Answer
$pH = 2.28$
Work Step by Step
1000ml = 1L
1. Find the numbers of moles:
$C(HCl) * V(HCl) = 0.1* 0.05 = 5 \times 10^{-3}$ moles
$C(NaOH) * V(NaOH) = 0.1* 0.045 = 4.5 \times 10^{-3}$ moles
2. Write the acid-base reaction:
$HCl(aq) + NaOH(aq) -- \gt NaCl(aq) + H_2O(l)$
- Total volume: 0.05 + 0.045 = 0.095L
3. Since the base is the limiting reactant, only $ 0.0045$ mol of the compounds will react.
Therefore:
Concentration (M) = $\frac{n(mol)}{Volume(L)}$
$[HCl] = 0.005 - 0.0045 = 5 \times 10^{-4}$ moles.
Concentration: $\frac{5 \times 10^{-4}}{ 0.095} = 5.3 \times 10^{-3}M$
$[NaOH] = 0.0045 - 0.0045 = 0 $ moles
- Since $HCl$ is a strong acid:
$[HCl] = [H_3O^+] = 5.3 \times 10^{-3}M$
5. Calculate the pH Value
$pH = -log[H_3O^+]$
$pH = -log( 5.3 \times 10^{- 3})$
$pH = 2.28$
