Answer
$pH = 4.61$
Work Step by Step
For the acid:
1. Calculate the molar mass:
1.01* 1 + 12.01* 2 + 1.01* 3 + 16* 2 = 60.06g/mol
2. Calculate the number of moles
$n(moles) = \frac{mass(g)}{mm(g/mol)}$
$n(moles) = \frac{ 10}{ 60.06}$
$n(moles) = 0.1665$
3. Find the concentration in mol/L:
$C(mol/L) = \frac{n(moles)}{volume(L)}$
$ C(mol/L) = \frac{ 0.1665}{ 0.15} $
$C(mol/L) = 1.11$
For the base:
4. Calculate the molar mass:
22.99* 1 + 12.01* 2 + 1.01* 3 + 16* 2 ) = 82.04g/mol
5. Calculate the number of moles
$n(moles) = \frac{mass(g)}{mm(g/mol)}$
$n(moles) = \frac{ 10}{ 82.04}$
$n(moles) = 0.1219$
6. Find the concentration in mol/L:
$C(mol/L) = \frac{n(moles)}{volume(L)}$
$ C(mol/L) = \frac{ 0.1219}{ 0.15} $
$C(mol/L) = 0.8126$
7. Calculate the pKa Value
$pKa = -log(Ka)$
$pKa = -log( 1.8 \times 10^{- 5})$
$pKa = 4.745$
8. Using the Henderson–Hasselbalch equation:
$pH = pKa + log(\frac{[Base]}{[Acid]})$
$pH = 4.745 + log(\frac{0.813}{1.11})$
$pH = 4.745 + log(0.7324)$
$pH = 4.745 + (-0.1352)$
$pH = 4.61$
