Calculate the deltaS univ for the dissolving of NaCl at room temp. S' NaCl(s)=72.11 J/k*mol; S' NaCl(aq)=115.5 J/k*mol;deltaH' NaCl(s)=-411.12 kJ/mol; deltaH' NaCl(aq)=-407.27 kJ/mol.
To calculate the change in entropy of the universe (ΔS univ) for the dissolving of NaCl at room temperature, you can use the equation:
ΔS univ = ΔS sys + ΔS surroundings
First, let's calculate the change in entropy of the system (ΔS sys) using the given values:
ΔS sys = S' NaCl(aq) - S' NaCl(s)
= 115.5 J/k*mol - 72.11 J/k*mol
= 43.39 J/k*mol
Next, we need to calculate the change in entropy of the surroundings (ΔS surroundings). Since the dissolution of NaCl is an exothermic process, heat (energy) is released to the surroundings. The equation to calculate ΔS surroundings is:
ΔS surroundings = -ΔH sys / T
Where ΔH sys is the change in enthalpy of the system and T is the temperature in Kelvin. Given that ΔH' NaCl(s) = -411.12 kJ/mol, and ΔH' NaCl(aq) = -407.27 kJ/mol, we need to convert these values to J/mol:
ΔH NaCl(s) = -411.12 kJ/mol * 1000 J/kJ = -411120 J/mol
ΔH NaCl(aq) = -407.27 kJ/mol * 1000 J/kJ = -407270 J/mol
Assuming room temperature is 25°C = 298 K, we can calculate ΔS surroundings as follows:
ΔS surroundings = -ΔH sys / T
= (-ΔH NaCl(aq) - (-ΔH NaCl(s))) / T
= (-(-407270 J/mol) - (-411120 J/mol)) / 298 K
= (407270 J/mol - 411120 J/mol) / 298 K
= -3850 J/mol / 298 K
= -12.93 J/K*mol
Finally, we can calculate ΔS univ by adding ΔS sys and ΔS surroundings:
ΔS univ = ΔS sys + ΔS surroundings
= 43.39 J/K*mol + (-12.93 J/K*mol)
= 30.46 J/K*mol
Therefore, the change in entropy of the universe for the dissolving of NaCl at room temperature is 30.46 J/K*mol.