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AP EAMCET202315 May 2023Morning ShiftChemistryThermodynamics (C)Actual

If the standard enthalpy change ( _ r H ^ ) for a certain reaction at 298 ~K and constant pressure is -1860 ~kJ mol ⁻¹ , the standard entropy change ( _ sys s ^ ) of the same reaction is -550 ~J ~K ⁻¹ ~mol ⁻¹ , which one of the following statements is correct?

Options

  1. A( _ sys S^ )+ _ surr S^ =-7692 ~J ~mol ⁻¹ ~K ⁻¹ , the reaction is spontaneous
  2. B( _ sys S ^ )+ _ surr S ^ =-5692 ~J ~mol ⁻¹ ~K ⁻¹ , the reaction is non-spontaneous
  3. C( _ sys S ^ )+ _ surr S ^ =+5692 ~J ~mol ⁻¹ ~K ⁻¹ , the reaction is spontaneous
  4. D( _ sys S^ )+ _ surr S^ =+7692 ~J ~mol ⁻¹ ~K ⁻¹ , the reaction is non-spontaneous

Correct answer

C. ( _ sys S ^ )+ _ surr S ^ =+5692 ~J ~mol ⁻¹ ~K ⁻¹ , the reaction is spontaneous

Step-by-step solution

aligned & G ^ = H ^ - T s ^ & = (-1860 10^3 )-298(-550) & =-1696.1 ~kJ Mol ⁻¹ aligned Thus, the reaction is Spontaneous as G ^ is negative. Now, Since the system loses the heat, the surrounding must gain it and therefore, aligned & H ^ _ Surrounding =+1860 10^3 ~J ~mol ⁻¹ . & S _ surrounding ^ = H _ surrounding ^ T aligned aligned & = +1860 10^3 298 & =6241.6 ~J & S_ total ^ = S_ system ^ + S_ surrounding ^ & =(-550)+(6241.6) & =+5692 ~J ~mol ⁻¹ ~K ⁻¹ . aligned

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