Math Problem Statement

What is the concentration of a solution made by diluting 25 mL of 6.0 M HCl to a final volume of 750 mL?

Solution

To solve this problem, we will use the dilution equation:

C1V1=C2V2C_1 V_1 = C_2 V_2

Where:

  • C1C_1 is the initial concentration (6.0 M),
  • V1V_1 is the initial volume (25 mL),
  • C2C_2 is the final concentration (what we are trying to find),
  • V2V_2 is the final volume (750 mL).

Rearranging the equation to solve for C2C_2:

C2=C1V1V2C_2 = \frac{C_1 V_1}{V_2}

Substituting the values:

C2=6.0M×25mL750mL=150750=0.2MC_2 = \frac{6.0 \, \text{M} \times 25 \, \text{mL}}{750 \, \text{mL}} = \frac{150}{750} = 0.2 \, \text{M}

So, the final concentration is 0.2 M.

Would you like more details or have any further questions?

Here are five related questions to expand this topic:

  1. How does changing the final volume affect the concentration of the solution?
  2. What happens to the concentration if the initial volume is doubled?
  3. How would the process change if the substance is not HCl but a different acid or base?
  4. Can you calculate the final concentration if the dilution involves adding more than one substance?
  5. What is the difference between a molarity-based dilution and a mass-based dilution?

Tip: When performing dilutions, always make sure the units for volume are consistent throughout the calculation.

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Math Problem Analysis

Mathematical Concepts

Dilution
Molarity
Algebra

Formulas

C1V1 = C2V2
C2 = (C1 * V1) / V2

Theorems

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Suitable Grade Level

Grades 9-12