Math Problem Statement

By titration, 19.90 mL of 0.157 M NaOH is needed to neutralize 25.0 mL of HCl. Calculate the concentration of the HCl solution.

Solution

The image you uploaded contains a titration problem for calculating the concentration of an HCl solution. Here’s a summary and solution approach based on the content visible:

Problem Overview:

  • A titration was performed, and 19.90 mL of 0.157 M NaOH was needed to neutralize 25.0 mL of HCl.
  • The balanced chemical equation is: HCl(aq)+NaOH(aq)NaCl(aq)+H2O(l)\text{HCl(aq)} + \text{NaOH(aq)} \rightarrow \text{NaCl(aq)} + \text{H}_2\text{O(l)} This indicates a 1:1 molar ratio between HCl and NaOH.

Formula to Use:

  • The problem suggests using the titration formula: MAVA=MBVBM_A V_A = M_B V_B where:
    • MAM_A is the molarity of HCl (unknown),
    • VAV_A is the volume of HCl (25.0 mL),
    • MBM_B is the molarity of NaOH (0.157 M),
    • VBV_B is the volume of NaOH (19.90 mL).

Solution Steps:

  1. Rearrange the formula to solve for MAM_A: MA=MBVBVAM_A = \frac{M_B V_B}{V_A}
  2. Substitute the values: MA=0.157×19.9025.0M_A = \frac{0.157 \times 19.90}{25.0}
  3. Perform the calculation: MA=3.124325.0=0.12497M0.125MM_A = \frac{3.1243}{25.0} = 0.12497 \, \text{M} \approx 0.125 \, \text{M}

Answer: The concentration of the HCl solution is approximately 0.125 M.

Would you like more detailed steps or explanations? Here are 5 related questions you might explore:

  1. What are the units for molarity and why are they important?
  2. How does the 1:1 molar ratio between HCl and NaOH affect the calculation?
  3. Could this method be used if the molar ratio were not 1:1?
  4. What is the significance of the balanced chemical equation in titration problems?
  5. How would you handle experimental errors in a real titration process?

Tip: Always ensure volumes are in the same units when applying the titration formula.

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Math Problem Analysis

Mathematical Concepts

Stoichiometry
Titration
Molarity

Formulas

M_A V_A = M_B V_B

Theorems

1:1 molar ratio in neutralization

Suitable Grade Level

Grades 10-12