The kit consists of a weighing frame which replaces the weigh pan and adapter, a sinker (the pan that hold the unknown sample), a 400ml beaker, a frame that supports the weight of the beaker (with its fluid, bracket, and thermometer) and passes the weight to the frame of the scale (not the weigh frame). This apparatus will be used to measure the weight of the sample in air, called the dry weight (Wd), and to determine the weight of the same sample immersed completely in a fluid, called the wet weight (Ww).  The difference between these two (Wd-Ww) is the buoyancy of the sample in the fluid.

It is important to discuss some of the factors which affect the accuracy of density measurements using this technique:

1.    The density of the fluid causing buoyancy changes with temperature.
2.    The change in the immersion level of the pan hanging assembly when the sample displaces fluid.
3.    The air buoyancy caused by weighing in air.
4.    Liquid adhesion on the suspension wire of the pan hanging assembly.
5.    Air bubbles on the surface of the sample.

Item 1. This item is compensated for by the spreadsheet (using a built in table) when the user enters the fluid temperature to the nearest 0.1 C as measures by the thermometer during the measurement.

Item 2. This effect can be determined from the ratio of the diameters of the suspension wire and the beaker.  The use of a beaker with a large inner diameter helps to reduce this effect.  The spreadsheet uses a factor determined by the 400ml beaker and the furnished suspension wire.  If either of these is changed in diameter the calculation will be affected.

Item 3. The density of air at sea level, 50% humidity, and 20 C is approximately 0.0012 g/cubic cm.  This can produce a third place error in density measurements and should be compensated for in the calculation.  The spreadsheet uses this 0.0012 g/cubic cm in its calculations in order to correct for air buoyancy.

Item 4. This effect is largely self canceling since the Sinker (sample holding pan) is immersed for both dry weight and wet weight measurements and the balance is tared at the beginning of each measurement.  This effect can also be reduced by adding a drop or two of ordinary non-staining dishwasher detergent to the fluid to minimize the meniscus effect.  The spreadsheet ignores this effect.  
   
Item 5. Air bubbles can have a significant effect on density measurements.  They can be brushed off, or the sample can be pre-soaked to eliminate them.  The spreadsheet has no way to correct for this problem, and the user must be diligent in this area.

    In its simplest form the equation for density as performed this way is:
                                  
    D =  [ Wd / ( Wd – Ww ) ] x Dw,  where Dw = density of water

    In its final spreadsheet form it looks like this:

    D = [ Wd x (Dw – Dair)] / [ Kimmersion x ( Wd – Ww ) ] +  Dair],  where Dw is temp corrected

Note:  Wd – Ww = Buoyancy (G), its use can simplify the expressions somewhat.
        



MAKING THE MEASUREMENTS

Determining the Density (Specific Gravity) of Solids with density >1.  

Be sure that the sinker and suspension wire have been cleaned before starting.   Distilled water will be used as the fluid.  Two drops of dishwasher detergent may be added to reduce meniscus effects for optimal results.  Center the 400ml beaker on the beaker support frame so that it is centered under the suspension wire for the sinker (sample holder assembly).  Attach the thermometer to the retaining bracket and place in the beaker.  Fill the beaker to the 400ml level.
 
Determining Wd (Dry Weight)

       1.  Tare the balance
       2.  Place the sample on the upper frame pan (not the Sinker).
       3.  Record the result (Wd)

Determining Ww (Wet Weight)

1.    Tare the balance
2.    Place the sample on the Sinker (wet sample holder).  Best done with forceps.
3.    Record the result (Ww)

Determining the Temperature

1.    Read the temperature from the thermometer to the nearest 0.1 C
2.    Record the result

Calculating the Density

1.    Enter the 2 or 3 values recorded above into the appropriate cells in Torbal Density Calculator spreadsheet running in Excel on a standard PC, or
2.    Use the spreadsheet formula furnished above where Dw must be obtained from a table, Dair can be approximated at 0.0012 g/cubic cm, and Kimmersion = 0.99989 for the 400ml beaker.  Remember that Buoyancy = Wd - Ww


Determining the Density (Specific Gravity) of Solids with density <1.

    Same as above, only when determining the Ww place the sample under the Sinker (wet sample holder).  This is the application where the name “Sinker” makes sense.  If the Sinker is not heavy enough to hold the sample down simply add weight to the Sinker pan and start over from the beginning.

Determining the Density of fluids

Determining the volume of the Sinker (this need only be done once)

1.    With the beaker empty and the Sinker in place on the support wire, Tare the balance.
2.    Fill the beaker with distilled water to the 400ml level.
3.    Record the negative weight reading (which equals the buoyancy of the sinker and the small piece of support wire which is immersed).
4.    Record the fluid temperature to the nearest 0,1 C

Calculating the volume

1.    Enter the two values into the top portion of the spreadsheet where the Sinker volume is calculated, or
2.    Use the formula;  Volume in cubic cm = Buoyancy in g / Density in g/cubic cm

Determining the buoyancy of the Sinker in the unknown fluid

1.    Repeat the 4 steps used to determine the Sinker volume above, but replace the distilled water with the fluid whose density is to be determined.

Calculating the fluid density

1.    Enter the two values into the Fluid Density portion of the spreadsheet where the Fluid Density is calculated, or
2.    Use the formula;  Density in g/cubic cm = Volume in cubic cm / Buoyancy in g