Chapter 4

Calculate average molar heat capacity at constant volume of gaseous mixture contained 2 mole of each of two ideal gases \(A\left(C_{\mathrm{v}, m}=\frac{3}{2} R\right)\) and \(B\left(C_{\mathrm{v}, m}=\frac{5}{2} R\right):\) (a) \(R\) (b) \(2 R\) (c) \(3 R\) (d) \(8 R\)

One mole of an ideal gas undergoes a change of state \((2.0 \mathrm{~atm}, 3.0 \mathrm{~L})\) to \((2.0 \mathrm{~atm}, 7.0 \mathrm{~L})\) with a change in internal energy \((\Delta U)=30 \mathrm{~L}-\mathrm{atm} .\) The change in enthalpy \((\Delta H)\) of the process in L-atm : (a) 22 (b) 38 (c) 25 (d) None of thése

One mole of a non-ideal gas undergoes a change of state from \((1.0 \mathrm{~atm}, 3.0 \mathrm{~L}, 200 \mathrm{~K})\) to \((4.0\) atm, \(5.0 \mathrm{~L}, 250 \mathrm{~K}\) ) with a change in internal energy \((\Delta U)=40 \mathrm{~L}\) -atm. The change in enthalpy of the process in L-atm : (a) 43 (b) 57 (c) 42 (d) None of these

Which of the following expression for an irreversible process: (a) \(d S>\frac{d q}{T}\) (b) \(d S=\frac{d q}{T}\) (c) \(d S<\frac{d q}{T}\) (d) \(d S=\frac{d U}{T}\)

Which of the following expressions is known as Clausius inequality? (a) \(\oint \frac{d q}{T} \leq 0\) (b) \(\oint \frac{d s}{T}=0\) (c) \(\oint \frac{T}{d q} \leq 0\) (d) \(\oint \frac{d q}{T} \geq 0\)

If one mole of an ideal gas \(\left(C_{p, m}=\frac{5}{2} R\right)\) is expanded isothermally at 300 until it's volume is tripled, then change in entropy of gas is : (a) zero (b) infinity (c) \(\frac{5}{2} R \ln 3\) (d) \(R \ln 3\)

When one mole of an ideal gas is compressed to half of its initial volume and simultaneously heated to twice its initial temperature, the change in entropy of gas \((\Delta S)\) is : (a) \(C_{p, m} \ln 2\) (b) \(C_{v, m} \ln 2\) (c) \(R \ln 2\) (d) \(\left(C_{v, m}-R\right) \ln 2\)

What is the change in entropy when \(2.5\) mole of water is heated from \(27^{\circ} \mathrm{C}\) to \(87^{\circ} \mathrm{C} ?\) Assume that the heat capacity is constant. \(\left(C_{p, m}\left(\mathrm{H}_{2} \mathrm{O}\right)=4.2 \mathrm{~J} / \mathrm{g}-\mathrm{K} \ln (1.2)=0.18\right)\) (a) \(16.6 \mathrm{~J} / \mathrm{K}\) (b) \(9 \mathrm{~J} / \mathrm{K}\) (c) \(34.02 \mathrm{~J} / \mathrm{K}\) (d) \(1.89 \mathrm{~J} / \mathrm{K}\)

Calculate standard entropy change in the reaction $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ Given : \(S_{m}^{\circ}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{~S}\right)=87.4, S_{m}^{\circ}(\mathrm{Fe}, S)=27.3\) \(S_{m}^{\circ}\left(\mathrm{H}_{2}, g\right)=130.7, S_{m}^{\circ}\left(\mathrm{H}_{2} \mathrm{O}, l\right)=69.9 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\)

Calculate the entropy change \((\mathrm{J} / \mathrm{mol} \mathrm{K})\) of the given reaction. The molar entropies [J/K-mol] are given in brackets after each substance. \(2 \mathrm{PbS}(s)[91.2]+3 \mathrm{O}_{2}(g)[205.1] \longrightarrow 2 \mathrm{PbO}(s)[66.5]+2 \mathrm{SO}_{2}(g)[248.2]\) (a) \(-113.5\) (b) \(-168.3\) (c) \(+72.5\) (d) \(-149.2\)