Chemistry and the Aquarium: Specific Gravity: Oh How Complicated!
Welcome to the surprisingly complicated world of specific gravity!
One question that every marine aquarist faces is the amount of salt to add to the tank. Most beginning texts choose to describe the salinity in terms of specific gravity, and go on to relate how one measures it with a hydrometer. While not nearly as precise as measuring salinity with a conductivity probe or a refractometer, hydrometers are chosen by many because they are inexpensive and easy to use. For many aquarium purposes, they are perfectly adequate.
Unfortunately, measurements of specific gravity are far more
complicated than most hobbyists recognize. Additionally, there
has been a great deal of misinformation provided about how
salinity relates to specific gravity and hydrometer readings, and
how such values vary with temperature. This article will endeavor
to make these relationships clear.
What I won't address in this article is the question of what salinity values are "optimal" for keeping marine aquaria. That has been addressed in previous articles, such as this article by Ron Shimek.
One further point on salinity: in this article, as in the chemical oceanography literature, the salinity of seawater is now defined as a dimensionless unit, S. In older literature it has the units of ppt (parts per thousand by weight), and that is roughly the way to think of it, but it is now defined as the ratio of the seawater conductivity to that of a potassium chloride solution of defined composition. Consequently, seawater has S=35 (or some similar number). Other solutions, like simple sodium chloride, are not defined in this way, and are still reported as ppt. This definition of salinity is described in detail in "Chemical Oceanography" by Frank Millero (1996).
What is specific gravity?
Specific gravity is defined as the ratio of the density of a liquid compared to the density of pure water. Since the density of pure water varies with temperature, one needs to specify the temperature of the pure water to usefully define specific gravity. For many scientific endeavors (such as mineralogy), the temperature standard chosen is 3.98 °C (39.2 °F; defined as the temperature of maximum density of pure water). At that temperature, the density of pure water is 1.0000 g/cm3. If this is the standard chosen, it is easy to see that the specific gravity is just the density of the sample at 3.98 °C when measured in g/cm3 (without any units since specific gravity is a unitless measure).
Why is specific gravity useful to aquarists? Primarily because it is a simple and quantitative way to tell how much of something is in water. If things less dense than water are dissolved in it, then the specific gravity will drop. Ethanol, for example, is less dense than water, and makes the specific gravity drop. This fact is used by brewers to gauge the amount of alcohol in their brews.
Likewise, if things denser than water are dissolved in it, the specific gravity goes up. Nearly all inorganic salts are denser than water, so dissolving them in water makes the specific gravity rise. This rise can be used by aquarists to gauge how much salt is in their water. Of course, it cannot tell you what is in the water, but if you are using an appropriate salt mix, it can tell you how much is there and whether it approximates natural seawater or not.
How Do Standard Hydrometers Measure Specific Gravity?
Standard hydrometers work on Archimedes Principle. This principle states that the weight of a hydrometer (or other object, like an iceberg or a ship) equals the weight of the fluid that it displaces. Consequently, the hydrometer will sink until it displaces its own weight. When it is put into solutions of different densities, it floats higher or lower, until it just displaces its own weight. In denser fluids it floats higher (displacing less fluid) and in less dense fluids it floats lower. In essence, this principle is a reflection of the fact that the gravitational potential energy of the system is minimized when the hydrometer just displaces it's own weight. Any different displacement puts forces on the water and hydrometer that cause them to move toward the optimal position.
Swing Arm Hydrometers
Swing arm hydrometers are a bit different since none of the arm is above the water line. In this case, the swing arm responds to the density difference by rotating an arm with nonuniform weight distribution. Typical hobby swing arm hydrometers use an arm made of two different materials (Figure 2). The density difference between the water and one of the materials forces the arm to swing in one direction, and the density difference between the water and second of the materials forces the arm to swing in the opposite direction. At the equilibrium position these forces cancel out, and the hydrometer gives a steady reading. Again, the final result is a minimization of the gravitational potential energy of the system.
Do Ion Imbalances Impact Specific Gravity?
One question often asked is whether changes in various ions impact specific gravity. The answer is that, to a hobbyist using a normal salt mix, they do not. To get a ballpark understanding of this effect, it is reasonable to assume that all ions contribute to specific gravity in an amount proportional to their weight percentage in seawater. For example, I looked up the specific gravity of 15 different inorganic salts at the same "salinity" (100 ppt at 20 °C). All were very similar, with less than a factor of two difference between the highest (zinc sulfate, specific gravity = 1.1091 g/cm3) and the lowest (lithium chloride; specific gravity = 1.0579).
