What molar ratio of acetic acid to sodium acetate is required to create a buffer solution having a pH of 4.83 at 25 Celsius? Ka for HC2H3O2 is 1.8 x10^-5 a)0.82 b)0.55 c)3.5 d)1.2 e)2.0
The answer I got was 8.2 ..(help!)
Use the Henderson-Hasselbalch equation.
pH = pKa + log base/acic
4.83 = 4.74 + log(Ac^-)/(HAc)
(Ac^-)/(HAc) = 1.23 but the problem asks for the (acid)/(base) ratio to that is 1/1.23 = 0.82
To determine the molar ratio of acetic acid (HC2H3O2) to sodium acetate (NaC2H3O2) required to create a buffer solution with a pH of 4.83, we can use the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Where:
pH is the desired pH of the buffer solution (4.83 in this case)
pKa is the dissociation constant for the weak acid (HC2H3O2) - given as 1.8 x 10^-5
[A-] is the concentration of the conjugate base (C2H3O2-) - sodium acetate
[HA] is the concentration of the weak acid (HC2H3O2) - acetic acid
Rearranging the equation to solve for the pKa:
pKa = pH - log([A-]/[HA])
Now, we can substitute the given pH value to calculate the pKa:
pKa = 4.83 - log([A-]/[HA])
Next, we can calculate the ratio of the concentration of [A-]/[HA] using the pKa value:
pKa = -log(Ka) (since Ka = 10^(-pKa))
pKa = -log(1.8 x 10^-5) = 4.7448
Now, we need to determine the ratio [A-]/[HA] needed for the given pH of 4.83:
4.83 = 4.7448 - log([A-]/[HA])
Rearranging the equation:
log([A-]/[HA]) = 4.7448 - 4.83
log([A-]/[HA]) = -0.085
To calculate the ratio [A-]/[HA], we can convert the logarithmic form into exponential form:
[A-]/[HA] = 10^(-0.085)
Using a calculator, we evaluate 10^(-0.085) to be approximately 0.9187.
Therefore, the molar ratio of acetic acid to sodium acetate required to create the buffer solution with a pH of 4.83 is approximately:
1:0.9187
Since the ratio is close to 1:1, the correct answer choice from the given options would be (d) 1.2.