A student pours a 10.0mL sample of a solution containing HC2H3O2(pKa=4.8) and NaC2H3O2 into a test tube. The student adds a few drops of bromocresol green to the test tube and observes a yellow color, which indicates that the pH of the solution is less than 3.8. Based on this result, which of the following is true about the relative concentrations of HC2H3O2 and NaC2H3O2 in the original solution?
A. [HC2H3O2]>[NaC2H3O2]
B. [HC2H3O2]=[NaC2H3O2]
C. [HC2H3O2]<[NaC2H3O2]
D. The relative concentrations cannot be determined without knowing the value of pKb for C2H3O2−.
pH = pKa + log [(acetate)/(acetic acid)]
3.8 = 4.8 + log base/acid
-1.0 = log base/acied
base/acid = 10^-1 = 0.1 or
base = 0.1*acid
so base (NaC2H3O2) < acid (HC2HO2)
To determine the relative concentrations of HC2H3O2 and NaC2H3O2 in the original solution, we need to understand the relationship between pH, pKa, and the ionization of weak acids.
The pKa value represents the acid dissociation constant for a weak acid. It tells us the pH at which exactly half of the acid molecules are ionized and half are not. In this case, the pKa of HC2H3O2 is given as 4.8.
Adding a few drops of bromocresol green to the solution tells us that the pH is less than 3.8. This information is crucial in determining the relative concentrations of HC2H3O2 and NaC2H3O2.
When the pH is lower than the pKa, it means that the solution is more acidic and contains a higher concentration of the acid (HC2H3O2) compared to its conjugate base (C2H3O2-).
Therefore, based on the given information, we can conclude that:
A. [HC2H3O2]>[NaC2H3O2]
The answer is A. [HC2H3O2]>[NaC2H3O2], indicating that the concentration of HC2H3O2 is higher than the concentration of NaC2H3O2 in the original solution.
To determine the relative concentrations of HC2H3O2 and NaC2H3O2 in the original solution based on the observed pH and color change, we need to consider the acid-base equilibrium between the two species.
The pKa of a weak acid, such as HC2H3O2, represents the pH at which half of the acid is dissociated. Since the observed pH is less than the pKa of HC2H3O2 (4.8), this indicates that HC2H3O2 is mostly dissociated and exists in its conjugate base form, C2H3O2-.
The bromocresol green indicator changes color over the pH range 3.8-5.4, transitioning from yellow at pH less than 3.8 to blue at pH greater than 5.4. The yellow color suggests that the pH is acidic, which supports the idea that HC2H3O2 is mostly dissociated.
Based on this information, we can conclude that [HC2H3O2]<[NaC2H3O2]. This means that the concentration of the acetate ion, C2H3O2-, derived from the dissociation of HC2H3O2, is greater than the concentration of the acid, HC2H3O2, in the original solution.
Therefore, the correct answer is C. [HC2H3O2]<[NaC2H3O2].