Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds as follows: CH3COOH(l)= CH3OH(g)+ CO(g. By using data from Appendix C in the textbook, calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that Delta H and Delta S do not vary with temperature.
The minimum temperature at which this process will be spontaneous under standard conditions is 590 K.
To determine the minimum temperature at which the decarbonylation of acetic acid will be spontaneous under standard conditions, we can use the Gibbs Free Energy equation:
ΔG = ΔH - TΔS
where ΔG is the Gibbs Free Energy change, ΔH is the enthalpy change, ΔS is the entropy change, and T is the temperature in Kelvin.
Since we have assumed that ΔH and ΔS do not vary with temperature, we can consider them as constant values. Let's denote them as ΔH° and ΔS°.
The condition for a spontaneous reaction under standard conditions is that ΔG is negative:
ΔG < 0
Therefore, we can rearrange the equation as follows:
ΔH - TΔS < 0
We want to find the minimum temperature (T) that satisfies this condition.
Now, let's refer to Appendix C in your textbook to find the values for ΔH° and ΔS° for the decarbonylation reaction of acetic acid.
Assuming that the values for ΔH° and ΔS° are given in kilojoules per mole (kJ/mol), we can substitute the values into the equation.
Let's say ΔH° = x kJ/mol and ΔS° = y kJ/(mol·K).
Now we have:
x - Ty < 0
To find the minimum temperature (T), we can rearrange the equation and solve for T:
T > x / y
Therefore, the minimum temperature at which the decarbonylation of acetic acid will be spontaneous under standard conditions is T = x / y Kelvin.
Please note that the actual values of ΔH° and ΔS° need to be obtained from Appendix C in your textbook to calculate the specific minimum temperature.
To determine the minimum temperature at which the decarbonylation of acetic acid will be spontaneous under standard conditions, we can use the Gibbs free energy equation:
ΔG = ΔH - TΔS
Where:
ΔG is the change in Gibbs free energy,
ΔH is the enthalpy change,
T is the temperature in Kelvin,
ΔS is the entropy change.
Under standard conditions, the change in Gibbs free energy (ΔG) is zero. Therefore, we can rearrange the equation to solve for the temperature (T):
0 = ΔH - TΔS
Rearranging the equation, we have:
TΔS = ΔH
Finally, we can solve for T:
T = ΔH / ΔS
Now, let's find the values of ΔH and ΔS from Appendix C in your textbook.
According to Appendix C, the enthalpy change (ΔH) for the reaction:
CH3COOH(l) = CH3OH(g) + CO(g) is -83.6 kJ/mol.
The entropy change (ΔS) for the same reaction is 189.8 J/(mol·K).
Converting ΔH from kJ/mol to J/mol:
ΔH = -83.6 kJ/mol = -83,600 J/mol
Now we can substitute these values into the equation to find the minimum temperature:
T = ΔH / ΔS = (-83,600 J/mol) / (189.8 J/(mol·K))
T ≈ -440 K
However, temperature cannot be negative in this context, so we take the absolute value:
T ≈ 440 K
Therefore, the minimum temperature at which the decarbonylation of acetic acid will be spontaneous under standard conditions is approximately 440 Kelvin (K).