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Chapter 12 Solutions 12.5 Molarity and Dilution

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**Molarity (M) Molarity (M) is a concentration term for solutions**

the moles of solute in 1 L of solution moles of solute liter of solution

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**Preparing a 6.0 M Solution A 6.00 M NaOH solution is prepared**

by weighing out 60.0 g of NaOH (1.50 mol) and adding water to make L of a 6.00 MNaOH solution

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**Preparation of Solutions**

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**Preparation of Solutions**

A solution of a desired concentration can be prepared by diluting a small volume of a more-concentrated solution, a stock solution, with additional solvent. – Calculate the number of moles of solute desired in the final volume of the more-dilute solution and then calculate the volume of the stock solution that contains the amount of solute. – Diluting a given quantity of stock solution with solvent does not change the number of moles of solute present. – The relationship between the volume and concentration of the stock solution and the volume and concentration of the desired diluted solution is (Vs) (M s) = moles of solute = (Vd) (M d).

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**Preparation of Solutions**

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Calculating Molarity

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**Example of Calculating Molarity**

What is the molarity of L of a NaOH solution if it contains 6.00 g of NaOH? STEP 1 State the given and needed quantities. Given g of NaOH in L of solution Need molarity (M) STEP 2 Write a plan to calculate molarity. molarity (M) = moles of solute liters of solution grams of NaOH moles of NaOH molarity

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**Example of Calculating of Molarity (continued)**

STEP 3 Write equalities and conversion factors needed. 1 mol of NaOH = g of NaOH 1 mol NaOH and g NaOH 40.01 g NaOH mol NaOH STEP 4 Set up problem to calculate molarity. 6.00 g NaOH x 1 mol NaOH = mol of NaOH 40.01 g NaOH 0.150 mol NaOH = mol 0.500 L solution 1 L = M NaOH solution

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Learning Check What is the molarity of 325 mL of a solution containing g of NaHCO3? A M NaHCO3 solution B M NaHCO3 solution C M NaHCO3 solution

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**Solution STEP 1 State the given and needed quantities.**

Given g of NaHCO3 in L of solution Need molarity (M) STEP 2 Write a plan to calculate molarity. molarity (M) = moles of solute liters of solution grams of NaHCO moles of NaHCO molarity

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Solution (continued) STEP 3 Write equalities and conversion factors needed. 1 mol of NaHCO3 = g of NaHCO3 1 mol NaHCO3 and g NaHCO3 84.01 g NaOH mol NaHCO3 STEP 4 Set up problem to calculate molarity. 46.8 g NaHCO3 x 1 mol NaHCO3 = mol of NaHCO g NaHCO3 0.557 mol NaHCO3 = M NaHCO3 solution 0.325 L

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**Molarity Conversion Factors**

The units of molarity are used as conversion factors in calculations with solutions.

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**Example of Using Molarity in Calculations**

How many grams of KCl are needed to prepare 0.125 L of a M KCl solution? STEP 1 State the given and needed quantities. Given L of a M KCl solution Need grams of KCl STEP 2 Write a plan to calculate mass or volume. liters of KCl solution moles of KCl grams of KCl

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**Example of Using Molarity in Calculations (continued)**

STEP 3 Write equalities and conversion factors needed. 1 mol of KCl = g of KCl 1 mol KCl and g KCl 74.55 g KCl mol KCl 1 L of KCl solution = mol of KCl 1 L KCl solution and mol KCl 0.720 mol KCl L KCl solution

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**Example of Using Molarity in Calculations (continued)**

STEP 4 Set up problem to calculate mass or volume. 0.125 L x mol KCl x g KCl = 6.71 g of KCl 1 L mol KCl

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**Learning Check How many grams of AlCl3 are needed to prepare**

37.8 mL of a M AlCl3 solution? A g of AlCl3 B g of AlCl3 C g of AlCl3

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**Solution STEP 1 State the given and needed quantities.**

