\) are \(-390\) and \(-280\) kJ/mol respectively.
(a) The heat of formation of gaseous n-heptane at 25\(^\circ \)C is ––––- kJ/mol
{#1}

(b) The heat of formation of gaseous ethyl alcohol at 25\(^\circ \)C is ––––- kJ/mol
{#2}

GATE-CH-1998-13-pc-5mark

1000 kg/h of a thermic fluid, to be used as a heat transfer medium, is being indirectly heated in a heater, from 380 K to 550 K. (i) Calculate the heat load on the heater, in kW. (ii) Also estimate the mean heat capacity in kJ/(kg.K) of the thermic fluid over the temperature range of interest. The heat capacity equation for the thermic fluid is:
\(C_P = 1.436 + 0.00218 T\)
where \(C_P\) is in kJ/(kg.K), and \(T\) is in K.

 
(i) ____________
{#1}

(ii) ____________
{#2}

GATE-CH-2004-40-41-pc-4mark

One mole of methane undergoes complete combustion in a stoichiometric amount of air. The reaction proceeds as: CH₄+2 O₂   \(\rightarrow\) CO₂ + 2H₂O. Both the reactants and products are in gas phase. \(\Delta H_{298}^{\circ } = -730\) kJ/mol of methane.

(i) Mole fraction of water vapor in the product gases is about

{#1}

(ii) If the average specific heat of all the gases/vapor is 40 J/(mol.K), the maximum temperature rise of the exhaust gases in ^oC  would be approximately equal to

{#2}

GATE-CH-2008-33-pc-2mark

600 kg/h of saturated steam at 1 bar (enthalpy 2675.4 kJ/kg) is mixed adiabatically with superheated steam at 450^oC and 1 bar (enthalpy 3382.4 kJ/kg). The product is superheated steam at 350^oC and 1 bar (enthalpy 3175.6 kJ/kg). The flow rate of the product is

• 711 kg/h
• 1111 kg/h
• 1451 kg/h
• 2051 kg/h

GATE-CH-2016-31-pc-2mark

A jacketed stirred tank with a provision for heat removal is used to mix sulphuric acid and water in a steady state flow process. H₂SO₄(l) enters at a rate of 4 kg/h at 25^oC and H₂O(l) enters at a rate of 6 kg/h at 10^oC. The following data are available:

Specific heat capacity of water = 4.2 kJ.kg^-1.K^-1.
Specific heat capacity of aqueous solution of 40 mass% H₂SO₄ = 2.8 kJ.(kg solution)^-1.K^-1.

Assume the specific heat capacities to be independent of temperature.

Based on reference states of H₂SO₄(l) and H₂O(l) at 25^oC, the heat of mixing for aqueous solution of 40 mass% H₂SO₄ = -650 kJ.(kg H₂SO₄)^-1.

If the mixed stream leaves at 40^oC, what is the rate of heat removal (in kJ/h)?

• 1802
• 2558
• 5702
• 6458

GATE-CH-1987-11-iii-pc-2mark

The reaction, \(A(g) + 2B(g) \rightarrow 2C(g) + 3D(g)\), with a standard heat of reaction \(\Delta H_R^o = -10^3\) kJ/mol of \(A\) reacted, is carried out in a reactor in which the feed enters at 25\(^\circ \)C and the product stream emerges as a gas at 300\(^\circ \)C. The feed consists of 100 mol \(A\)/h and 250 mol \(B\)/h. \(A\) is completely consumed during the reaction. Calculate the heat transferred (in kJ/h) to or from the reactor, assuming the operation at approximately 1 atm.
Data: Specific enthalpies at 300\(^\circ \)C
(Datum: Specific enthalpies of all components at 25\(^\circ \)C = 0 kJ/mol).

• Answer

GATE-CH-1988-11-ii-pc-6mark

Dry methane is burned with dry air. Both are initially at 300 K. The flame temperature is 1570 K. If complete combustion is assumed, how much excess air (in %) was used?
Data: Mean molar specific heat values in J/mol.K are:
\(\ce {CO2}\) = 51.8, \(\ce {H2O}\) = 40.2, \(\ce {N2}\) = 32.2 and \(\ce {O2}\) = 32.4
Standard heat of formation at 300 K = \(-8 \times 10^5\) J/mol of \(\ce {CH4}\)

