Chemists deal with amounts of molecules every day. Our reactions are described as so many molecules of compound A reacting with so many molecules of compound B to form so many molecules of compound C. When we determine how much reagent to use, we need to know the number of molecules in a given volume of the reagent. Percent solutions only tell us the number of grams, not molecules. A 100 mL solution of 2% NaCl will have a very different number of molecules than a 2% solution of CsCl. So we need another way to talk about numbers of molecules. Chemists primarily need the concentration of solutions to be expressed in a way that accounts for the number of particles that react according to a particular chemical equation. Since percentage measurements are based on either mass or volume, they are generally not useful for chemical reactions. A concentration unit based on moles is preferable. The molarity (M) of a solution is the number of moles of solute dissolved in one liter of solution. To calculate the molarity of a solution, you divide the moles of solute by the volume of the solution expressed in liters.  Note that the volume is in liters of solution and not liters of solvent. When a molarity is reported, the unit is the symbol M and is read as “molar”. For example a solution labeled as 1.5 M NH 3 is read as “1.5 molar ammonia solution”. Sample Problem: Calculating MolarityA solution is prepared by dissolving 42.23 g of NH 4 Cl into enough water to make 500.0 mL of solution. Calculate its molarity. Step 1: List the known quantities and plan the problem. The mass of the ammonium chloride is first converted to moles. Then the molarity is calculated by dividing by liters. Note the given volume has been converted to liters. Step 2: Solve. Step 3: Think about your result. The molarity is 1.579 M, meaning that a liter of the solution would contain 1.579 mol NH 4 Cl. Four significant figures are appropriate. In a laboratory situation, a chemist must frequently prepare a given volume of solutions of a known molarity. The task is to calculate the mass of the solute that is necessary. The molarity equation can be rearranged to solve for moles, which can then be converted to grams. See sample problem 16.3. Sample Problem:A chemist needs to prepare 3.00 L of a 0.250 M solution of potassium permanganate (KMnO 4 ). What mass of KMnO 4 does she need to make the solution? Step 1: List the known quantities and plan the problem. Known
Unknown Moles of solute is calculated by multiplying molarity by liters. Then, moles is converted to grams. Step 2: Solve. Step 3: Think about your result. When 119 g of potassium permanganate is dissolved into water to make 3.00 L of solution, the molarity is 0.250 M. Watch a video of molarity calculations:
Read the material and work the problems at the site below: http://www.occc.edu/kmbailey/Chem1115Tutorials/Molarity.htm
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Learning Objective
Rather than qualitative terms (Section 11.2 - Definitions) we need quantitative ways to express the amount of solute in a solution; that is, we need specific units of concentration. In this section, we will introduce several common and useful units of concentration. Molarity (M) is defined as the number of moles of solute divided by the number of liters of solution: \[molarity \: =\: \frac{moles\: of\: solute}{liters\: of\: solution}\] which can be simplified as \[M\: =\: \frac{mol}{L},\; or\; mol/L\] As with any mathematical equation, if you know any two quantities, you can calculate the third, unknown, quantity. For example, suppose you have 0.500 L of solution that has 0.24 mol of NaOH dissolved in it. The concentration of the solution can be calculated as follows: \[molarity \: =\: \frac{0.24\: mol\: NaOH}{0.500\:L}=0.48\, M\; NaOH\] The concentration of the solution is 0.48 M, which is spoken as “zero point forty-eight molarity” or “zero point forty-eight molar.” If the quantity of the solute is given in mass units, you must convert mass units to mole units before using the definition of molarity to calculate concentration. For example, what is the molar concentration of a solution of 22.4 g of HCl dissolved in 1.56 L? First, convert the mass of solute to moles using the molar mass of HCl (36.5 g/mol): \[22.4\cancel{g\:HCl}\times \frac{1\: mol\: HCl}{36.5\cancel{g\:HCl}}=0.614\, moles\; HCl\] Now we can use the definition of molarity to determine a concentration: \[M \: =\: \frac{0.614\: mol\: HCl}{1.56\:L}=0.394\, M\]
Example \(\PageIndex{1}\): What is the molarity of a solution made when 32.7 g of NaOH are dissolved to make 445 mL of solution? Solution To use the definition of molarity, both quantities must be converted to the proper units. First, convert the volume units from milliliters to liters: \[445\cancel{mL}\times \frac{1\: L}{1000\: \cancel{mL}}=0.445\, L\] Now we convert the amount of solute to moles, using the molar mass of NaOH, which is 40.0 g/mol: \[32.7\cancel{g\:NaOH}\times \frac{1\: mol\: NaOH}{40.0\cancel{g\:NaOH}}=0.818\, mol\: NaOH\] Now we can use the definition of molarity to determine the molar concentration: \[M \: =\: \frac{0.818\: mol\: NaOH}{0.445\:L}=1.84\, M\: NaOH\]
Exercise \(\PageIndex{1}\) What is the molarity of a solution made when 66.2 g of C6H12O6 are dissolved to make 235 mL of solution? Answer 1.57 M The definition of molarity can be used to determine the amount of solute or the volume of solution, if the other information is given. Example 4 illustrates this situation.
Example \(\PageIndex{1}\): How many moles of solute are present in 0.108 L of a 0.887 M NaCl solution? Solution We know the volume and the molarity; we can use the definition of molarity to mathematically solve for the amount in moles. Substituting the quantities into the definition of molarity: \[0.887\, M \: =\: \frac{mol\: NaCl}{0.108\:L}\] We multiply the 0.108 L over to the other side of the equation and multiply the units together; “molarity × liters” equals moles, according to the definition of molarity. So mol NaCl = (0.887 M)(0.108 L) = 0.0958 mol
Exercise \(\PageIndex{1}\) How many moles of solute are present in 225 mL of a 1.44 M CaCl2 solution? Answer 0.324 mol If you need to determine volume, remember the rule that the unknown quantity must be by itself and in the numerator to determine the correct answer. Thus rearrangement of the definition of molarity is required.
Example \(\PageIndex{1}\): What volume of a 2.33 M NaNO3 solution is needed to obtain 0.222 mol of solute? Solution Using the definition of molarity, we have \[2.33\, M \: =\: \frac{0.222\:mol}{L}\] To solve for the number of liters, we bring the 2.33 M over to the right into the denominator, and the number of liters over to the left in the numerator. We now have \[L \: =\: \frac{0.222\:mol}{2.33\, M}\] Dividing, the volume is 0.0953 L = 95.3 mL.
Exercise \(\PageIndex{1}\) What volume of a 0.570 M K2SO4 solution is needed to obtain 0.872 mol of solute? Answer 1.53 L |
What is the molarity of a solution made by dissolving 3.090 moles of alp in 1500 mL of solution
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