Given mL of a M AlCl3 solution Need grams of AlCl3 STEP 2 Write a plan to calculate mass or volume. milliliters of AlCl3 solution liters of AlCl3 solution moles of AlCl grams of AlCl3

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Solution (continued) STEP 3 Write equalities and conversion factors needed. 1 mol of AlCl3 = g of AlCl3 1 mol AlCl and g AlCl3 g AlCl mol AlCl3 1000 mL of AlCl3 solution = 1 L of AlCl3 solution 1000 mL AlCl3 solution and L AlCl3 solution 1 L AlCl3 solution mL AlCl3 solution 1 L of AlCl3 solution = mol of AlCl3 1 L AlCl3 solution and mol AlCl3 0.150 mol AlCl L AlCl3 solution

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Solution (continued) STEP 4 Set up problem to calculate mass or volume. 37.8 mL x L x mol x g 1000 mL L mol = g of AlCl3 (B)

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**Learning Check How many milliliters of a 2.00 M HNO3 solution**

contain 24.0 g of HNO3? A mL of HNO3 solution B mL of HNO3 solution C mL of HNO3 solution

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**Solution STEP 1 State the given and needed quantities.**

Given g of HNO3; 2.00 M HNO3 solution Need milliliters of HNO3 solution STEP 2 Write a plan to calculate mass or volume. g of solution moles of HNO mL of HNO3

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Solution (continued) STEP 3 Write equalities and conversion factors needed. 1 mol of HNO3 = g of HNO3 1 mol HNO and g HNO3 63.02 g HNO mol HNO3 1000 mL of HNO3 = mol of HNO3 1000 mL HNO3 and mol HNO3 2.00 mol HNO mL HNO3

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Solution (continued) STEP 4 Set up problem to calculate mass or volume. 24.0 g HNO3 x 1 mol HNO3 x mL 63.02 g HNO mol HNO3 = mL of HNO3 solution (C)

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**Dilution In a dilution, water is added volume increases**

concentration decreases

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NO3- Na+ Moles = 1.0 Volume = 1.0 L Molarity = 1.0 M NaNO3 solution

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**Solution volume is doubled Moles of solute remain the same**

NO3- Na+ Moles = 1.0 Volume = 2.0 L Molarity = 0.50 M Solution volume is doubled Moles of solute remain the same Solution concentration is halved

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**Comparing Initial and Diluted Solutions**

In the initial and diluted solution, the moles of solute are the same the concentrations and volumes are related by the equation M1V1 = M2V2 initial diluted

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**Calculating Dilution Quantities**

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**Example of Dilution Calculations**

What is the final molarity of the solution when 0.180 L of M KOH is diluted to L? STEP 1 Prepare a table of the initial and diluted volumes and concentrations. Initial Solution Diluted Solution M1 = M M2 = ? V1 = L V2 = L

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**Example of Dilution Calculations (continued)**

STEP 2 Solve the dilution expression for the unknown quantity. M1V1 = M2V2 V V2 M = M1V1 V2 STEP 3 Set up the problem by placing known quantities in the dilution expression. M2 = M1V1 = (0.600 M)(0.180 L) = M V L

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**Learning Check What is the final volume, in milliliters, if 15.0 mL**

of a 1.80 M KOH solution is diluted to give a 0.300 M KOH solution? A mL of M KOH solution B mL of M KOH solution C mL of M KOH solution

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Solution STEP 1 Prepare a table of the initial and diluted volumes and concentrations. Initial Solution Diluted Solution M1= M V1 = mL M2= M V2 = ?

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Solution (continued) STEP 2 Solve the dilution expression for the unknown quantity. M1V1 = M2V2 M M2 V2 = M1V1 M2 STEP 3 Set up the problem by placing known quantities in the dilution expression. V2 = M1V1 = (1.80 M)(15.0 mL) M M = mL (C )

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