Reef Alchemy by Randy Holmes-Farley

Temperature Corrections for Hydrometers


Salinity is one of the most important chemical parameters to monitor in reef aquaria. While there are a variety of ways to measure salinity, including using refractometers and electronic conductivity meters, hydrometers can be an accurate and inexpensive method. Unfortunately, not all hydrometers are suitably accurate, and last month's column gave a recipe for a standard solution with which to calibrate, or at least check the operation of, typical hydrometers.

In addition to such calibration issues, however, is the significant problem of temperature effects on hydrometers. This article describes how and why temperature affects some hydrometers, and not others. It also provides a table and a calculator for performing temperature corrections on one of the most common types of hydrometers used by reef aquarists.

I won't address in this article the question of what salinity values are "optimal" for keeping marine aquaria. That has been addressed previously, such as in this article by Ron Shimek.

One further point on salinity: in this article, as in the chemical oceanography literature, the salinity of seawater is frequently defined as a dimensionless unit, S (often referred to as PSU, Practical Salinity Units). In older literature, salinity was traditionally expressed as units of ppt (parts per thousand by weight), which is roughly the correct way to think of it, but it is now defined as the ratio of the seawater's conductivity to that of a potassium chloride solution of defined composition. Consequently, seawater has S=35 (or some similar number).1 Other solutions, like simple sodium chloride, are not defined in this way, and are still reported in units of ppt.

Figure 1. The SeaTest swing arm hydrometer.

Summary of Temperature Corrections

For those who already have a good understanding of how and why hydrometers are suitable for measuring salinity, or who do not care, this section provides a simple way to deal with temperature issues involving hydrometers. For those with a greater interest in understanding what is being measured and why, the subsequent sections of this article provide the necessary information.

    1. Swing Arm hydrometers (Figure 1). These types of hydrometers need no temperature correction, both by their own claim, and by some limited testing that I reported in a previous article. Whether accurate or not, the salinity values determined with such a hydrometer are fairly independent of temperature.

    2. Standard Floating hydrometers. These hydrometers generally do need a temperature correction when used at any temperature other than the one at which the hydrometer is intended to be used. What correction to use depends on the hydrometer, as indicated below.

    3. For hydrometers calibrated at 77F (such as the Tropic Marin, Figure 2), ), the correct relationship between the salinity, the measurement temperature, and the hydrometer reading can be found in Table 1 below (supplied by Johan Thelander) and in this linked calculator (written by Simon Huntington).

      For hydrometers calibrated at 15C (or 60F; a common calibration temperature for scientific hydrometers) many online tables are available.

      For those hydrometers calibrated at other temperatures, corrections are more complicated (and less accurate) since tables are not generally available. In this case, my suggestion is to add 0.00035 to the hydrometer reading for every 1ºC (or 0.00019 per 1ºF) by which the measurement temperature exceeds the calibration temperature, to get a corrected specific gravity. Likewise, subtract that amount if the temperature is below the calibration temperature.

Table 1. Click on image for larger Adobe Acrobat version.

Figure 2. The Tropic Marin floating hydrometer, showing the calibration temperature of 77°F.

What is Specific Gravity?

Specific gravity is defined as the ratio of a liquid's density to the density of pure water. Since the density of pure water varies with its temperature, the temperature of the pure water must be specified in order to usefully define specific gravity. In many scientific endeavors (such as mineralogy), the temperature standard chosen is 3.98°C (39.2°F, the temperature of pure water's maximum density). At that temperature, the density of pure water is 1.0000 g/cm3, or 1.0000g/ml. 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 chemicals less dense than water are dissolved in it, then its specific gravity will drop. Ethanol, for example, is less dense than water, and therefore lowers specific gravity. This fact is used by brewers to gauge the amount of alcohol in their brews.

Likewise, if chemicals denser than water are dissolved in it, its specific gravity rises. Nearly all inorganic salts are denser than water, so dissolving them in water raises the specific gravity. This increase can be used by aquarists to gauge how much salt is in their water. Of course, it cannot tell what is in the water, but for aquarists using an appropriate salt mix, it can tell how much is there and whether or not it approximates natural seawater.

Hydrometers

Two fundamental types of hydrometers are encountered by aquarists. The first is the standard floating hydrometer, which consists of a glass "float" that is put into the water. How high it floats in the water is an indication of the specific gravity of the solution. The second type is often called a swing arm hydrometer. It has a plastic float attached at a pivot point, and that float swings up to a certain position depending on the specific gravity of the solution.

These two types of hydrometers are different in some important aspects. In the context of this article, the most important of these differences is that swing arm hydrometers do not usually require any corrections for temperature effects over the range normally used by aquarists, while standard hydrometers often do.

How Do Standard Hydrometers Measure Specific Gravity?

Standard hydrometers work on the Archimedes Principle. which states that the weight of a hydrometer (or any other object, such as an iceberg or a ship) equals the weight of the fluid that it displaces. Consequently, the hydrometer will sink only until it has displaced its own weight. When it is put into solutions of different densities, it floats higher or lower, just displacing 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 its own weight. Any other displacement puts forces on the water and hydrometer that cause them to move toward the equilibrium position.

How Do Swing Arm Hydrometers Measure Specific Gravity?

