Concept Explanation: pH Calculation for Acid-Base Neutralization

This problem involves mixing an acid (H₂SO₄) and a base (NaOH) and finding the pH of the resultant solution. The key steps are:

1. Step 1: Determine the molarity of each solution.

   Molarity (M) = (mass of solute in grams) / (molar mass × volume in liters)

   For Solution A (NaOH): Molar mass = 40 g/mol, Volume = 100 L, Mass = 4 g

   $M_A=\frac{4}{40\times 100}=0.001M$

   For Solution B (H₂SO₄): Molar mass = 98 g/mol, Volume = 100 L, Mass = 9.8 g

   $M_B=\frac{9.8}{98\times 100}=0.001M$

2. Step 2: Find the number of moles of acid and base mixed.

   Moles = Molarity × Volume (in liters) used

   Moles of NaOH from 40 L of A: $0.001M\times 40L=0.04\mathrm{moles}$

   Moles of H₂SO₄ from 10 L of B: $0.001M\times 10L=0.01\mathrm{moles}$

   Since H₂SO₄ is diprotic, it provides 2 moles of H⁺ per mole.

   Moles of H⁺ = $2\times 0.01=0.02\mathrm{moles}$

   Moles of OH^- from NaOH = $0.04\mathrm{moles}$

3. Step 3: Determine the limiting reactant and find excess moles.

   The neutralization reaction is: $H^{+}+{\mathrm{OH}}^{-}\to H_{2}O$

   Moles of H⁺ available = 0.02 moles

   Moles of OH^- available = 0.04 moles

   H⁺ is the limiting reactant. It will completely react with 0.02 moles of OH^-.

   Excess moles of OH^- remaining = 0.04 - 0.02 = $0.02\mathrm{moles}$

4. Step 4: Calculate the concentration of OH^- in the final mixture.

   Total volume of mixture = 40 L + 10 L = $50L$

   Concentration of OH^-, [OH^-] = moles / volume = $\frac{0.02}{50}=0.0004M$

5. Step 5: Calculate pOH and then pH.

   pOH = -log₁₀[OH^-] = $-\log \left(0.0004\right)=-\log (4\times {10}^{-4})$

   $=-\left[\log \right(4)+\log ({10}^{-4}\left)\right]=-[0.6021-4]=-[-3.3979]=3.3979\approx 3.4$

   Since pH + pOH = 14,

   pH = 14 - pOH = $14-3.4=10.6$

Final Answer: The pH of the resultant solution is 10.6

Related Topics & Formulae

1. Molarity: The concentration of a solution, defined as the number of moles of solute per liter of solution.
Formula: $M=\frac{\text{moles of solute}}{\text{volume of solution in liters}}$

2. pH and pOH: pH is a measure of the acidity or basicity of a solution. pOH is its equivalent for hydroxide ion concentration. They are related by the following formulae in aqueous solutions at 25°C.
Formulae: $pH=-{\log }_{10}\left[H^{+}\right]$ $pOH=-{\log }_{10}[O^H-]$ $pH+pOH=14$

3. Neutralization Reaction: A reaction between an acid and a base which results in the formation of water and a salt. The core reaction is:
$H^{+}+{\mathrm{OH}}^{-}\to H_{2}O$

4. Diprotic Acid: An acid that can donate two protons (H⁺ ions) per molecule, such as H₂SO₄. This must be accounted for when calculating the number of moles of H⁺ available for reaction.