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.

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