Consider the reaction described by the chemical equation shown.
C2H4(g)+H2O(l)⟶C2H5OH(l)Δ∘rxn=−44.2 kJ

Use the data from the table of thermodynamic properties to calculate the value of Δ∘rxn
at 25.0 ∘C.


ΔS∘rxn= ? J⋅K−1

Calculate Δ∘rxn.

ΔG∘rxn= ? kJ


In which direction is the reaction, as written, spontaneous at 25 ∘C
and standard pressure?
reverse
both
neither
forward

Answer:

To calculate Δ∘rxn, we can use the following formula:

ΔG∘rxn = ΔH∘rxn - TΔS∘rxn

where ΔH∘rxn is the enthalpy change of the reaction, T is the temperature in Kelvin, and ΔS∘rxn is the entropy change of the reaction.

We know that ΔH∘rxn = -44.2 kJ and we want to find ΔS∘rxn at 25.0 ∘C (298 K). We can use the following formula to calculate ΔS∘rxn:

ΔG∘rxn = -RTlnK

where R is the gas constant (8.314 J/mol K), T is the temperature in Kelvin, and K is the equilibrium constant.

We can find K using the following formula:

ΔG∘rxn = -RTlnK K = e^(-ΔG∘rxn/RT)

We know that ΔG∘rxn = -44.2 kJ/mol and R = 8.314 J/mol K, so we can calculate K:

K = e^(-(-44.2 kJ/mol)/(8.314 J/mol K * 298 K)) K = 1.9 x 10^7

Now we can use K to calculate ΔS∘rxn:

ΔG∘rxn = -RTlnK ΔS∘rxn = -(ΔH∘rxn - ΔG∘rxn)/T ΔS∘rxn = -((-44.2 kJ/mol) - (-8.314 J/mol K * 298 K * ln(1.9 x 10^7)))/(298 K) ΔS∘rxn = -0.143 kJ/K

Therefore, ΔS∘rxn is -0.143 kJ/K.

To determine whether the reaction is spontaneous at 25 ∘C and standard pressure, we can use Gibbs free energy (ΔG). If ΔG < 0, then the reaction is spontaneous in the forward direction; if ΔG > 0, then it is spontaneous in the reverse direction; if ΔG = 0, then it is at equilibrium.

We know that ΔG∘rxn = -44.2 kJ/mol and T = 25 ∘C (298 K). We can use the following formula to calculate ΔG:

ΔG = ΔG∘ + RTlnQ

where Q is the reaction quotient.

At equilibrium, Q = K (the equilibrium constant). Since we calculated K earlier to be 1.9 x 10^7, we can use this value for Q.

ΔG = ΔG∘ + RTlnQ ΔG = (-44.2 kJ/mol) + (8.314 J/mol K * 298 K * ln(1.9 x 10^7)) ΔG = -43.6 kJ/mol

Since ΔG < 0, the reaction is spontaneous in the forward direction at 25 ∘C and standard pressure.