Question

you need to produce a buffer solution that has a ph of 5.270. you already have a solution that contains 10.0 mmol of acetic acid. how many mmol of sodium acetate will you need to add to this solution? pka = 4.752.
h₃ccooh ⇌ h₃ccoo⁻ + h⁺

Explanation:

Step1: Use Henderson - Hasselbalch equation

The Henderson - Hasselbalch equation is \(pH = pK_a+\log\frac{[A^-]}{[HA]}\), where \(A^-\) is the conjugate base (sodium acetate), \(HA\) is the weak acid (acetic acid). Given \(pH = 5.270\), \(pK_a=4.752\), and \([HA]=10.0\ mmol\).

Step2: Rearrange the Henderson - Hasselbalch equation to solve for \(\frac{[A^-]}{[HA]}\)

$$
LATEXBLOCK0
$$

Step3: Use the property of logarithms (\(y = \log x\) implies \(x = 10^y\))

$$
LATEXBLOCK1
$$

Step4: Solve for \([A^-]\)

Since \(\frac{[A^-]}{[HA]} = 3.29\) and \([HA]=10.0\ mmol\), then \([A^-]=3.29\times[HA]\)

$$ [A^-]=3.29\times10.0\ mmol = 32.9\ mmol $$

Answer:

\(32.9\ mmol\)