# 8.4 Percent Concentration

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8.4 Percent Concentration
Chapter 8 Solutions 8.4 Percent Concentration

Concentration The concentration of a solution
is the amount of solute dissolved in a specific amount of solution concentration = amount of solute amount of solution

Mass Percent Concentration
Mass percent (m/m) concentration is the percent by mass of solute in a solution calculated using the formula: Mass = mass of solute(g) x 100% percent mass of solute(g) + mass of solvent(g) Mass percent = mass of solute(g) x 100% mass of solution(g)

Mass of Solution

Calculating Mass Percent
The calculation of mass percent (m/m) requires the grams of solute (g of KCl) and grams of solution (g of KCl solution) g of KCl = g g of solvent (water) = g g of KCl solution = g 8.00 g of KCl (solute) x 100% = 16.0% (m/m) 50.00 g of KCl solution

Guide to Calculating Solution Concentrations

Learning Check 1) 15.0%(m/m) Na2CO3 2) 6.38%(m/m) Na2CO3
A solution is prepared with 15.0 g of Na2CO3 and 235 g of H2O. What is the mass percent (m/m) of the solution? 1) 15.0%(m/m) Na2CO3 2) 6.38%(m/m) Na2CO3 3) 6.00%(m/m) Na2CO3

Solution 3) 6.00% (m/m) Na2CO3 STEP 1 Given: 15.0 g of Na2CO3; 235 g of H2O Need: mass percent (m/m) of Na2CO3 solution STEP 2 Plan: mass percent(m/m) = g of solute x 100% g of solution Calculate mass of solution = g g = 250 g of Na2CO3 solution

Solution (continued) STEP 3 Write equalities and conversion factors:
15.0 g of Na2CO3 = 250 g of solution 15.0 g Na2CO3 and g solution 250 g solution g of Na2CO3 STEP 4 Set up problem: mass = g Na2CO3 x 100 = 6.00%(m/m) Na2CO3 percent g solution (m/m)

Volume Percent The volume percent (v/v) is
percent by volume of solute (liquid) in a solution volume % (v/v) = volume of solute x 100% volume of solution volume solute (mL) in 100 mL of solution. volume % (v/v) = mL of solute 100. mL of solution

Mass/Volume Percent The mass/volume percent (m/v) is
mass/volume % (m/v) = grams (g) of solute x 100% volume(mL) of solution mass of solute(g) in 100 mL solution = g of solute mL of solution

Preparation of a Solution: Mass/Volume Percent

Percent Conversion Factors
Two conversion factors can be written for each type of percent concentration.

Learning Check Write two conversion factors for each solution:
A % (m/m) NaOH B % (v/v) ethanol C. 4.8% (m/v) HCl

Solution A. 8.50% (m/m) NaOH 8.50 g NaOH and 100 g solution
100 g solution g NaOH B % (v/v) ethanol 5.75 mL ethanol and mL solution 100 mL solution mL ethanol C. 4.8% (m/v) HCl 4.8 g HCl and mL HCl 100 mL solution g HCl

Guide to Using Concentration to Calculate Mass or Volume

Example of Using Percent Concentration (m/m) Factors
How many grams of NaCl are needed to prepare 225 g of a 10.0% (m/m) NaCl solution? STEP 1 Given: 225 g of solution; 10.0% (m/m) NaCl Need: g of NaCl (solute) STEP 2 Plan: g of solution g of NaCl 17

Solution STEP 3 Write equalities and conversion factors:
10.0 g of NaCl = 100 g of NaCl solution 10.0 g NaCl and 100 g NaCl solution 100 g NaCl solution g NaCl STEP 4 Set up problem to cancel grams of solution: 225 g NaCl solution x g NaCl = 22.5 g of NaCl g NaCl solution

Learning Check 1) 10.5 g of NaOH 2) 75.0 g of NaOH 3) 536 g of NaOH
How many grams of NaOH are needed to prepare g of 14.0% (m/m) NaOH solution? 1) g of NaOH 2) g of NaOH 3) 536 g of NaOH

Solution STEP 1 Given: 75.0 g of NaOH solution;
14.0% (m/m) NaOH solution Need: g of NaOH (solute) STEP 2 g of solution g of NaOH STEP 3 Write equalities and conversion factors: 14.0 g of NaOH = 100 of NaOH solution 14.0 g NaOH and 100 g NaOH solution 100 g NaOH solution g NaOH STEP 4 Set up problem to cancel the grams of solution: 75.0 g NaOH solution x g NaOH = 10.5 g of NaOH g NaOH solution

Learning Check 1) 2.56 mL 2) 12.9 mL 3) 39.1 mL
How many milliliters of a 5.75% (v/v) ethanol solution can be prepared from 2.25 mL of ethanol? 1) mL 2) mL 3) mL

Solution STEP 1 Given: 2.25 mL of ethanol (solute)
5.75% (v/v) ethanol solution Need: mL of ethanol solution STEP 2 Plan: mL of ethanol mL of solution STEP 3 Write equalities and conversion factors: 100 mL of solution = 5.75 mL of ethanol 5.75 mL ethanol and mL solution 100 mL solution mL ethanol STEP 4 Set up problem to cancel the mL of ethanol: 2.25 mL ethanol x 100 mL solution = mL of solution mL ethanol

Example Using Percent Concentration (m/v) Factors
How many mL of a 4.20% (m/v) will contain 3.15 g KCl? STEP 1 Given: g of KCl (solute) 4.20% (m/v) KCl solution Need: mL of KCl solution STEP 2 Plan: g of KCl mL of KCl solution 23

Using Percent Concentration(m/v) Factors (continued)
STEP 3 Write equalities and conversion factors: 4.20 g KCl = 100 mL of KCl solution 4.20 g KCl and mL KCl solution 100 mL KCl solution g KCl STEP 4 Set up the problem: 3.15 g KCl x 100 mL KCl solution = mL of KCl g KCl

Learning Check How many grams of NaOH are needed to prepare 125
mL of a 8.80% (m/v) NaOH solution? 1) g of NaOH 2) g of NaOH 3) g of NaOH

Solution 2) 11.0 g of NaOH STEP 1 Given: 125 mL of NaOH (solution)
8.80% (m/v) NaOH solution Need: g of NaOH (solute) STEP 2 Plan: mL of NaOH solution g of NaOH

Solution (continued) STEP 3 Write equality and conversion factors:
8.80 g of NaOH = 100 mL of NaOH solution 8.80 g NaOH and 100 mL NaOH solution 100 mL NaOH solution g NaOH STEP 4 Set up the problem: 125 mL NaOH solution x g NaOH 100 mL NaOH solution = 11.0 g of NaOH

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