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26 November, 07:25

A beaker with 1.60*102 mL of an acetic acid buffer with a pH of 5.000 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.100 M. A student adds 7.10 mL of a 0.460 M HCl solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.740. Express your answer numerically to two decimal places. Use a minus (-) sign if the pH has decreased. View Available Hint (s) ΔpH = Previous Answers Incorrect; Try Again; 16 attempts remaining Provide Feedback.

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  1. 26 November, 10:01
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    The pH will change 0.16 (from 5.00 to 4.84)

    Explanation:

    Step 1: Data given

    volume of acetic acid buffer = 160 mL

    The total molarity of acid and conjugate base in this buffer is 0.100 M

    A student adds 7.10 mL of a 0.460 M HCl solution to the beaker.

    The pKa of acetic acid is 4.740

    pH = 5.00

    Step 2: Calculate concentration of acid

    Consider x = concentration acid

    Consider y = concentration conjugate base

    x + y = 0.100

    5.00 = 4.740 + log y/x

    5.00 - 4.740 = log y/x

    0.26 = log y/x

    10^0.26 = 1.82 = y/x

    1.82 x = y

    Since x+y = 0.100

    x + 1.82 x = 0.100

    2.82 x = 0.100

    x = 0.0355 M = concentration acid

    Step 3: Calculate concentration of conjugate base

    y = 0.100 - x

    0.100 - 0.0355 = 0.0645 M = concentration conjugate base

    Step 4: Calculate moles of acid

    Moles = volume * molarity

    moles acid = 0.160 L * 0.0355 M = 0.00568 moles

    Step 5: Calculate moles of conjugate base

    moles conjugate base = 0.0645 M * 0.160 L=0.01032 moles

    Step 6: Calculate moles HCl

    moles HCl = 7.10 * 10^-3 L * 0.460 M=0.003266 moles

    Step 7: Calculate new moles

    A - + H + = HA

    moles conjugate base = 0.01032 - 0.003266 = 0.007054 moles

    moles acid = 0.00568 + 0.003266=0.008946 moles

    Step 8: Calculate the total volume

    total volume = 160 + 7.10 = 167.1 mL = 0.1671 L

    Step 9: Calculate the concentration of the acid

    concentration acid = 0.008946 / 0.1671 = 0.0535 M

    Step 10: Calculate the concentration of conjugate base

    concentration conjugate base = 0.007054 / 0.1671 = 0.0422 M

    Step 11: Calculate the pH

    pH = 4.740 + log 0.0535 / 0.0422=4.84

    change pH = 5.00 - 4.84=0.16

    The pH will change 0.16
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