• Answer

GATE-CH-1989-11-iii-pc-4mark

In a laboratory experiment pure methane is burnt with theoretical quantity of air. Only part of the methane burns but the part that burns goes to \(\ce {CO2}\) and \(\ce {H2O}\). If the methane and air are initially at 25\(^\circ \)C and the products leave at 400\(^\circ \)C with water in vapor form, what % of the methane is burnt? Data:
For the oxidation of \(\ce {CO2}\) and \(\ce {H2O}\) (vapor) the standard heat of reaction \(\Delta H_R^\circ \) = -802.9 kJ/mol of \(\ce {CH4}\) reacted.
Specific enthalpies at 400\(^\circ \)C in kJ/mol (Reference: Specific enthalpy at 25\(^\circ \)C = 0 kJ/mol)

\(\ce{O2}\)	\(\ce{N2}\)	\(\ce{CH4}\)	\(\ce{CO2}\)	\(\ce{H2O}\)
11.64	11.13	17.22	16.43	13.2

• Answer

GATE-CH-1994-8-pc-5mark

The heat of reaction at 300 K and at one atmosphere pressure for the following gas phase reaction: \[ A + 3B \rightarrow C \] is \(-50,000\) calories per mole of \(A\) converted. Data on the molar heat capacity at constant pressure (cal/mol.K) of the various components are:

\(C_P\) for \(A = -0.4 + 80 \times 10^{-3}T, \quad T\) in K
\(C_P\) for \(B = 7\)
\(C_P\) for \(C = 26\)

Calculate the heat of reaction (in cal/mol of \(A\) converted) at 500 K and at one atmosphere pressure.

• Answer

GATE-CH-1995-12-pc-5mark

Pure \(\ce {CO}\) is mixed with 100% excess air and burnt. Only 80% of \(\ce {CO}\) burns. The reactants are at 100\(^\circ \)C and the products are at 300\(^\circ \)C. Calculate the amount of heat added or removed (in kJ) per kmol of \(\ce {CO}\) fed to the reactor. Data: Mean molal specific heats between 25\(^\circ \)C and \(T\)\(^\circ \)C (given below in kJ/kmol.K) are:

Standard heat of formation at 25\(^\circ \)C in kJ/kmol are: \(\ce {CO}\) = \(-110524\); \(\ce {CO2}\) = \(-393514\).

• Answer

GATE-CH-1997-13-pc-5mark

A feed at 1298 K, consisting of flue gas (\(\ce {CO2}\), \(\ce {O2}\) and \(\ce {N2}\)) and air, is passed through a bed of pure carbon. The reactions that occur both go to completion. \[ \begin {align*} \ce {CO2(g)} + \ce {C(s)} &\rightarrow 2\ce {CO(g)}, \quad \Delta H^\circ _R \text { at 298 K = 170 kJ/mol} \\
\ce {O2(g)} + 2\ce {C(s)} &\rightarrow 2\ce {CO(g)}, \quad \Delta H^\circ _R \text { at 298 K = \(-\)220.4 kJ/mol} \end {align*} \] The combustor is adiabatic and the product gases exit at 1298 K. Calculate the required moles of \(\ce {CO2}\) per mole of \(\ce {O2}\) in the feed stream, so that the net heat generated is zero and the bed temperature remains constant at 1298 K.
Data: Mean molar heat capacities, \(C_{Pm}\)

Substance	\(\ce{C}\)	\(\ce{O2}\)	\(\ce{CO}\)	\(\ce{CO2}\)
\(C_{Pm}\) (kJ/mol.K)	0.02	0.03	0.03	0.05

• Answer

GATE-CH-2002-13-pc-5mark

Ammonia is produced by the following reaction \[ \text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3 \] In a commercial process for ammonia production, the feed to an adiabatic reactor contains 1 kmol/s of nitrogen and stoichiometric amount of hydrogen at 700 K. What is the maximum allowable conversion (in percentage) in the reactor, if the adiabatic temperature rise across the reactor should not exceed 100 K. Assume the feed and product streams to be ideal gas mixtures. The heat of reaction at 700 K for the above reaction is calculated to be -94.2 kJ/mol. Mean molar heat capacities (\(C_P\)), in the range  700 - 800 K, are 0.03, 0.0289 and 0.0492 kJ/mol.K for nitrogen, hydrogen and ammonia respectively.

• Answer

GATE-CH-2014-42-pc-2mark

Carbon monoxide (CO) is burnt in presence of 200% excess pure oxygen and the flame temperature achieved is 2298 K. The inlet streams are at 25^oC. The standard heat of formation (at 25^oC) of CO and CO₂ are -110 kJ.mol^-1 and -390 kJ.mol^-1, respectively. The heat capacities (in J.mol^-1.K^-1) of the components are \[ C_{P_{\text{O}_2}}= 25 + 14\times10^{-3}T \qquad C_{P_{\text{CO}_2}} = 25 + 42\times10^{-3}T \] where, \(T\) is the temperature in K. The heat loss (in kJ) per mole of CO burnt is _______. 

• Answer