How much 0.5 M NaOH is required to prepare a 10 L solution of 0.1 M NaOH?

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To solve this problem, we’ll use the dilution formula:

M₁V₁ = M₂V₂

where:

  • M₁ is the initial molarity of the concentrated solution (0.5 M NaOH)
  • V₁ is the initial volume of the concentrated solution (what we want to find)
  • M₂ is the final molarity of the diluted solution (0.1 M NaOH)
  • V₂ is the final volume of the diluted solution (10 L)

Rearranging the formula to solve for V₁:

V₁ = (M₂V₂) / M₁

Substituting the given values:

V₁ = (0.1 M * 10 L) / 0.5 M

Calculating V₁:

V₁ = 2 L

Therefore, 2 liters of 0.5 M NaOH is required to prepare a 10 L solution of 0.1 M NaOH.