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Calculate the pKa of acetic acid (CH3CO₂H).

Chemistry

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Answer

5.01

Step-by-step solution

2 steps
  1. Calculate the pKa\text{p}K_a of acetic acid (CH3CO2H\text{CH}_3\text{CO}_2\text{H}).

    The acid dissociation constant (KaK_a) for CH3CO2H\text{CH}_3\text{CO}_2\text{H} is given as 1.76×10−51.76 \times 10^{-5}.

    pKa=−log⁡10(Ka)\text{p}K_a = -\log_{10}(K_a) pKa=−log⁡10(1.76×10−5)\text{p}K_a = -\log_{10}(1.76 \times 10^{-5}) pKa≈4.754\text{p}K_a \approx 4.754
  2. Use the Henderson-Hasselbalch equation to calculate the pH.

    The Henderson-Hasselbalch equation is:

    pH=pKa+log⁡10([A−][HA])\text{pH} = \text{p}K_a + \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)

    We are given:
    [HA]=[CH3CO2H]=0.25 M[\text{HA}] = [\text{CH}_3\text{CO}_2\text{H}] = 0.25 \text{ M}
    [A−]=[CH3CO2−]=0.45 M[\text{A}^-] = [\text{CH}_3\text{CO}_2^-] = 0.45 \text{ M}
    pKa=4.754\text{p}K_a = 4.754
    Substitute these values into the equation:

    pH=4.754+log⁡10(0.45 M0.25 M)\text{pH} = 4.754 + \log_{10}\left(\frac{0.45 \text{ M}}{0.25 \text{ M}}\right) pH=4.754+log⁡10(1.8)\text{pH} = 4.754 + \log_{10}(1.8) pH=4.754+0.255\text{pH} = 4.754 + 0.255 pH=5.009\text{pH} = 5.009

    Rounding to a reasonable number of significant figures (e.g., two decimal places for pH), the pH is 5.01. If rounded to the nearest whole number as shown in the provided solution, it is 5.

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