For double-helix formation, change in Gibbs free energy, ΔG, can be measured to be −54 kJ⋅mol^−1 (−13 kcal⋅mol^−1) at pH 7.0 in 1M NaCl at 25 °C ( 298 K). The heat released indicates an enthalpy change, ΔH, of −251 kJ⋅mol−1 (−60 kcal⋅mol^−1). For this process, calculate the entropy change for the system, ΔS system, and the entropy change for the surroundings, ΔS surroundings.

ΔS system =  -661 j/mol.K,  ΔS (surrounding) = 842 j/mol.K

Explanation:

Given that;

ΔG system  = -54 kj/mol = -54000 j/mol

ΔH system = -251 kj/mol = -251000 j/mol

Temperature T = 25 degree Celsius = 298 Kelvin

Now

ΔG system = ΔH system  -  T(in kelvin) * ΔS system

SO WE SUBSTITUTE

-54000 = -251000 - 298 * ΔS system

ΔS system =  -661 j/mol.K

q(surroundings) (heat flow into surroundings) = -q(system) (heat flow into system), and q(system) = -ΔH(system) at constant pressure.

Thus q(surroundings) = -ΔH(system).

now q(surroundings) = -ΔH system = +251000 j/mol

so

ΔS (surrounding) = q(surroundings) / T

ΔS (surrounding) = 251000 / 298

ΔS (surrounding) = 842 j/mol.K