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Chemistry

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2 parts
1
3.46
2
3.28

Step-by-step solution

8 steps

Part 1· 2 steps

a) Calculate the pH of this solution.

  1. Calculate the pKa\text{p}K_a of \ce{HF}.

    The acid dissociation constant (KaK_a) for \ce{HF} is given as 3.5×10−43.5 \times 10^{-4}.

    pKa=−log⁡(Ka)\text{p}K_a = -\log(K_a) pKa=−log⁡(3.5×10−4)\text{p}K_a = -\log(3.5 \times 10^{-4}) pKa=3.46\text{p}K_a = 3.46
  2. Use the Henderson-Hasselbalch equation to calculate the pH.

    The solution contains a weak acid (\ce{HF}) and its conjugate base (\ce{F-}, from \ce{NaF}). This is a buffer solution.
    Given concentrations: [\ceHF]=0.250 M[\ce{HF}] = 0.250\ \text{M} and [\ceF−]=0.250 M[\ce{F-}] = 0.250\ \text{M}.

    pH=pKa+log⁡([conjugate base][weak acid])\text{pH} = \text{p}K_a + \log \left( \frac{[\text{conjugate base}]}{[\text{weak acid}]} \right) pH=3.46+log⁡([\ceF−][\ceHF])\text{pH} = 3.46 + \log \left( \frac{[\ce{F-}]}{[\ce{HF}]} \right) pH=3.46+log⁡(0.250 M0.250 M)\text{pH} = 3.46 + \log \left( \frac{0.250\ \text{M}}{0.250\ \text{M}} \right) pH=3.46+log⁡(1)\text{pH} = 3.46 + \log(1) pH=3.46+0\text{pH} = 3.46 + 0 pH=3.46\text{pH} = 3.46

    The pH of the solution is:

    3.46\boxed{3.46}

Part 23.28

b) Calculate the pH of the solution after 0.050 mol of \ce{HCl} is added to it. (Assume no change in volume.)

  1. Calculate initial moles of \ce{HF} and \ce{F-}.

    The initial volume of the solution is 1.00 L.
    Moles of \ce{HF} = 0.250 M×1.00 L=0.250 mol0.250\ \text{M} \times 1.00\ \text{L} = 0.250\ \text{mol}
    Moles of \ce{F-} = 0.250 M×1.00 L=0.250 mol0.250\ \text{M} \times 1.00\ \text{L} = 0.250\ \text{mol}

  2. Determine the reaction with added \ce{HCl}.

    When 0.050 mol of \ce{HCl} (a strong acid) is added, it reacts with the conjugate base (\ce{F-}).

    \ceF−(aq)+H+(aq)−>HF(aq)\ce{F- (aq) + H+ (aq) -> HF (aq)}

    Initial moles: \ceF−=0.250 mol\ce{F-} = 0.250\ \text{mol}, \ceH+=0.050 mol\ce{H+} = 0.050\ \text{mol}, \ceHF=0.250 mol\ce{HF} = 0.250\ \text{mol}
    Change: \ceF−\ce{F-} reacts with \ceH+\ce{H+}, so \ceF−\ce{F-} decreases by 0.050 mol0.050\ \text{mol}, \ceH+\ce{H+} decreases by 0.050 mol0.050\ \text{mol}, and \ceHF\ce{HF} increases by 0.050 mol0.050\ \text{mol}.
    After reaction:
    Moles of \ce{F-} = 0.250 mol−0.050 mol=0.200 mol0.250\ \text{mol} - 0.050\ \text{mol} = 0.200\ \text{mol}
    Moles of \ce{HF} = 0.250 mol+0.050 mol=0.300 mol0.250\ \text{mol} + 0.050\ \text{mol} = 0.300\ \text{mol}

  3. Calculate the new concentrations.

    Since the volume remains 1.00 L:
    [\ceF−]=0.200 mol1.00 L=0.200 M[\ce{F-}] = \frac{0.200\ \text{mol}}{1.00\ \text{L}} = 0.200\ \text{M}
    [\ceHF]=0.300 mol1.00 L=0.300 M[\ce{HF}] = \frac{0.300\ \text{mol}}{1.00\ \text{L}} = 0.300\ \text{M}

  4. Use the Henderson-Hasselbalch equation to calculate the new pH.

    The pKa\text{p}K_a for \ce{HF} is 3.46 (calculated in part a).

    pH=pKa+log⁡([\ceF−][\ceHF])\text{pH} = \text{p}K_a + \log \left( \frac{[\ce{F-}]}{[\ce{HF}]} \right) pH=3.46+log⁡(0.200 M0.300 M)\text{pH} = 3.46 + \log \left( \frac{0.200\ \text{M}}{0.300\ \text{M}} \right) pH=3.46+log⁡(0.6666...)\text{pH} = 3.46 + \log(0.6666...) pH=3.46−0.18\text{pH} = 3.46 - 0.18 pH=3.28\text{pH} = 3.28

    The pH of the solution after adding \ce{HCl} is:

    3.28\boxed{3.28}

Part 3· 2 steps

c) Calculate the pH of the solution after 0.050 mol of \ce{NaOH} is added to it. (Assume no change in volume.)

  1. Calculate initial moles of \ce{HF} and \ce{F-}.

    The initial volume of the solution is 1.00 L.
    Moles of \ce{HF} = 0.250 M×1.00 L=0.250 mol0.250\ \text{M} \times 1.00\ \text{L} = 0.250\ \text{mol}
    Moles of \ce{F-} = 0.250 M×1.00 L=0.250 mol0.250\ \text{M} \times 1.00\ \text{L} = 0.250\ \text{mol}

  2. Determine the reaction with added \ce{NaOH}.

    When 0.050 mol of \ce{NaOH} (a strong base) is added, it reacts with the weak acid (\ce{HF}).

    \ceHF(aq)+OH−(aq)−>F−(aq)+H2O(l)\ce{HF (aq) + OH- (aq) -> F- (aq) + H2O (l)}

    Initial moles: \ceHF=0.250 mol\ce{HF} = 0.250\ \text{mol}, \ceOH−=0.050 mol\ce{OH-} = 0.050\ \text{mol}, $\ce{F-} = 0.250\

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