In a 0.10 M solution of glutaric acid, HO2C(CH2)3CO2H (K1 = 4.6 ´ 10-5, K2 = 3.9 ´ 10-6), the species present in the next to highest concentration is
A. H3O+(aq).
B. HO2C(CH2)3CO2H(aq).
C. HO2C(CH2)3COO-(aq).
D. -O2C(CH2)3COO-(aq).
E. OH-(aq).
If we look at this as H2T, then
H2T ==> H^+ + HT^-
HT^-==> H^+ + T^-2
Ignoring k2 for the moment,
H^+ from k1 is
(H^+)(HT^-)/(H2T).
Substituting and solving for (H^+) gives us (H^+)=0.00214 M.
(HT^-) = 0.00214 EXCEPT that k2 it is so close that it will ionize almost as easily as k1 will; therefore, we will get more (H^+) from k2 which probably makes (H^+) the most concd of the ions @ about 0.0021+. The unionized acid, H2T, is about 0.098 which should make it the highest of the species. That leaves HT^- and T^-2 to be placed. The HT^- is about 0.0021- ionization products and T^-2 is about k2. So I'm making an educated guess that the next to the highest is H3O^+. I'm ranking them
H2T, H3O^+, HT^-, T2^-, OH^- which is B, A, C, D, E. Check my thinking.
To determine the species present in the next to highest concentration in a 0.10 M solution of glutaric acid, we need to consider the acid dissociation constants (K1 and K2).
Glutaric acid, HO2C(CH2)3CO2H, can dissociate into two possible ions: HO2C(CH2)3COO- (glutarate ion) and H+ (proton).
The first dissociation constant, K1 = 4.6 ´ 10-5, indicates the extent to which the acid dissociates into the glutarate ion and H+:
HO2C(CH2)3CO2H ⇌ HO2C(CH2)3COO- + H+
The second dissociation constant, K2 = 3.9 ´ 10-6, indicates the further dissociation of the glutarate ion:
HO2C(CH2)3COO- ⇌ -O2C(CH2)3COO- + H+
Considering these dissociation steps, we can determine the species present in the next to highest concentration.
Since K2 is smaller than K1, the second dissociation is less favorable, meaning that the concentration of -O2C(CH2)3COO- will be lower compared to the concentration of HO2C(CH2)3COO-.
Therefore, the species present in the next to highest concentration in the solution is HO2C(CH2)3COO- (glutarate ion).
So, the correct answer is C. HO2C(CH2)3COO-(aq).
To determine the species present in the next to highest concentration in a 0.10 M solution of glutaric acid, we need to consider the dissociation of glutaric acid and the values of the equilibrium constants (K1 and K2) provided.
The dissociation of glutaric acid can be represented by the following equations:
HO2C(CH2)3CO2H (glutaric acid) ↔ HO2C(CH2)3CO2- (glutarate ion) + H+ (proton)
The equilibrium constant K1 is given as 4.6 ´ 10-5 and represents the acidity constant (Ka1) for the first dissociation step:
K1 = [HO2C(CH2)3CO2-][H+] / [HO2C(CH2)3CO2H]
Similarly, the second dissociation step can be represented as:
HO2C(CH2)3CO2- (glutarate ion) ↔ -O2C(CH2)3CO2- (glutarate ion) + H+ (proton)
The equilibrium constant K2 is given as 3.9 ´ 10-6 and represents the acidity constant (Ka2) for the second dissociation step:
K2 = [-O2C(CH2)3CO2-][H+] / [HO2C(CH2)3CO2-]
Considering the given equilibrium constants and the initial concentration of 0.10 M glutaric acid, we can solve for the concentrations of the species at equilibrium using an ICE table (Initial, Change, Equilibrium).
Since K1 is larger than K2, we expect the first dissociation to be more significant compared to the second dissociation. Therefore, at equilibrium, we can expect the concentration of the glutarate ion, HO2C(CH2)3CO2-, to be higher than the concentration of the -O2C(CH2)3CO2- ion.
Therefore, the species present in the next to highest concentration in the solution is C. HO2C(CH2)3COO-(aq).