the acid-dissociation constanstant for acetic acid
CH3COOH(aq)<->H+(aq)+CH3COO-(aq) is known to be 1.8X10^-5 at 25C
Caclulate G0f forCH3COO-(aq).
G0f=-396.56KJ/mol for CH3COOH (aq), 0 Kj/mol for H+
explain your answer
To calculate the standard Gibbs free energy of formation (ΔG°f) for CH3COO-(aq), we need to use the following formula:
ΔG°f(CH3COO-(aq)) = ΣnΔG°f(products) - ΣmΔG°f(reactants)
In this case, the reactant is CH3COOH(aq) and the product is CH3COO-(aq). The value of ΔG°f for CH3COOH(aq) is given as -396.56 kJ/mol, and the value for H+(aq) is given as 0 kJ/mol.
However, we don't have the value of ΔG°f for CH3COO-(aq) directly. So, we need to relate it to the acid-dissociation constant (Ka) of acetic acid. The relationship is as follows:
Ka = ([H+][CH3COO-])/[CH3COOH]
In this equation, [H+] represents the concentration of H+, [CH3COO-] represents the concentration of CH3COO-, and [CH3COOH] represents the concentration of CH3COOH. At equilibrium, the ratio of products to reactants is equal to Ka.
Rearranging the equation, we have:
[CH3COO-] = (Ka * [CH3COOH])/[H+]
Substituting the given values, we have:
[CH3COO-] = (1.8 * 10^-5 * [CH3COOH])/[H+]
Now, since ΔG°f is related to the standard-state concentrations of the species involved, we can write:
ΔG°f(CH3COO-(aq)) = RT * ln([CH3COO-])
where R is the ideal gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin.
To find ΔG°f(CH3COO-(aq)), we will:
1. Calculate the concentration of [CH3COO-] using the given Ka and [CH3COOH].
2. Convert ΔG°f from J to kJ using the appropriate conversion factor.
3. Calculate ΔG°f(CH3COO-(aq)) using the formula ΔG°f(CH3COO-(aq)) = RT * ln([CH3COO-]), where R is in J/(mol·K) and T is in Kelvin.
Note: Since we are given the Ka and not the concentrations, we cannot determine the actual concentration of CH3COOH. So, we will use the symbol [CH3COOH] to represent the concentration.
Let's proceed with the calculations.