Determining the Specific Gravity of a Mineral
Last Updated: 9th Jan 2018By Donald B Peck
Osmium probably has the highest Specific Gravity among minerals approved by the IMA. Ice probably has the lowest.
The Specific Gravity as a property of minerals is often overlooked by amateur collectors, probably because it is considered to be too difficult. . . and that is a mistake. It is one of the most definitive properties of a mineral. With inexpensive electronic balances that are available today and simple calculators the means of determining the specific gravity of that unknown mineral collected last weekend is within reach.
Just What Is Specific Gravity
The Specific Gravity of an object is the ratio of the density of the object to the density of water. Density is the ratio of the mass of the material to the volume it occupies, usually determined in grams/centimeter cubed. Since Specific Gravity is the ratio of two densities, considering only the units, we have (g/cm^{3})/(g/cm^{3}). Mathematically the units divide out leaving us with a value of 1 (one). Numerically for a given substance, density and specific gravity are equal; but having no units, specific gravity is often easier with which to work.
Methods of Determination
There are two distinctly different methods of determining a specific gravity (Sp.G.). One uses heavy liquids that are mixed until a fragment of the unknown mineral exhibits neutral buoyancy in the solution, not sinking nor rising. The liquids are both expensive and toxic. Further, a Westphal Balance, or something similar, is required to measure the resulting density of the solution. Due to the expense, the hazard (although minimal), and the specialized instruments required, this is an operation to be used only in professional laboratories.
The second method employs some sort of balance to measure the mass of the mineral fragment in air and again in water. From the two values, the Sp.G. is calculated. Balances vary widely from modern day electronic balances to chemists analytical balances, from Jolly spring scales to home shop built wooden balances. But whatever the type of balance, the principles of use are the same.
There is a third method, a variation on the second, that uses a small volumetric flask, called a pycnometer. It is employed for very small specimens or grains. It involves four weighings on an analytical balance: empty, containing water, containing the sample, and containing the sample and water. Generally, it requires an analyst trained, and practiced, in its use.
This article will concentrate on the use of an electronic balance.
Tools You Will Need
Before choosing an electronic balance, you need to know the approximate mass of the samples you will be working with. If your samples are likely to be larger than about 100 grams you will want a balance with a precision of 0.01 grams. For smaller samples, you will need a precision of 0.001 grams. Such balances are available on eBay for well under $100 US. You will need a scientific calculator. There is almost certainly one on your computer. After that, a small plastic cup, a spool of silk or polyester thread, and a jar for water.
Selecting Specimens
Each specimen for a Sp.G. determination should be pure. It should not include other minerals. But how does one know? In reality, unless the sample is transparent, one does not know. Small pieces are less likely than large pieces to contain another mineral. So the best approach is to choose small pieces where grains of another mineral do not show on the exterior surfaces.
If possible, choose several pieces that are about the size of a small bean. Since every measurement will include experimental errors, it is best to take measurements of several pieces and average the results. The average is your best estimate of the true value. Three to seven determinations are good . . .the more the better.
Collecting Data
You need two quantities to calculate the Sp.G. of your unknown mineral: the mass of the sample, and its volume.
1. The day before, mix a drop or two of liquid detergent into about a half liter of water and set it aside so it comes to room temperature. The detergent is a wetting agent that discourages bubbles from adhering to the mineral sample or thread.
2. Make certain your balance is stable, level, and reading zero.
3. Each sample must be dry and at room temperature. Determine the mass of each being careful to record the result and keep it with its respective sample.
4. Tie a 20 or 30 cm length of silk or polyester thread to each specimen. (Silk and polyester do not absorb water.)
5. Place a small cup of water (room temperature) on your balance and Tare it (this returns the scale to zero, as though the cup and water were not there). The cup need be only large enough that you can lower the largest sample into the water without the sample touching the sides or bottom of the cup.
