Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Thermodynamics question

2023 · 1 Feb · Shift 2 · Q20
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Chemistry
  4. /Thermodynamics
  5. /2023 · 1 Feb · Shift 2 · Q20

Thermodynamics question

2023 · 1 Feb · Shift 2 · Q20

JEE MainChemistryThermodynamicsNumerical+4 / −1
0.3 g0.3 \mathrm{~g}0.3 g of ethane undergoes combustion at 27∘C27^{\circ} \mathrm{C}27∘C in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by 0.5∘C0.5^{\circ} \mathrm{C}0.5∘C. The heat evolved during combustion of ethane at constant pressure is ‾kJ mol−1\underline{\hspace{2cm}}\mathrm{kJ} ~\mathrm{mol}{ }^{-1}​kJ mol−1. (Nearest integer) [Given : The heat capacity of the calorimeter system is 20 kJ K−1,R=8.3 JK−1 mol−120 \mathrm{~kJ} \mathrm{~K}^{-1}, \mathrm{R}=8.3 ~\mathrm{JK}^{-1} \mathrm{~mol}^{-1}20 kJ K−1,R=8.3 JK−1 mol−1. Assume ideal gas behaviour. Atomic mass of C\mathrm{C}C and H\mathrm{H}H are 12 and 1 g mol−11 \mathrm{~g} \mathrm{~mol}^{-1}1 g mol−1 respectively]
Numerical answer
View written solutionFree

Correct answer: 1006

  1. Combustion reaction of ethane

For complete combustion,

C2H6(g)+72O2(g)→2CO2(g)+3H2O(l)\mathrm{C_2H_6(g) + \frac{7}{2}O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l)}C2​H6​(g)+27​O2​(g)→2CO2​(g)+3H2​O(l)
  1. Heat released in bomb calorimeter

Bomb calorimeter works at constant volume, so the heat measured is qv=ΔUq_v = \Delta Uqv​=ΔU for the sample burned.

Given:

  • Heat capacity of calorimeter system =20 kJ K−1= 20\,\mathrm{kJ\,K^{-1}}=20kJK−1
  • Temperature rise =0.5 K= 0.5\,\mathrm{K}=0.5K

Hence heat absorbed by calorimeter:

qcal=CΔT=20×0.5=10 kJq_{\text{cal}} = C\Delta T = 20 \times 0.5 = 10\,\mathrm{kJ}qcal​=CΔT=20×0.5=10kJ

Therefore, heat evolved by burning 0.3 0.3\,0.3g ethane at constant volume is:

qv=−10 kJq_v = -10\,\mathrm{kJ}qv​=−10kJ

So for 0.3 0.3\,0.3g ethane,

ΔU=−10 kJ\Delta U = -10\,\mathrm{kJ}ΔU=−10kJ
  1. Convert to molar internal energy change

Molar mass of ethane:

M(C2H6)=2(12)+6(1)=30 g mol−1M(\mathrm{C_2H_6}) = 2(12)+6(1)=30\,\mathrm{g\,mol^{-1}}M(C2​H6​)=2(12)+6(1)=30gmol−1

Moles of ethane burned:

n=0.330=0.01 moln = \frac{0.3}{30} = 0.01\,\mathrm{mol}n=300.3​=0.01mol

Thus molar ΔU\Delta UΔU is:

ΔUm=−100.01=−1000 kJ mol−1\Delta U_m = \frac{-10}{0.01} = -1000\,\mathrm{kJ\,mol^{-1}}ΔUm​=0.01−10​=−1000kJmol−1
  1. Convert ΔU\Delta UΔU to ΔH\Delta HΔH

Using

ΔH=ΔU+ΔngRT\Delta H = \Delta U + \Delta n_g RTΔH=ΔU+Δng​RT

where Δng=\Delta n_g =Δng​= moles of gaseous products −-− moles of gaseous reactants.

From the reaction:

  • Gaseous products: 2 CO22\,\mathrm{CO_2}2CO2​ gives 222
  • Gaseous reactants: 1+72=921 + \frac{7}{2} = \frac{9}{2}1+27​=29​

So,

Δng=2−92=−52\Delta n_g = 2 - \frac{9}{2} = -\frac{5}{2}Δng​=2−29​=−25​

At 27∘C=300 K27^\circ\mathrm{C} = 300\,\mathrm{K}27∘C=300K,

ΔngRT=−52×8.3×300 J mol−1\Delta n_g RT = -\frac{5}{2}\times 8.3 \times 300\,\mathrm{J\,mol^{-1}}Δng​RT=−25​×8.3×300Jmol−1 =−6225 J mol−1=−6.225 kJ mol−1= -6225\,\mathrm{J\,mol^{-1}} = -6.225\,\mathrm{kJ\,mol^{-1}}=−6225Jmol−1=−6.225kJmol−1

Therefore,

ΔH=−1000−6.225=−1006.225 kJ mol−1\Delta H = -1000 - 6.225 = -1006.225\,\mathrm{kJ\,mol^{-1}}ΔH=−1000−6.225=−1006.225kJmol−1
  1. Heat evolved at constant pressure

Since the question asks for heat evolved, we report the magnitude:

∣ΔH∣≈1006 kJ mol−1|\Delta H| \approx 1006\,\mathrm{kJ\,mol^{-1}}∣ΔH∣≈1006kJmol−1

Nearest integer:

1006\boxed{1006}1006​
PreviousNext

More from Thermodynamics

  • Consider the graph of Gibbs free energy G vs Extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is ​ A. Reaction is spontaneous at (a) and (b) B.… Includes diagram2023 · Numerical
  • The value of logK for the reaction A⇌B at 298 K is ​. (Nearest integer) Given: ΔH∘=−54.07 kJ mol−1ΔS∘=10 J K−1 mol−1…2023 · Numerical
  • Consider the following data Heat of combustion of H2​(g)=−241.8 kJ mol−1 Heat of combustion of C(s)=−393.5 kJ mol−1 Heat of…2023 · Numerical
  • When a 60 W electric heater is immersed in a gas for 100 s in a constant volume container with adiabatic walls, the temperature of the gas rises by 5∘C. The heat capacity of the given gas is ​JK−1…2023 · Numerical
  • For complete combustion of ethene. C2​H4​(g)+3O2​(g)→2CO2​(g)+2H2​O(l) the amount of heat produced as measured in bomb…2023 · Numerical
  • Given ΔH0 for the reaction C(graphite)+21​O2​(g)→CO(g) is : Includes table2023 · MCQ
  • The number of endothermic process/es from the following is ​. A. I2​( g)→2I(g) B. HCl(g)→H(g)+Cl(g)…2023 · Numerical
  • Solid fuel used in rocket is a mixture of Fe2​O3​ and Al(in ratio 1 : 2). The heat evolved (kJ) per gram of the mixture is ​. (Nearest integer) Given: ΔHfθ​(Al2​O3​)=−1700 kJ mol−1ΔHfθ​(Fe2​O3​)=−840 kJ mol−1…2023 · Numerical