For a hypothetical reaction nX −> mY, the value of ​​delH=-133kJ and delS=-145JK^-1. Calculate:-

1. the value of delG at 700K
2. value of delS_surr and delS_univ

To tackle this problem, we need to apply the principles of thermodynamics, specifically the Gibbs free energy equation, which relates enthalpy, entropy, and temperature. The equation is given by:

Gibbs Free Energy Calculation

The Gibbs free energy change (ΔG) can be calculated using the formula:

ΔG = ΔH - TΔS

Where:

• ΔG = change in Gibbs free energy
• ΔH = change in enthalpy
• T = temperature in Kelvin
• ΔS = change in entropy

Given Values

From the problem, we have:

• ΔH = -133 kJ = -133,000 J (since we need to convert kJ to J)
• ΔS = -145 J/K
• T = 700 K

Calculating ΔG

Now, substituting the values into the Gibbs free energy equation:

ΔG = -133,000 J - (700 K × -145 J/K)

Calculating the second term:

700 K × -145 J/K = -101,500 J

Now, substituting this back into the equation:

ΔG = -133,000 J + 101,500 J

ΔG = -31,500 J

Thus, ΔG = -31.5 kJ.

Entropy Changes in Surroundings and Universe

Next, we need to calculate the change in entropy of the surroundings (ΔS_surr) and the change in entropy of the universe (ΔS_univ).

Entropy Change of the Surroundings

The change in entropy of the surroundings can be calculated using the formula:

ΔS_surr = -ΔH / T

Substituting the values:

ΔS_surr = -(-133,000 J) / 700 K

ΔS_surr = 190.0 J/K

Entropy Change of the Universe

The change in entropy of the universe (ΔS_univ) is the sum of the change in entropy of the system and the surroundings:

ΔS_univ = ΔS + ΔS_surr

Substituting the values:

ΔS_univ = -145 J/K + 190.0 J/K

ΔS_univ = 45.0 J/K

Summary of Results

To summarize:

• ΔG at 700 K = -31.5 kJ
• ΔS_surr = 190.0 J/K
• ΔS_univ = 45.0 J/K

This indicates that the reaction is spontaneous at 700 K since ΔG is negative, and the universe's entropy increases, which is a favorable condition for spontaneous processes.