Determine ΔSuniv in J/K at a temperature of 272 K given ΔHrxn = 77 kJ and ΔSrxn = 162 J/K.
To determine the change in entropy of the surroundings (ΔSuniv), we need to use the Gibbs free energy equation:
ΔG = ΔH - TΔS
Where:
ΔG is the change in Gibbs free energy
ΔH is the change in enthalpy (ΔHrxn)
T is the temperature in Kelvin (272 K)
ΔS is the change in entropy (ΔSrxn)
We can rearrange the equation to solve for ΔSuniv:
ΔSuniv = -ΔG / T
Let's substitute the known values:
ΔSuniv = -77 kJ / (272 K)
First, let's convert the heat change from kilojoules to joules:
-77 kJ = -77,000 J
Now we can calculate ΔSuniv:
ΔSuniv = -77,000 J / (272 K)
ΔSuniv ≈ -283.8 J/K
Therefore, at a temperature of 272 K, the change in entropy of the surroundings (ΔSuniv) is approximately -283.8 J/K.