6. In turn, lower each sample into the water, such that it is completely submerged and does not touch the sides or the bottom of the cup. Try to check that there are no air bubbles attached to it. For each sample: record the mass registered on the scale. It is important to Tare the cup and water between samples to compensate for any water you may have removed. The value that you record for each sample is the mass of the volume of water displaced by the sample. Since one gram of water has a volume of one centimeter cubed, the number obtained is also the volume of the displaced water, which equals the volume of your sample.
If There Is Only a Single Sample
Sometimes there is only one small sample available. The best approach then is to do repeat determinations at long intervals so the sample has adequate time to dry. Usually, 24 hour intervals work. If you notice a significant increase in the mass of the first weighing, the sample is not dry. There should be near consistency across successive measurements. Repeat at least three times . . . more is better.
Calculations
Sp.G. = Density_{Sample}/Density_{Water} = mass of the mineral sample in air / volume of the mineral sample/ 1 g/cm^{3}
Calculate the Sp.G. of each of the samples that you ran by dividing the mass in air by the volume of the mineral sample. The volume of the mineral sample is equal to the volume, and the mass. of the displaced water.
The table below shows an example of the data and calculations for five samples of a mineral:
Calculations for An Unknown Mineral  

In lines 2 and 3, recall that the density of water is in g/cm^{3}, so numerically the mass equals the volume.
The Specific Gravity for minerals is customarily rounded to two decimal places.
The best estimate of the true Specific Gravity of your unknown mineral is the average Sp.G. of your samples. So sum the Sp. G. of the individual samples in Row 4 and divide by the number of samples, 5.
The average (mean) value, 4.66, is larger than that for each of the samples, except for #3. You may wish to throw out Sample #3. When is it legitimate to do that? Read on . . .
Checking the Purity of Your Sample
After you have collected all of your data and if your samples are opaque, it is a good idea to crush them and examine the results with magnification. Are there other minerals among the grains? If so, what are they? Suppose you have determined the Sp.G. of your specimens to be 4.66 and then you find grains of pyrite among the crushed residue of Sample #3. Pyrite has a Sp.G. = 6.00 to 6.50. Thus, the Sp.G. that you obtained for your unknown mineral is going to be a little high. How much too high? That will depend on the relative quantity of included pyrite. But, you know that the mineral you are working with has a Sp.G. a little less then 4.66. In any case, if you find other minerals, they will have affected your results.
Let us suppose that you found a little pyrite in Samples #3. If we eliminate that sample, we still have four samples remaining. A new Avg. SpG. = 4.63
How Large Is The Error of Measurement
(You can skip this, but it is useful)
We are going to use a little statistics and calculate what is known as the Standard Error of the Mean. Don't worry, it is not as difficult as it sounds . . . as long as we have a calculator. The following is assuming we eliminated Sample 3 due to the inclusion of pyrite.
Calculating the Standard Error: 4 Samples  

Row 1 is a list of the Sp.G.s of the individual samples, and the Average of the group.
Row 2 is the difference between the Avg, Sp.G. and each individual Sp.G. (+ or  is not relevant)
Row 3 is the square of the values in Row 2, followed by the sum of the squared differences.
Next, divide the sum of squares by the number of samples less one (3). 0.0003/3 = 0.0001
Take its square root: = 0.01. The Standard Error of the Mean is 0.01
You have a mean Specific Gravity = 4.63. When you search tables or a data bank it may be unlikely that you are looking for a value of exactly 4.63. By how much should you pad the value, both above and below to find your unknown. Standard Error to the rescue! You can be 95% certain that the mineral you are seeking has a Sp.G. = 4.63 + or  twice the Standard Error of the Mean. So search values between 4.61 and 4.65. However, your best bet is still 4.63.
The Standard Error of the Mean can be used in another way, too. Suppose you had not thrown out Sample #3 due to the included pyrite and you calculated the Standard Error. If the Sp.G. of Sample #3 differs by more than twice the Sp.G. #3 + or  the Standard Error, then you can be 95% certain that that value is in error and can be discarded. In this particular case with the values given above, the Sp.G, of Sample #3 falls just inside the limits and should not be discarded.
Calculating the Standard Error: 5 Samples  

Divide the sum of squares by 4 = 0.0034 and take its square root = 0.06 .
