Torbal DK1 Density Determination Guide - Manual

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Density Determination Guide
The Torbal Density Determination Kit (DDK) is designed to allow Torbal AD Series Precision
Balances to be used to determine the density of solids and fluids using Archimedes principle in a way
that eliminates the need for below the pan weighing. Torbal also makes available an Excel spreadsheet
which makes the calculations required for density determinations. Embedded in this spreadsheet is a
table of water density versus temperature from 15 C to 27 C in 0.1 C increments.
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.
Torbal Density Kit