Calculate the delta G naught prime f (free energy of formation) of the following compounds at 25 degrees celsius.
ethyl acetate (ethyl acetate + H2O <=> ethanol + acetate- + H): delta G naught prime =-19.7 kj/mol); the pka of acetic acid is 4.76)
Free Energies for:
H2O: -237.2, ethanol: -181.5, acetate: 369.2, H+: 0)
the solution is as follows:
free ENG f (ethanol) + free ENG f (OAc-) + free ENG f (H+) -free ENG f (H2O) - delta G prime
-181.5-369.2 + 0 + 237.2 - (delta G naught) = -313.5 - (delta G naught prime) + 20.1 RT
=-313.5 + 19.7 + 49.88 = -244.0 kj/mol
I don't understand where the 20.1 is coming from, can someone explain?
The 20.1 is coming from the equation for delta G naught prime, which is delta G naught + RT, where R is the gas constant and T is the temperature in Kelvin. In this case, the temperature is 25 degrees Celsius, which is 298.15 Kelvin. So, 20.1 is the result of RT, which is 8.314 x 298.15 = 2420.945.
The value 20.1 in the equation is derived from the equation for the standard Gibbs free energy change (ΔG°) at non-standard temperature (T):
ΔG = ΔG° + RT ln(Q)
where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and Q is the reaction quotient.
In this case, the temperature is specified as 25 degrees Celsius, which is equivalent to 298.15 Kelvin. The factor 20.1 RT is the contribution of the temperature to the Gibbs free energy change.
The term 20.1 RT is calculated as follows:
20.1 RT = 20.1 * (8.314 J/(mol·K)) * 298.15 K
Converting to kilojoules per mole, we have:
20.1 RT ≈ 49880 J/mol ≈ 49.88 kJ/mol
Therefore, when calculating the ΔG°prime for ethyl acetate, the 20.1 RT term is added to account for the non-standard temperature of 25 degrees Celsius.
The 20.1 in the equation is a constant and it represents the product of the temperature (25 degrees Celsius) in Kelvin (298K) and the gas constant (R = 8.314 J/(mol·K)). This value is used to convert the temperature into energy units (Joules) so that it can be consistent with the units of the free energy values (kJ/mol).
In this case, the equation is written as:
Free Energy (ethanol) + Free Energy (OAc-) + Free Energy (H+) - Free Energy (H2O) - ΔG° = -313.5 - ΔG°' + 20.1RT
The 20.1RT term is added to convert the temperature into energy units (Joules) and make the equation consistent.