In a sense, the more of any ion that is present regardless of chemical nature, the larger is the effect on specific gravity. Since that's exactly what salinity is (the weight of solids in the water), it is unlikely that any normal ion variation seen by marine aquarists will unduly skew specific gravity measurements. Since the top 4 ions in seawater (Na+, Mg++, Cl-, SO4--) comprise 97 weight percent of the total, any changes in other ions will have no significant impact on specific gravity.
What about changes in these top four ions? Let's take an extreme case where the salt consists of nothing but sodium chloride. It turns out that a 37 ppt solution of sodium chloride has the same specific gravity as S = 35 seawater. Thus, one can see that even big changes in the ionic balance result in fairly small changes in the relationship between specific gravity and salinity. For these reasons, it is safe for most aquarists to ignore any impact that differences in the ionic constituents would have on the relationship between specific gravity and salinity. Of course, if one has a grossly inaccurate seawater mix (consisting of just potassium bromide or magnesium sulfate, for example) then the relationship between specific gravity and salinity that is assumed for seawater will be broken. A pure potassium bromide solution with the same specific gravity as natural seawater (S = 35), for example, has a "salinity" of about 36 ppt. A similar pure magnesium sulfate solution has a "salinity" of only 26 ppt.
Temperature of the Standard
Unfortunately, the world of specific gravity is not as simple as described above. Different fields have apparently chosen different standard temperatures. In addition to the 3.98 °C standard, others include 20 ° C (68 °F) and 60 °F (15.6 °C). A quick look through several laboratory supply catalogs shows many examples of hydrometers using each of these two, and a few odd ones thrown in for good measure (such as 102 °F for milk). Most authors writing about marine aquaria assume that people are using the 60 °F standard, but in reality many aquarists are not, and in some cases they don't even know what they are using. Some hobby hydrometers use other standards, with 77 °F being quite popular (used by Tropic Marin, for example).
The density of pure water at 20 °C is 0.998206 g/cm3, and at 60 °F it is 0.9990247 g/cm3. While these seem close to 1, and are often simply claimed to be 1.00 in many contexts, the difference can be substantial. For example, the specific gravity of natural seawater (S =35) is 1.0278 using the 3.98 °C standard, 1.0269 using the 60 °F standard, 1.0266 using the 20 °C standard, and 1.0264 using the 77 °F standard. [I calculated these based on tables of the density of seawater, different tables may present slightly different densities that might then result in slightly different specific gravities]. While these differences are small, they are real. They arise because the density of pure water and seawater change in slightly different ways with temperature. Seawater becomes less dense faster than pure water as the temperature rises. This effect may relate to the interactions between ions and between ions and water in seawater that are broken up as the temperature rises, but that's beyond the scope of this article.
Unfortunately, it has been my experience that many aquarists quoting a specific gravity measurement for their tanks do not know what standard is being used by their hydrometer. Most quality lab hydrometers will have the standard used written on them or their supporting documents. Some hobby hydrometers, however, make no mention of the standard used. Note that there is NO "correction" table that can convert readings at temperatures other than the standard temperature unless you know the standard temperature. If you don't know it, using such a table will not give accurate values, and may give a value farther from the truth than the uncorrected reading.
Temperature of the Sample
As if the confusion about the temperature of the standard were not enough, the temperature of the sample is also a variable. Many quality lab hydrometers also have the expected sample temperature indicated directly on them. This is referred to as the "reference" temperature. In a great many cases (though not all), the standard temperature and the reference temperature are the same: either 60 °F or 20 °C. This is often written as "60 °F/60 °F", though it is sometimes written simply as "Temperature of Standardization: 60 °F". If a hydrometer is used at the reference temperature, no special corrections are necessary (though the answer one gets will depend a bit on the standard temperature chosen by the manufacturer as described above).
Why does the temperature of the sample matter? There are two reasons. One is that the hydrometer itself may change its density as a function of temperature, and thus give incorrect readings at any temperature except that for which it is specifically designed (i.e., it floats higher or lower as its density changes). Unfortunately, unless you have a table for your specific hydrometer (which is rarely supplied), this effect cannot be corrected by a table because of the different materials of construction of hydrometers. Various types of glass and plastic are used for hydrometers, and each will have it own particular change in density as a function of temperature. It should be noted that this effect is substantially smaller for glass hydrometers than the second effect described below because the change in density of glass with temperature is 8-25 times smaller than the change in density of aqueous fluids.
The second reason that the sample temperature is important is
that the sample itself will change its density as a function of
temperature. For example, the density of seawater (S = 35)
changes from 1.028 g/cm3 at 3.98 °C to 1.025 g/cm3 at 20 °C to
1.023 g/cm3 at a typical marine aquarium temperature of 80 °F.
