Concentration of Solution Sample Problems

A. Percent by Mass Sample Problems

     1.  What is percent by mass concentration of 12.5 g of NaCl dissolved in 200 g of water?

          Identify the given:   mass solute = 12.5 g NaCl
                                       mass solvent = 200 g water

          The problem is asking the percentage by mass of NaCl given the mass of solute and the mass of solution.  You have to take note that the mass of the solution is equal to the mass of solute + the mass of solvent.

          Formula:   

 

          Solution:

 

 

     2.   Calculate the percentage by mass of 30 g of KCl in 250 g of solution.

          Find the given:    mass of solute = 30 g KCl

                                    mass of solution = 250 g of solution

         Here the problem is asking to calculate the percentage by mass given the mass of the solute and the mass of the solution.

          Formula:

          Solution:

 

     3.  What is the mass of the CuSO4 present in 15% by mass 316 g of CuSO4 solution?

          

          Find the given:   Percent by mass = 15 %

                                   mass of solution =  316 g of solution

         The problem asked to calculate the mass of CuSO4, which is the solute of the solution.

          Formula : 

          Solution:
 

B. Percent by Volume Sample Problems

1.  A solution of hydrochloric acid is produced by dissolving 15 mL of HCl in enough water to make 240 mL of solution. What is the percentage composition of the solution?

     Find the given :    volume of solute = 15 mL

                                volume of solution = 240 mL

     This problem is asking the percentage  by volume of hydrochloric acid given the volume of solute and the volume of solution.

     Formula :

 

     Solution:

 

2.  Calculate the volume of alcohol present in 250 mL 70% alcohol solution and  40 % alcohol solution.

        Find the given:   volume of alcohol solution = 250 mL

                                 Percentage by Volume = 70 % and 40 %

        The problem is asking the volume of alcohol present in 70 % and 40% alcohol solution having 250 total volume of solution.  Two solutions are needed in this problem.

         Formula: 

          Solution:

     

          For 70% alcohol solution

 

          For 40% alcohol solution

 

 

     3. The average adult human body contains about 5 L of blood.  Only 0.72% consists of leukocytes (white blood cells).  What volume of leukocyte cells is present in the body of a small child, with only 2.5 L of blood?

         The given in this problem is the percent of white blood cells = 0.72% and the total volume of blood of a child blood = 2.5 L.

          The problem is asking to calculate the volume of leukocytes or the white blood cells.

         

         Formula:  

          Solution: 

C. Molarity Problems

1.  What is the molar concentration of the following solutions:

     a. 0.20 mol of NaCl in 0.25 L of solution.

     b.  5 g of sugar, C12H22O11 in 20 mL of solution.

     c.  3 g of KCl in 80 mL solution.

Formulas needed:

 

 Solutions:

     a.  Given :  mole solute = 0.20 mol

                      volume of solution = 0.25 L of solution

 

          Unit for Molarity can be mol/L or simply M.

     b.  Given:  mass of the substance = 5 g

                     volume of solution = 20 mL or 0.02 L

                     

           In this problem moles of solute should be calculated first, and needs the molar mass of sugar

    

           Molar mass of sugar = 12 (Atomic Mass of Carbon) + 22 (Atomic Mass of Hydrogen) + 11(Atomic Mass of Oxygen)

           Molar Mass of Sugar = 12(12) +22(1) + 11(16)

                                            =  144 + 22 + 176

                                            =  342 g/mol

           How to calculate mole of solute?

          Calculation of Molarity:

        

 

      c.  Given:  mass of the substance = 3 g of KCl 

                      volume of solution = 80 mL solution or 0.08 L 

          Molar mass of KCl = 1(atomic mass of K) + 1(Atomic Mass)

                                        =  1(39) + 1(35)

                                        =  39 + 35

                                        =  74 g/mol

         Calculation for mole of solute

 

         Calculation for molarity:

2.  What mass of solute is present in each of the following solutions?

      a.  400 mL of 0.05 M of  Calcium hydroxide, (Ca(OH)2) solution.

      b.  2.5 L of 1.00 M of sodium chloride, (NaCl) solution

       Solution:

      a.  Given :  Volume of solution = 400 mL or 0.4 L

                       molarity = 0.05 M or mol/L

          In this problem we need to calculate first the mole of the solute before we can calculate the mass.

        Calculating the moles of solute, formula is just rearrange:

   
         Calculating for the mass of solute, needs the molar mass of Ca(OH)2

          Molar Mass of Ca(OH)2 = 1(Atomic Mass Ca) + 2 (Atomic Mass O) + 2(atomic Mass H)

                                                 = 1(40g)  +  2(16g) + 2(1g)

                                                 =  40g + 32g + 2g

                                                  =  74 g/mol

           Calculating mass of the substance:

          

     b.  Given : volume of solution = 2.5 L
                      Molarity =  1 M of NaCl solution


         
            Before the mass can be calculated the mole of solute should be calculated first and the molar mass of the substance

            Molar Mass NaCl = 1 (23) + 1 (35)
                                         =  23 + 35
                                          =  58 g/mol

             Calculating the mole of solute:

                           

             Calculating mass of substance: