Solutions to Density Problems

Solutions to Density Problems

Density = mass
                 volume

1)  What is the volume of a tank that can hold 18 754 Kg of methanol whose density is 0.788g/cm³?

       D = m/v    
       v = m/D

       v = [18754 Kg][10³ g][      cm³]
                               [ 1 Kg][0.788 g]

       v = 2.38 x 10⁷ cm³

2) What is the density of a board whose dimensions are 5.54 cm x 10.6 cm X 199 cm and whose
     mass is 28.6 Kg?

     D = m/v
     D = [28.6 Kg][10³ g]                                              
                           [ 1 Kg][5.54cm x 10.6 cm x 199 cm]

     D = [28.6 Kg][10³ g]                     
                           [ 1 Kg][11686 cm³]

     D = 2.45 g   
                    cm³

3) CaCl₂ is used as a de-icer on roads in the winter. It has a density of 2.50 g/cm³. What is the
     mass of 15.0 L this substance?

     D = m/v
     m = Dv

     m = [2.50 g][15.0 L][10³ mL][1cm³]
            [    cm³]             [   1 L   ][ 1mL]

     m = 3.75 x 10⁴ g

4) In the Macy's Thanksgiving day parade, 2000, there was a new float, the Cheerios' bee, Buzzbee.  The
    jar of honey it was holding contained  36,763 L of helium.  The honey jar was 1/10 of the body size.
    What is the volume of the entire float?  If the density of helium is  0.000178 g/cm³, what is the mass of the 
     helium for the entire float in Kg?

     D = m/v
     m = Dv

     v = 36,763 L He x 10
        = 367,630 L He

     m = [0.000178 g][367,630 L][10³ mL][1cm³][ 1 Kg]
            [            cm³]                  [   1 L   ][ 1mL ][10³ g]

     m = 65.4 Kg

5) My gas tank in my car has a total volume of 68 L.  The manual says the gas gauge light will come on
     when there are only 5 L remaining in the tank and that the car will not be able to draw on the last 2 L
     in the tank.  Practically speaking, what is the functional volume of the gas tank?  If I ran out of gas, the
     car won't go,  and I put in 5 L of gas, what is the total volume of gas in my tank?  If 5 L of gas has a mass of
     450 Kg, what is the mass of the gas in my tank?  What is the density of the gas?

     D = m/v

     functional volume of tank is 68L - 2 L = 66 L  gas

     "empty tank" + 5 L = 7 L gas

      m = [7 L][450 Kg]
                     [     5  L]
      m = 630 Kg

     D = [630  Kg][10³ g]        [     1 L ][  1 mL]
                           [ 1 Kg][7 L][10³ mL][1 [cm³]

     D = 630 g  
               7 cm³

     D = 9.0 x 10¹ g  
                           cm³