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).

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Figure

Figure 1. An orange Epicystis crucifer
anemone that has been thriving in the author’s tank at
S=35.

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.

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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.

Figure

Figure 2. A SeaTest swing arm hydrometer
made by Aquarium Systems, showing the arm made of two different
materials.

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.

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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
into account.

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.

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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.

Figure

Figure 3. The end of the swing arm of a Deep
Six hydrometer made by Coralife. It is reading S=33, and is
easily read to ± 0.5.

Precision

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
that accurate.

Accuracy

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.

Figure

Figure 4. A Tropic Marin hydrometer showing
the meniscus rising to about 1.0260, but the actual reading is
about 1.0265.

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:

  1. 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)
  2. 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.
  3. Make sure that the hydrometer is at the same temperature as
    the water (and preferably the air).
  4. 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).
  5. Rinse with freshwater after use to reduce deposits.
  6. 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:

  1. Make sure that the hydrometer is completely level. A slight
    tilt to either side will change the reading.
  2. 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.

Conclusion

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.

Category:
  Advanced Aquarist
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 Randy Holmes-Farley

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