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5 August, 17:50

In order to make 14 oz of a milk-coffee drink with a pH of 5.8, how many ounces of each are required?

Round your answers to one decimal places.

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  1. 5 August, 17:56
    0
    We know that the pH of a solution is:

    pH = - log[H+]

    Let c be the fraction of coffee in the drink and m be the fraction of milk in the drink. Because these are the parts of a whole, they add up to 1. c + m = 1

    pH of coffee = 5

    pH of milk = 6

    [H + in solution] = c[H + in coffee] + m[H + in milk]

    [H + solution] = 10^ (-5.8) = 1.58 x 10⁻⁶

    [H + coffee] = 10^ (-5) = 1 x 10⁻⁵

    [H + milk] = 10^ (-6) = 1 x 10⁻⁶

    1.58 x 10⁻⁶ = c (1 x 10⁻⁵) + (1 - c) 1 x 10⁻⁶

    c = 0.064

    m = 0.936

    Amount of coffee = 14 x 0.064 = 0.896 oz

    Amount of milk = 14 - 0.896 = 13.104 oz
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