Mole Fraction, Molarity, and Molality

Concentration expressions are often based on the number of moles of one or more components of the solution. Recall from Section 10.6 that the mole fraction of a component of a solution is given by 

The symbol X is commonly used for mole fraction, with a subscript to indicate the component of interest. For example, the mole fraction of HCl in a hydrochloric acid solution is represented as Xhci- Thus, if a solution contains 1.00 mol of HCl (36.5 g) and 8.00 mol of water (144 g), the mole fraction of HCl is Xhci = (1.00 mol)/(1.00 mol + 8.00 mol) = 0.111. 

Mole fractions have no units because the units in the numerator and the denominator cancel. The sum of the mole fractions of all components of a solution must equal 1. Thus, in the aqueous HCl solution, XhjO = 1.000 — 0.111 = 0.889. Mole fractions are very useful when deahng with gases, as we saw in Section 10.6, but have limited use when dealing with hquid solutions. 

Recall from Section 4.5 that the molarity (M) of a solute in a solution is defined as 

For example, ifyou dissolve 0.500 mol of Na2C03 in enough water to form 0.250 L ofsolution, the molarity ofNa2C03 in the solution is (0.500 mol)/(0.250 L) = 2.00 M. Molarity is especially useful for relating the volume of a solution to the quantity of solute contained in that volume, as we saw in our discussions of titrations. OGD (Section 4.6) 

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C12-0037. A saturated solution of hydrogen peroxide in water contains 30.% by mass H2 O2 and has a density of 1.11 g/mL. Calculate the mole fractions, molarity, and molality of this solution. 

The three typical ways to describe solutions in chemistry are the mole fraction, molarity, and molality. The term normality is occasionally used, but the College Board specifically states that it is not on the test, so we ll skip it. The mole fraction is the same mole fraction we discussed earlier. The mole fraction of substance A is expressed in Equation 10.1 ... 

Several measures are used to specify the composition of a solution. Mass percentage (colloquially called weight percentage), frequently used in everyday applications, is defined as the percentage by mass of a given substance in the solution. In quantitative chemistry, the most useful measures of composition are mole fraction, molarity, and molality. 

Gas laws, including the ideal gas law, Dalton s law, and Graham s law Stoichiometric relations using the concept of the mole titration calculations Mole fractions molar and molal solutions... 

Quantitative study of a solution requires knowing its concentration, that is, the amount of solute present in a given amount of solution. Chemists use several different concentration units, each of which has advantages as well as limitations. Let us examine the four most common units of concentration percent by mass, mole fraction, molarity, and molality. 

The concentration of a solution can be expressed as percent by mass, mole fraction, molarity, and molality. The choice of units depends on the circumstances. 

A solution of phosphoric acid was made by dissolving 10.0 g H3PO4 in 100.0 mL water. The resulting volume was 104 mL. Calculate the density, mole fraction, molarity, and molality of the solution. Assume water has a density of 1.00 g/cm. ... 

The concentration of a solution can be expressed eidier qualitatively or quantitatively. The terms dilute and concentrated are used to describe a solution qualitatively. A solution widi a relatively small concentration of solute is said to be dilute one widi a laige concentration is said to be concentrated. 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. 

Solution Concentration—Any description of the composition of a solution must indicate the quantities of solute and solvent (or solution) present. Solution concentrations expressed as mass percent, volume percent, and mass/volume percent all have practical importance, as do the units, parts per million (ppm), parts per billion (ppb), and parts per trillion (ppt). However, the more fundamental concentration units are mole fraction, molarity, and molality. Molarity (moles of solute per liter of solution) is temperature dependent, but mole fraction and molality (moles of solute per kilogram of solvent) are not. 

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