## Reef Aquarium Water Parameters - Salinity, Density and Specific Gravity 2 January 2009

### Introduction

I have encountered many, many different interpretations and opinions on what Specific Gravity, Density and Salinity is within the context of sea water analysis - or more specific, when talking about our reef aquarium's water parameters.

I am no Chemical Engineer - however I have done considerable research and thus believe my understanding (as verified by Chemical Engineers and other scientists) is correct. So without further ado, let me explain the differences.

### Salinity

Salinity is not the amount of salts in a unit volume of water. That was a very old definition. The new (and accepted) definition is based on electrical conductivity, and is called the PSS (Practical Salinity Scale) - which is a dimensionless quantity:

The practical salinity, symbol S, of a sample of sea water, is defined in terms of the ratio K of the electrical conductivity of a sea water sample of 15°C and the pressure of one standard atmosphere, to that of a potassium chloride (KCl) solution, in which the mass fraction of KCl is 0.0324356, at the same temperature and pressure. The K value exactly equal to one corresponds, by definition, to a practical salinity equal to 35.

Formally, the practical salinity of sea water is defined as the conductivity ratio, K15, where:

K15 = Conductivity of sea water / Conductivity of standard KCl

The ratio is:

S = 0.0080 - 0.1692 K151/2 + 25.3853 K15 + 14.0941 K153/2 - 7.0261 K152 + 2.7081 K155/2

That gives us a very good starting point. For instance, it is clear from this definition that Practical Salinity is not temperature dependent purely because it was defined at 15°C. That means, a Salinity value is always based on what the conductivity would have been in a solution of KCl at 15°C - so if the actual conductivity was measured to be say 25°C, then to calculate S (Salinity) we would first use formulas to convert the actual conductivity reading at 25°C back to the conductivity at 15°C, then substitute it in this formula for PSS.

Practical Salinity of natural sea water is typically taken to be 35.00.

### Density

Density is not the same as Specific Gravity. From a purely formal perspective, they have different dimensionality. Density is measured (based on SI standards) in g/cm3. It is a measure of the mass per unit volume of a substance. For our purposes, it is the mass of a unit volume of sea water. But first lets talk about pure water (RO/DI or distilled water).

d = m / v

Pure water has a density of 1.0000g/cm3. But only when the water is under atmospheric pressure (760mmHg) and 3.98°C, as both pressure and temperature affects density. Pure water is at its highest density at 3.98°C - not at freezing point as some people might believe (this is why water is so peculiar - it is one of a few known substances where the solid form floats on top of the liquid form because the solid form is less dense).

A word about pressure - for all practical purposes for our hobby, reefs are in very shallow water hence the pressure can be neglected as always equals to 1 atmosphere. So I will not discuss that here any more.

When pure water heats up, the density decreases because the water molecules attain more kinetic energy and hence there is more empty space per molecule. When water cools down, the energy is lost and the density increases as molecules can now be spaced closer to each other. So at a temperature of 20°C for example, pure water has a density of 0.998206g/cm3. This might not seem to be a big difference, but it is definitely substantial. It is 0.002 units lower than what it is at 3.98°C.

The density of sea water is much higher, due to the dissolved salts and other elements in the water. Since density is temperature dependent, one cannot say what the density of sea water is without specifying the temperature of the sample. At 20°C, sea water has a typical density of 1.025g/cm3 if at a Salinity of 35. However this density changes much more dramatically than pure water, for the density is 1.028g/cm3 at 3.98°C and 1.023g/cm3 at 27.8°C. To put this in to perspective, if one guy keeps a reef aquarium at 28°C and another keeps his at 24°C, the density difference for the same Salinity would be 0.00125.

### Specific Gravity

Specific Gravity is defined as the ratio of the density of sea water to the density of pure water (for our use of the definition). This clearly indicates that Specific Gravity does not have a dimension - it is dimensionless. So formally (as used in oceanographic studies),

s.g.t = 103(ρ/ρm - 1)

where s.g.t is the Specific Gravity at a temperature t, ρ is the density of the sample sea water and ρm is the maximum density of pure water (later redefined as SMOW water - but we can ignore the difference). This value is similar to the one most aquarists are familiar with, but it is presented slightly differently. A value of 1.025 which most people are used to becomes 25, since one is subtracted from the density ration and then multiplied by 1000. So sea water at a density of 1.025g/cm3 becomes:

s.g.t = 103(1.025/1.0000 - 1)
= 103(1.025 - 1)
= 103(0.025)
= 25

I will use the formats 1.025 and 25 interchangeably.

The BIG problem comes in when we need to ask the question - but at what temperature? So you say it is s.g.t meaning it is at the temperature the sample was measured at... But then I'd ask - and at what temperature is the pure water? If you are clever, you'll note that it was the maximum density of pure water, so it is implicitly defined to be 3.98°C. At least that is what one can deduce from this equation. The problem is not everyone uses this definition from Processing of Oceanographic Station Data" Unesco 1991. For example, many refractometers display the little symbol d20/20 in the SG scale - this means the density of sea water at 20°C divided by the density of pure water also at 20°C.

There are many other standards, such as d4/4 (3.98°C rounded to 4°C), d15/4 etc. A common reference temperature for many hydrometers is 15°C/15°C. This is most likely due to desirable characteristics of water at this temperature.

