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 non-uniform weight distribution. Typical hobby swing arm hydrometers use an arm made of two different materials. 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.
(CONT)
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 non-uniform weight distribution. Typical hobby swing arm hydrometers use an arm made of two different materials. 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.
(CONT)