Twice 0.06 = 0.12 and the difference between the Avg Sp.G. and the Sp.G. of Sample #3 is 0.10.
Since 0.12 is greater than 0.10, on statistical grounds alone, Sample #3 should not be discarded. Statistically it is considered to be within the limits of probability.
Should Sample #3 have been discarded? Yes. We know from examination of the crushed grains that it contained pyrite, unlike the other four samples. Further, we know that the pyrite elevated the value of the Sp.G. and there was no need to calculate the Standard Error with the Sp.G. of Sample #3 included. The calculation of the Standard Error for five samples, above, was simply it illustrate its use in excluding data points that are probably outside the set.
Corrections for Temperature
Recall that Specific Gravity is the ratio of the density of a substance to the density of water. The density of water varies less than 1.5 mg/cm^{3} over the narrow range of normal temperatures. Between 20^{o}C and 25^{o}C the density of water is essentially 1 g/cm^{3}. The volume expansion of the solid mineral is insignificant. Unless one is working with specimens with a mass less than 1 g (1000 mg) it usually is not necessary to make a correction for temperature. However, should you be working with tiny samples, a simple approach is to boil and cool your water to room temperature (to drive out dissolved air), carefully determine the temperature of the water, find the density of the water in the table below, and divide your calculated average Sp.G, by that density.
Temperature Vs Density of Water  

References
https://en.wikipedia.org/wiki/Specific_gravity  Wikipedia, Specific Gravity.
https://en.wikipedia.org/wiki/Density  Wikipedia, Density.
https://en.wikipedia.org/wiki/Standard_error  Wikipedia, Standard Error.
Dana, Edward Salisbury, Ford, William E.  Editor (1991) A Textbook of Mineralogy. John Wiley & Sons, Inc., New York
Peck, Donald B. (2007) Mineral Identification: A Practical Guide for the Amateur Mineralogist. Mineralogical Record, Tucson, Arizona. 2122.
Pough, Frederick H, (1996) A Field Guide to Rocks and Minerals. Houghton Mifflin Company, Boston. 303.
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Comments
I measure specific gravity by the same way, with a few slight changes. I boil the water and allow it to cool before using it. This eliminates dissolved air, which prevents bubble formation. Instead of using thread to tie the sample I use very thin copper wire, which can be simply twisted on. It is a lot easier to put on than thread.
Howard Heitner
3rd Jan 2018 2:59am
Howard Heitner
3rd Jan 2018 2:59am
Hello Howard,
Thank you for your comment, I agree with you that copper wire is easier to fasten around a mineral sample than is thread. But I choose to go with the thread in this article, because I am afraid that the reader may use a heavier gauge of wire and thus obtain a SpG that is too low. In the Help Identify forum about 3 or 4 months ago, one collector posted a photo of how he did it. The copper wire was wrapped about three times around his sample and was probably about 16 gauge. He had enough copper to substantially affect his result. 24 to 28 gauge wire probably would be fine, however.
Don
Donald B Peck
3rd Jan 2018 3:35am
Thank you for your comment, I agree with you that copper wire is easier to fasten around a mineral sample than is thread. But I choose to go with the thread in this article, because I am afraid that the reader may use a heavier gauge of wire and thus obtain a SpG that is too low. In the Help Identify forum about 3 or 4 months ago, one collector posted a photo of how he did it. The copper wire was wrapped about three times around his sample and was probably about 16 gauge. He had enough copper to substantially affect his result. 24 to 28 gauge wire probably would be fine, however.
Don
Donald B Peck
3rd Jan 2018 3:35am
Thank you for this article, and the one on hardness  they are both excellent and easy to follow!
Becky Coulson
6th Jan 2018 9:41am
Becky Coulson
6th Jan 2018 9:41am
Becky and Paul, thank you for your very kind comments. I like to write, and at 87 years of age I cannot stop teaching.
Don
Donald B Peck
6th Jan 2018 5:23pm
Don
Donald B Peck
6th Jan 2018 5:23pm
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