We introduced molarity ( M) in Section 4.5. Mole fractions are very useful when dealing with gases as we saw in Section 10.6 but have limited use when dealing with liquid solutions.
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The sum of the mole fractions of all components of a solution must equal 1. Note that mole fractions have no units because the units in the numerator and the denominator cancel. Thus a solution containing 1.00 mol of HCl (36.5 g) and 8.00 mol of water (144 g) has a mole fraction of HCl of X HCl = (1.00 mol)/(1.00 mol + 8.00 mol) = 0.111. For example, the mole fraction of HCl in a hydrochloric acid solution is represented as X HCl. The symbol X is commonly used for mole fraction, with a subscript to indicate the component of interest. Recall from Section 10.6 that the mole fraction of a component of a solution is given by The three we use most commonly are mole fraction, molarity, and molality.
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We often use concentration expressions based on the number of moles of one or more components of the solution. What is the mass of NaOCl in a bottle containing 2500 g of bleaching solution? Answer: (a) 2.91 percent (b) 90.5 g of NaOCl (b) A commercial bleaching solution contains 3.62 mass percent sodium hypochlorite, NaOCl. (a) Calculate the mass percentage of NaCl in a solution containing 1.50 g of NaCl in 50.0 g of water. The mass percentage of water in this solution is (100 - 11.9)% = 88.1%. The mass of the solution is the sum of the mass of solute (glucose) and the mass of solvent (water). SOLUTION (a) We calculate the mass percentage by using Equation 13.5. What is the concentration of Zn 2+ in parts per million? What is the mass percentage of solute in this solution? (b) A 2.5-g sample of groundwater was found to contain 5.4 g of Zn 2+. (a) A solution is made by dissolving 13.5 g of glucose, C 6H 12O 6, in 0.100 kg of water. Thus, the allowable concentration of arsenic in water can be expressed as 50 ppb. A concentration of 1 ppb represents 1 g of solute per billion (10 9) grams of solution, or 1 microgram ( g) of solute per liter of solution. For example, the maximum allowable concentration of arsenic in drinking water in the United States is 0.05 ppm that is, 0.05 mg of arsenic per liter of water.įor solutions that are even more dilute, parts per billion (ppb) is used.
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The acceptable maximum concentrations of toxic or carcinogenic substances are often expressed in ppm. Thus, 1 ppm also corresponds to 1 mg of solute per liter of solution. Because the density of water is 1 g/mL, 1 kg of a dilute aqueous solution will have a volume very close to 1 L. We often express the concentrations of very dilute solution in parts per million (ppm), defined asĪ solution whose solute concentration is 1 ppm contains 1 g of solute for each million (10 6) grams of solution or, equivalently, 1 mg of solute per kilogram of solution. Where we have abbreviated solution as "soln." Thus, a solution of hydrochloric acid that is 36 percent HCl by mass contains 36 g of HCl for each 100 g of solution. One of the simplest expressions of concentration is the mass percentage of a component in a solution, given by We use several different ways to express concentration in quantitative terms, and we examine four of these in this section: mass percentage, mole fraction, molarity, and molality. A solution with a relatively small concentration of solute is said to be dilute one with a large concentration is said to be concentrated. The terms dilute and concentrated are used to describe a solution qualitatively. The concentration of a solution can be expressed either qualitatively or quantitatively. Chemistry: The Central Science, Chapter 13, Section 4 13.4 Ways of Expressing Concentration