It takes 28.61 mL of 0.216 M sodium hydroxide solution to titrate 10.00 mL of sulfuric acid solution. What is the molarity of the sulfuric acid?
The correct answer and explanation is :
To find the molarity of the sulfuric acid (H₂SO₄) solution, we can use the concept of molarity and the balanced chemical equation for the titration reaction between sodium hydroxide (NaOH) and sulfuric acid (H₂SO₄).
Step 1: Write the balanced chemical equation
The balanced equation for the reaction between sodium hydroxide and sulfuric acid is:
$$
H_2SO_4 (aq) + 2NaOH (aq) \rightarrow Na_2SO_4 (aq) + 2H_2O (l)
$$
From this equation, we can see that 1 mole of sulfuric acid reacts with 2 moles of sodium hydroxide.
Step 2: Use the titration formula
The titration formula is:
$$
M_1 V_1 = M_2 V_2
$$
Where:
- $M_1$ is the molarity of the sodium hydroxide solution
- $V_1$ is the volume of the sodium hydroxide solution used
- $M_2$ is the molarity of the sulfuric acid solution (this is what we’re trying to find)
- $V_2$ is the volume of the sulfuric acid solution
We are given:
- $M_1 = 0.216 \, \text{M}$ (molarity of NaOH)
- $V_1 = 28.61 \, \text{mL} = 0.02861 \, \text{L}$ (volume of NaOH solution)
- $V_2 = 10.00 \, \text{mL} = 0.01000 \, \text{L}$ (volume of H₂SO₄ solution)
Step 3: Adjust for the stoichiometric ratio
According to the balanced equation, 2 moles of NaOH react with 1 mole of H₂SO₄, so we need to account for this ratio by dividing the volume of NaOH by 2 in the calculation.
Thus, the effective volume of NaOH is:
$$
V_1′ = \frac{V_1}{2} = \frac{0.02861}{2} = 0.014305 \, \text{L}
$$
Step 4: Solve for $M_2$, the molarity of sulfuric acid
Now, using the titration formula, we substitute the values and solve for $M_2$:
$$
M_1 V_1′ = M_2 V_2
$$
$$
0.216 \, \text{M} \times 0.014305 \, \text{L} = M_2 \times 0.01000 \, \text{L}
$$
$$
M_2 = \frac{0.216 \times 0.014305}{0.01000}
$$
$$
M_2 = 0.309 \, \text{M}
$$
Final Answer:
The molarity of the sulfuric acid solution is 0.309 M.
Explanation:
In this titration problem, we used the concept of molarity, the stoichiometric relationship between NaOH and H₂SO₄, and the titration formula to determine the molarity of the sulfuric acid solution. By adjusting the volume of NaOH for the 2:1 ratio with H₂SO₄ and applying the formula, we obtained the final result.