Water treatment plants commonly use chlorination to destroy...

Water treatment plants commonly use chlorination to destroy bacteria. A byproduct is chloroform $\left(\mathrm{CHCl}_{3}\right),$ a suspected carcinogen, produced when HOCl, formed by reaction of $\mathrm{Cl}_{2}$ and water, reacts with dissolved organic matter. The United States, Canada, and the World Health Organization have set a limit of $100 . \mathrm{ppb}$ of $\mathrm{CHCl}_{3}$ in drinking water. Convert this concentration into molarity, molality, mole fraction, and mass percent.

Key Concepts

Mass Percent

Mass percent is the concentration expressed as the mass of the solute divided by the total mass of the solution, multiplied by 100. It provides a clear indication of the composition of a mixture in terms of weight, which is especially useful in industrial applications and when dealing with mixtures of substances with similar densities.

Mole Fraction

Mole fraction is the ratio of the number of moles of a component to the total number of moles in the mixture. This dimensionless quantity is important in thermodynamics and physical chemistry because it is independent of the units of measurement and provides a straightforward way to express the composition of mixtures in terms of proportions of individual components.

Parts per Billion (ppb)

Parts per billion is a unit of concentration that denotes one part of a substance per one billion parts of the solution. It is frequently used to express very low concentrations, such as contaminants in water, and requires careful conversion for chemical calculations because it is typically defined by mass-to-mass or volume-to-volume relationships.

Molarity

Molarity is defined as the number of moles of solute per liter of solution. It is a key concentration unit used in chemistry because it directly relates the mass of a substance to its volume, assuming the density of the solution is known or can be approximated, which is essential for reaction stoichiometry and mixing calculations.

Molality

Molality is the measure of the moles of solute per kilogram of solvent. Unlike molarity, molality is independent of the solution volume, which can change with temperature. This makes it particularly useful in scenarios where precise measurements of concentration are needed at varying temperatures or when dealing with colligative properties.

Transcript

00:01 We'll work on problem 135 from chapter 13.

00:07 In this problem, we're talking about chloroform, which is formed as a byproduct when water treatment plants use chlorination to make sure bacteria do not live in the water.

00:27 And so different organizations have set the limit for safe exposure to chloroform, at 100 parts per billion in drinking water.

00:40 And so we want to convert this concentration into malarity, molality, mole fraction, and mass percent.

00:49 So 100 pvb.

00:53 And it would be helpful to think of parts per billion as grams per milliliter times 10 to the ninth.

01:04 So first, let's go ahead and convert pbb to molarity.

01:17 So we have right now our concentration in terms of grams per milliliter.

01:26 So we need to change to moles to get to molarity.

01:31 So we can divide by the molar mass of chloroform, which is 11 .38 grams per mole.

01:40 We have grams per milliliter.

01:44 So we need to convert from a millimeter to liter.

01:47 So we can multiply by 1 ,000 for this conversion.

01:55 And then we can divide by 10 to the 9th because we need to get rid of this part here, the billion part in parts per billion.

02:08 So when we do this, grams and milliliters cancels with the pbb, and then we're left with a concentration of moles per liter, and we get 8 .38 times 10 to the 1 .3 .3 .5 .2.

02:24 The negative 7 molarity.

02:27 So that's our concentration in molarity...

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