Question #73137

1 Answer
Stefan V.
May 10, 2015

The concentration of triclosan will be #2.5 * 10^(-2)"ppb"#.

You can write a concentration expressed in parts per billion, or ppb, as 1 gram of solute, in your case triclosan, per 1 billion grams of solvent, in your case water.

A 1 ppb concentration means that you have 1 gram of triclofan in 1 billion grams of water

#"1 ppb" = "1 g triclosan"/(10^9"g water") = 10^(-9)#

This means that if you multiply the ratio between the mass of solute and the mass of solution by #10^(9)#, you'll get the concentration in ppb.

You can convert volume to grams by using water's density

#1.5cancel("L") * "1000 g"/(1cancel("L")) = 1.5 * 10^(3)"g water"#

Expressed in grams, the mass of triclosan will be

#38cancel("ng") * ("1 g")/(10^(9)cancel("ng")) = 38 * 10^(-9)"g"#

The ratio between the mass of triclosan and the mass of the solution will be

#(38 * 10^(-9)cancel("g"))/(1.5 * 10^(3) * cancel("g")) = 2.533 * 10^(-11)#

Multiply this by #10^(9)# to get concentration in ppb

#2.533 * 10^(-11) * 10^(9) = color(green)(2.5 * 10^(-2))#

(the answer is rounded to two sig figs).

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