Swing arm hydrometers are a bit different since no part of their arm is above the water line. Instead, the swing arm responds to the density differential by rotating an arm having nonuniform weight distribution. Typical hobby swing arm hydrometers use an arm made of two different materials (Figure 1). The density difference between the water and one material forces the arm to swing in one direction, and the density difference between the water and the other material forces the arm to swing in the opposite direction. At the equilibrium position these forces cancel out, and the hydrometer gives a steady reading. As with floating hydrometers, the final result is a minimization of the gravitational potential energy of the system.

Do Ion Imbalances Impact Specific Gravity?

understanding of this effect, note that it is reasonable to assume that all ions contribute to specific gravity in an amount proportional to the percentage of their weight in the 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 a difference of less than a factor of two 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 its chemical nature, the larger its effect on specific gravity. Since that's exactly what salinity is (the weight of dissolved solids in the water), it is unlikely that any normal ion variation seen by marine aquarists will unduly skew specific gravity measurements. Since the four most abundant ions in seawater (Na+, Mg+=, Cl-, SO4--) comprise 97% of the total weight, any changes in other ions will not significantly impact specific gravity.

What about changes in these four ions? Let's take an extreme case where the salt consists of nothing but sodium chloride. It turns out that a 37.1 ppt solution of sodium chloride has the same specific gravity as S = 35 seawater. Thus, we 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 the seawater mix were grossly inaccurate (consisting of only 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). Many authors writing about marine aquaria assume that hobbyists are using the 60°F standard, but in reality many are not, and probably in most cases they don't even know what they are using. Many modern hobby hydrometers use other standards, with 77°F (25°C) 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 as temperature changes. 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, many aquarists quoting a specific gravity measurement for their tanks do not know what standard their hydrometer is using. Most quality lab hydrometers will have the standard used written on them or found in 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 the standard temperature is known. If it isn't known, 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 (the standard floating type) also have the expected sample temperature indicated directly on them (Figure 2). This is referred to as the "reference" temperature. In a great many cases (although 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 measurement 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 there is a table for that specific hydrometer (which is rarely supplied), this effect cannot be corrected by a table because of the different materials of which hydrometers are constructed. Various types of glass and plastic are used, and each will have its own particular change in density as a function of temperature. It should be noted that this effect is substantially smaller for glass hydrometers than is 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.

Temperature Corrections for Standard Floating Hydrometers

For standard floating hydrometers, the impact of temperature on the density of the sample can be corrected with a table, assuming that we know how the density of the sample would change with temperature (which is well known for seawater), and also that we know the hydrometer's temperature of standardization. For example, a hydrometer calibrated at 60°F/60°F needs to be corrected for the difference in density between the sample at 60°F, and the sample at the temperature at which it is tested. If the actual sample were measured at 86°F, then the correction is the ratio of seawater's density 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.

If the temperature of standardization is unknown, then 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.

The corrections to use for standard hydrometers are given in the summary at the beginning of this article.

Temperature Corrections for Swing Arm Hydrometers

Some marine hobby hydrometers, often called swing arm hydrometers, claim to be accurate at all temperatures (68 - 85°F; these include SeaTest, Deep Six, Instant Ocean and eSHa Marinomat). Such a device could be designed, if its change in density as a function of temperature were exactly the same as seawater at all temperatures.

I have tested two of these swing arm hydrometers and reported on the results in a previous article. While one was not very accurate (reading S=32 when the solution was S=35), both of them did give results that were roughly independent of temperature between 68 and 80°F.

Consequently, swing arm hydrometers should not be subjected to any temperature corrections in the normal range of use for a reef aquarium. They may, however, benefit from having their calibration checked with a standard solution.

How to Use a Standard Hydrometer

Here are a few additional tips for using a standard 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 it in dilute acid (such as vinegar or diluted muriatic acid).
2. Make sure that no air bubbles are 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 the same temperature as the water (and preferably the air).
4. Read the hydrometer at the plane of the water's surface, not along the meniscus (Figure 3; 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 hydrometer's hydrophobicity).
5. Rinse with purified freshwater after use to reduce deposits.
6. Do not leave the hydrometer floating in the tank between uses. If left in the aquarium, deposits may form that will be difficult to remove.

Figure 3. The Tropic Marin floating hydrometer, showing the meniscus rising to
about 1.0260, but the actual reading is about 1.0265.

How to Use a Swing Arm Hydrometer

In addition to those described above, here are some special tips for using swing arm hydrometers:

7. Make sure that the hydrometer is completely level. A slight tilt to either side will change the reading.
8. Some swing arm hydrometers recommend "seasoning" the needle by filling it with water for 24 hours prior to use. This presumably permits the water absorbed into the plastic to reach equilibrium. In the case of the hydrometer that I tested in a previous article, the hydrometer became slightly less accurate after "seasoning."


Conclusion

Hydrometers are an inexpensive and easy way to measure salinity in marine aquaria. In order to most effectively use hydrometers, aquarists need to know when they should apply a temperature correction to the hydrometer reading to get an accurate specific gravity reading, and when this isn't necessary. This article should enable aquarists to properly apply such corrections.



If you have any questions about this article, please visit my author forum on Reef Central.

Reference:

1. Millero, Frank J.; Editor. Chemical Oceanography, Second Edition. (1996), 496 pp.




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Temperature Corrections for Hydrometers by Randy Holmes-Farley - Reefkeeping.com