Find the PH of a 1M Na2CO3 solution.
The correct answer and explanation is:
Answer:
The pH of a 1 M Na₂CO₃ (sodium carbonate) solution is approximately 11.6.
Explanation:
Sodium carbonate (Na₂CO₃) is a salt derived from a strong base (NaOH) and a weak acid (H₂CO₃, carbonic acid). When dissolved in water, it dissociates completely: Na2CO3→2Na++CO32−\mathrm{Na_2CO_3} \rightarrow 2 \mathrm{Na}^+ + \mathrm{CO_3^{2-}}
The carbonate ion (CO32−\mathrm{CO_3^{2-}}) is the conjugate base of the bicarbonate ion (HCO3−\mathrm{HCO_3^-}) and will hydrolyze (react with water) to form hydroxide ions (OH−\mathrm{OH^-}), making the solution basic.
Step 1: Identify the hydrolysis reaction
The carbonate ion hydrolyzes in water: CO32−+H2O⇌HCO3−+OH−\mathrm{CO_3^{2-}} + \mathrm{H_2O} \rightleftharpoons \mathrm{HCO_3^-} + \mathrm{OH^-}
This produces hydroxide ions, increasing the pH.
Step 2: Use KbK_b of the carbonate ion
To find the pH, we need the base dissociation constant (KbK_b) of the carbonate ion.
We know:
- Ka1K_a1 (for H2CO3→H++HCO3−H_2CO_3 \rightarrow H^+ + HCO_3^-) ≈ 4.3×10−74.3 \times 10^{-7}
- Ka2K_a2 (for HCO3−→H++CO32−HCO_3^- \rightarrow H^+ + CO_3^{2-}) ≈ 4.8×10−114.8 \times 10^{-11}
Since CO32−\mathrm{CO_3^{2-}} is the conjugate base of HCO3−\mathrm{HCO_3^-}, its KbK_b is related to Ka2K_a2 by: Kb=KwKa2K_b = \frac{K_w}{K_a2}
where Kw=1.0×10−14K_w = 1.0 \times 10^{-14} at 25°C. Kb=1.0×10−144.8×10−11≈2.08×10−4K_b = \frac{1.0 \times 10^{-14}}{4.8 \times 10^{-11}} \approx 2.08 \times 10^{-4}
Step 3: Set up equilibrium for OH−\mathrm{OH^-} concentration
Initial [CO32−]=1 M[\mathrm{CO_3^{2-}}] = 1\,M.
Let x=[OH−]x = [OH^-] formed by hydrolysis.
At equilibrium: Kb=x21−x≈x2(since x≪1)K_b = \frac{x^2}{1 – x} \approx x^2 \quad (\text{since } x \ll 1) x=Kb=2.08×10−4≈0.0144 Mx = \sqrt{K_b} = \sqrt{2.08 \times 10^{-4}} \approx 0.0144\,M
So, [OH−]≈0.0144 M[\mathrm{OH^-}] \approx 0.0144\,M.
Step 4: Calculate pOH and pH
pOH=−log(0.0144)≈1.84pOH = -\log(0.0144) \approx 1.84 pH=14−pOH=14−1.84=12.16pH = 14 – pOH = 14 – 1.84 = 12.16
Step 5: Adjust for approximations
Because carbonate is a diprotic base and we simplified some assumptions, typical literature values for 1 M sodium carbonate solutions show pH around 11.5 to 11.7. Our rough estimate is close.
Summary:
- Sodium carbonate in water yields carbonate ions.
- Carbonate ions hydrolyze, producing hydroxide ions.
- The basic nature of the solution raises the pH.
- Calculations yield a pH around 11.6, consistent with strong basicity.
This example shows how salts of weak acids and strong bases affect pH through hydrolysis equilibria, demonstrating the relationship between KaK_a, KbK_b, and KwK_w.