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Match the follwoing: {: ( "Column I", ...

Match the follwoing:
`{: ( "Column I", " Column II"),( "(a)Entropy of vapoursation", " (p)decreases") , ("(b) K for spontaneous process " , "(q)is always positive"),(" (c)Crystalline solid state" , "(r)lowest entropy") , ( "(d)"DeltaU "in adiabatic" , " (s)"(DeltaH_(vap))/(T_(b))):}`

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The correct Answer is:
To solve the matching question, we will analyze each item in Column I and find the correct match in Column II. ### Step-by-Step Solution: 1. **(a) Entropy of vaporization**: - The entropy of vaporization (ΔS_vap) is defined as the heat absorbed during vaporization (ΔH_vap) divided by the temperature at which the vaporization occurs (T_b). - The formula is: ΔS_vap = ΔH_vap / T_b. - Since ΔH_vap is positive (heat is absorbed), ΔS_vap is also positive. - Therefore, (a) matches with (s) because ΔS_vap = ΔH_vap / T_b. 2. **(b) K for spontaneous process**: - For a spontaneous process, the Gibbs free energy change (ΔG) must be negative. The relationship between ΔG and the equilibrium constant (K) is given by ΔG = -RT ln K. - If ΔG is negative, it implies that K must be greater than 1, which means K is positive. - Therefore, (b) matches with (q) because K for spontaneous processes is always positive. 3. **(c) Crystalline solid state**: - The entropy of a crystalline solid is low because the particles are arranged in a highly ordered structure, leading to minimal randomness. - Entropy is a measure of disorder, and crystalline solids have the lowest entropy compared to liquids and gases. - Therefore, (c) matches with (r) because crystalline solids have the lowest entropy. 4. **(d) ΔU in adiabatic process**: - In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). According to the first law of thermodynamics, ΔU = Q + W. - Since Q = 0, ΔU = W. If work is done on the system, ΔU will increase; if work is done by the system, ΔU will decrease. - However, in the context of this question, we can conclude that ΔU can decrease in an adiabatic expansion. - Therefore, (d) matches with (p) because ΔU decreases in an adiabatic process. ### Final Matches: - (a) Entropy of vaporization → (s) - (b) K for spontaneous process → (q) - (c) Crystalline solid state → (r) - (d) ΔU in adiabatic process → (p)
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