Question 9.11: The maximum allowable concentration of chloroform, CHCl3, in...

The maximum allowable concentration of chloroform, CHCl_3, in drinking water is 100 ppb. What is the maximum amount (in grams) of chloroform allowed in a glass containing 400 g (400 mL) of water?
ANALYSIS We are given a solution amount (400 g) and a concentration (100 ppb). This concentration of 100 ppb means

100  ppb = \frac{Mass  of  solute  (g)}{Mass  of  solution  (g)} \times 10^9

This equation can be rearranged to find the mass of solute.
BALLPARK ESTIMATE A concentration of 100 ppb means there are 100 \times 10^{-9}  g  (1 \times 10^{-7}  g) of solute in 1 g of solution. In 400 g of solution, we should have 400 times this amount, or 400 \times 10^{-7}  g = 4 \times 10^{-5}  g.

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Mass  of  solute  (g) = \frac{Mass  of  solution  (g)}{10^9} \times 100  ppb \\                                  =\frac{400  g}{10^9} \times 100  ppb = 4 \times 10^{-5}  g  (or  0.04  mg)

BALLPARK CHECK: The calculated answer matches our estimate.

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