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A comic book villain is holding you at gun point and is making you drink a sample of acid. She gives you a beaker with 100ml of a strong acid with pH=5. She also gives you a beaker of a strong base with a pH=10. You can add as much of the strong base to the strong acid as you want, and you must then drink the solution. You'd be best off trying to make the solution neutral before drinking it. How much of the base should you add?

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Answer:

We should add 10 mL of the strong base.

Explanation:

Assuming the acid is monoprotic, then the number of H⁺ moles in 100 mL of the solution with pH=5 would be:

  • 5 = -log[H⁺]
  • -5 = log[H⁺]
  • [tex]10^{-5}[/tex] = [H⁺]
  • 1x10⁻⁵ M * 0.100 L = 1x10⁻⁶ moles H⁺

In order to make the solution neutral, we should add the same amount of OH⁻ moles (1x10⁻⁶).

To calculate [OH⁻] of the strong base, we can use pOH:

  • pH + pOH = 14
  • 10 + pOH = 14
  • pOH = 4

Once again, assuming the strong base is monobasic:

  • pOH = -log[OH⁻]
  • 4 = -log[OH⁻]
  • 10⁻⁴ = [OH⁻]

Finally we calculate the required volume:

  • 1x10⁻⁶ moles OH⁻ ÷ 1x10⁻⁴M = 0.010 L
  • 0.010 L ⇒ 0.010 * 1000 = 10 mL

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