The reason why hydrometers are calibrated to a reference temperature is because the Specific Gravity is dependent both on temperature as well as salinity. It is not easy to build a simple device like a hydrometer that accounts for both. So they fix one variable - the temperature - at a reference value. The other variable is then measured - salinity (and converted via calibrated markers to Specific Gravity). The problem is when people want to know what a SG reading of 1.027 means. If the hydrometer was calibrated to 15°C, then it means a reading of 1.027 is the Specific Gravity of the sample based on the density characteristics at 15°C - which it is usually not since we run our reefs much hotter. Since the density characteristics are different at 30°C, we look up in a conversion table at a reference temperature of 15°C for the SG of 1.027 and the sample temperature of 30°C, and the table will yield a value of 40.8ppt. .

To the solution to all the confusion is to understand that we (as aquarists) never work with actual Specific Gravities. We always convert them (indirectly) back based on a reference temperature of 15°C. So oceanographers and aquarists alike speak once again the same language - based on 15°C.

In summary, for sea water at 15°C and at a Practical Salinity of 35.00 the actual (in situ) Specific Gravity is 1.02597, for the same sea water at a temperature of 25°C the actual Specific Gravity is 1.0233 and at 27°C the actual Specific Gravity is 1.0227. But for all those different temperatures we would use the Specific Gravity at 15°C - namely 1.02597 even if the actual water temperature is different.

Just to clarify something - the above discussion only applies to Standard Floating Hydrometers - not Swing Arm Hydrometers as these auto correct for temperature differences by having their density change in similar proportions as sea water based on temperature fluctuations.

Before any chemical boffins jump on me, the Specific Gravity values I gave above are correct, but based on the definition above. In our reefkeeping hobby, we do not use that exact definition of Specific Gravity. In specific, we do not use a reference temperature of fresh water at 3.98°C. , but rather at 15°C:

s.g.t = 103(ρsw/ρfw15 - 1)

where s.g.t is the Specific Gravity at a temperature t, ρsw is the density of the sample sea water and ρfw15 is the density of pure water at 15°C. And for standardised values (non in-situ), we use this definition:

s.g.15 = 103(ρsw15/ρfw15 - 1)

where s.g.15 is the Specific Gravity at a temperature 15°C, ρsw15 is the density of the sample sea water converted back to 15°C and ρfw15 is the density of pure water at 15°C. For this reason, for our purposes S.G. is never the same as Density - not even numerically. The density of fresh water at 15°C is 0.999099g/cm3 - not 1.

So to reformulate the statement above in terms of this new definition (the only one we care about),

In summary, for sea water at 15°C and at a Practical Salinity of 35.00 the actual (in situ) Specific Gravity is 1.0269, for the same sea water at a temperature of 25°C the actual Specific Gravity is 1.0243 and at 27°C the actual Specific Gravity is 1.0236. But for all those different temperatures we would use the Specific Gravity at 15°C - namely 1.0269 even if the actual water temperature is different.

### Refractometers

Without going in too much detail, I just want to explain how refractometers handle temperature effects. Firstly, refractometers is based on the principle that light refracts when changing medium - such as from air to sea water. The amount of salts in the sea water changes the amount by which light is refracted, which reads as a white area on the scale.

The refractive index of a liquid is highly dependent on temperature. Handheld refractometers mostly utilizes bimetallic strips - a piece of metal that expands and contracts due to the temperature of the sample - exactly canceling the effect of the sample's temperature on the refractive index by moving the optics up or down. This is called ATC (Automatic Temperature Compensation).

Based on this, assuming the aquarist has a decent ATC refractometer designed for sea water, temperature compensation is not necessary and both the Salinity and Specific Gravity scales will be very accurate and temperature compensated. But once again, it will be compensated to a reference temperature of 15°C - so that everyone can compare apples with apples.

### Hanna 9828 Multiparameter Meter

My Hanna electronic meter is a very handy device. I used it to show experimental proof of the theoretical discussion above.

Salinity: 35ppt (Tropic Marine Pro Reef Salt + 200ml RO water)

``````Temp   Density(SWEoS)   σt (Measured) s.g.t      σ15      s.g.15   Refractometer
15°C   1.02597          1.0260        1.0269     1.0260  1.0269   1.0265 (35ppt), 20/20
20°C   1.02476          1.0247        1.0257     1.0260  1.0269
25°C   1.02334          1.0234        1.0243     1.0260  1.0269
27°C   1.02272          1.0227        1.02365    1.0260  1.0269   1.0265 (35ppt), 20/20``````

with σ15 the Density at 15°C and σt the in situ Density, s.g15 the Specific Gravity at 15°C, and s.g.t the in situ Specific Gravity. Note that only the σt and σ15 values have been measured by the Hanna, the s.g. and Density (SWEoS) values have been calculated from first principles.

It is clear the Hanna's σt mode shows actual Density (not Specific Gravity), and the σ15 mode shows you the internationally accepted standard of 15°C reference values - independent of the sample's actual temperature. Only when the sample is itself at 15°C do these two values match each other. Just for fun, my Deltec refractometer's ATC is working very well as can clearly be seen - the reading is unaffected by the temperature difference of 12°C.

Thanks to Boomer @ ReefCentral for his invaluable input and patience with me.