Student sNameHH ake-home Bonus Quiz on Thermodynamics Vrite the acid ionization
ID: 1029553 • Letter: S
Question
Student sNameHH ake-home Bonus Quiz on Thermodynamics Vrite the acid ionization reaction equation for dichloroacetic acid (CHCI,COOH): Due: ) Calculate A0 na for the ionization of dichloroacetic acid at 25 C, K,- 33x 10-1. What is Gna at ? c) Determine AGn for the ionization of 0.0880 M dichloroacetic acid at pH 250 at 25 C, when the molar concentration of the dichloroacetate anion is 6.8 x 104 M a) What is the meaning of the answer to part c)? State the numerical answers to parts a)-c) here a) b) c) CHEM 1202-E.CookExplanation / Answer
a) Consider the ionization or dichloroacetic acid as below.
CHCl2COOH (aq) <=======> CHCl2COO- (aq) + H+ (aq)
Ka = [CHCl2COO-][H+]/[CHCl2COOH] …..(1)
Ka is a thermodynamic equilibrium constant and hence is related to the standard free energy of the reaction, G0rxn as
G0rxn = -R*T*ln (Ka) where T = 25°C = (25 + 273) K = 298 K is the standard temperature of the reaction.
Plug in values and obtain
G0rxn = -(8.314 J/mol.K)*(298 K)*ln (3.3*10-1) = 2746.79 J/mol = (2746.79 J/mol)*(1 kJ/1000 J) = 2.74679 kJ/mol 2.75 kJ/mol (ans).
b) Kindly explain what is meant by at =m? There’s no prior information on what =m denotes, kindly check.
c) We have pH = 2.50. We define pH as pH = -log [H+]; therefore,
-log [H+] = 2.50
======> log [H+] = -2.50
======> [H+] = antilog (-2.50) = 3.16*10-3 M 3.2*10-3 M.
We have [CHCl2COO-] = 6.8*10-4 M and [CHCl2COOH] = 0.0880 M. Assume small ionization and determine the reaction quotient as
Q = [CHCl2COO-][H+]/[CHCl2COOH] = (6.8*10-4)*(3.2*10-3)/(0.0880) = 2.47*10-5 2.5*10-5
We define the free energy of the reaction G at temperature T = 25°C = 298 K as
Grxn = G0rxn + R*T*ln Q
=====> Grxn = (2746.79 J/mol) + (8.314 J/mol.K)*(298 K)*ln (2.5*10-5) = (2746.79 J/mol) + (2477.572 J/mol)*(-10.59966) = (2746.79 J/mol) + (-26253.83946 J/mol) = -23507.04946 J/mol = (-23507.04946 J/mol)*(1 kJ/1000 J) = -23.50704946 kJ/mol -23.51 kJ/mol (ans).
a) We have seen that G0rxn = 2.75 kJ/mol. The standard concentration is defined as 1 M.
We know that a reaction is spontaneous, i.e, proceeds easily when G < 0. However, since G0rxn > 0, the reaction is non-spontaneous at 25°C and with the standard concentration of dichloroacetic acid.
However, the same reaction becomes spontaneous at the same temperature when the concentration of dichloroacetic acid is reduced to 0.0880 M from 1 M (we have deduced Grxn < 0).