Since the density of the sample is changing with temperature, the
measured specific gravity will also change, unless this is taken
The impact of temperature on the density of the sample can be corrected in a table, assuming that one knows how the density of the sample would change with temperature (which is well known for seawater), and also that one knows the temperature of standardization of the hydrometer. For example, if you have a hydrometer calibrated for 60 °F/60 °F, then you will be correcting for the difference in density between the sample at 60 °F, and the temperature at which you measured it. If the actual sample were measured at 86 °F, then the correction is the ratio of the density of seawater at 86 °F (approximately 1.0217 g/cm3) divided by the density at 60 °F (approximately 1.0259 g/cm3), or 0.996. Thus a specific gravity reading, or more correctly, a hydrometer reading, of 1.023 would be corrected to an "actual" reading of 1.027.
Again, if you do not know the temperature of standardization, you are out of luck, and a correction using a table is as likely to cause bigger errors, as it is to correct any. Likewise, using a "correction" table that does not specify what it is intended to correct is equally risky.
Some marine hobby hydrometers claim to be accurate at all temperatures (68 - 85 °F; these include SeaTest, Deep Six, and eSHa Marinomat). Such a device can be designed, if its change in density as a function of temperature were exactly the same as seawater at all temperatures. Two of these tested below (the SeaTest and the Deep Six) do a fair job of temperature correction, but in fact slightly overcorrect.
How precise is salinity determined via specific gravity? If one measures specific gravity to 2 significant figures, then the uncertainty in the salinity is ± 0.7 (assuming that the specific gravity is correctly and accurately measured). For example, if the specific gravity were 1.027 (assuming the uncertainty of ± 0.0005 implied by 2 significant figures), then the corresponding salinity will be 35.2 ± 0.7. Similarly, a specific gravity of 1.023 corresponds to a salinity of 30 ± 0.7. Of course, more precise measurements of specific gravity will yield more precise salinity values, and a factor of 2-5 can likely be picked up using a high precision hydrometer.
Of the three hobby hydrometers examined, all were fairly
precise by hobbyist standards. There was no difficulty
reproducibly reading any of them to a salinity of ± 0.5 or better
(Figure 3). This is not to say, however, that the devices were
Accuracy, of course, is not the same as precision. Precision can be represented by significant figures, and the measured value of 1.025763 is far more precise than 1.026. However, if the actual specific gravity of the fluid were 1.0261000000, then the second reading is much more accurate (i.e., closer to the real value) than the first.
So how do these hydrometers measure up? In my tank the water was measured to be S=35 ± 0.5 by conductivity. Using the Deep Six swing arm hydrometer I got readings of S=32.5 ± 0.5 at 81 °F and S=32 ± 0.5 at 68 °F. Using the SeaTest I got S=34.5 ± 0.5 at 81 °F and S=34 ± 0.5 at 68 °F.
For the standard type Tropic Marin hydrometer, I got a 77 °F/ 77 °F specific gravity of about 1.0265 ± 0.0003 (Figure 4), which compares well to the expected value of 1.0264.
How to Use a Standard Hydrometer
Beyond those issues already described, here are a few tips in using a hydrometer:
- Make sure that the hydrometer is completely clean (no salt deposits) and that the part of the hydrometer above the water line is dry. Tossing it in so it sinks deeply and then bobs to the surface will leave water on the exposed part that will weigh down the hydrometer and give a falsely low specific gravity reading. Salt deposits above the water line will have the same effect. If any deposits won't easily dissolve, try washing in dilute acid (such as vinegar or dilute muriatic acid)
- Make sure that there are no air bubbles attached to the hydrometer. These will help buoy the hydrometer and yield a falsely high specific gravity reading.
- Make sure that the hydrometer is at the same temperature as the water (and preferably the air).
- Read the hydrometer at the plane of the water surface, not along the meniscus (Figure 4; the meniscus is the lip of water that either rises up along the shaft of the hydrometer, or curves down into the water, depending on the hydrophobicity of the hydrometer).
- Rinse with freshwater after use to reduce deposits.
- Do not leave the hydrometer floating around the tank between uses. If you do, difficult to remove deposits may form over time.
How to Use a Swing Arm Hydrometer
In addition to those described above, here are some special tips for swing arm hydrometers:
- Make sure that the hydrometer is completely level. A slight tilt to either side will change the reading.
- The Deep Six hydrometer recommends "seasoning" the needle by filling it with water for 24 h prior to use. Presumably this permits the water absorbed into the plastic to reach equilibrium. In the case of the hydrometer tested in this paper, the reading became slightly less accurate after seasoning.
If nothing more, I hope this article alerts aquarists to some of the issues behind the use of hydrometers and specific gravity for measuring salinity. For those interested in additional discussion of hydrometers and how they relate to specific gravity and salinity, there is a nice discussion in Stephen Spotte's "Captive Seawater Fishes", along with a chart for correcting 60 °F/60 °F specific gravity measurements made at other temperatures.