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Concentration - Quantitative notation

Concentration - Quantitative notation: Encyclopedia II - Concentration - Quantitative notation

Quantitative notation of concentration is far more informative and useful from a scientific point of view. There are a number of different ways to quantitatively express concentration; the most common are listed below. Note: Many units of concentration require measurement of a substance's volume, which is variable depending on ambient temperature and pressure. Unless otherwise stated, all the following measurements are assumed to be at standard state temperature and pressure (that is, 25 degrees Celsius at 1 atmosphere or 101.325 kPa).

Concentration: Encyclopedia II - Concentration - Quantitative notation

Concentration - Quantitative notation

Note: Many units of concentration require measurement of a substance's volume, which is variable depending on ambient temperature and pressure. Unless otherwise stated, all the following measurements are assumed to be at standard state temperature and pressure (that is, 25 degrees Celsius at 1 atmosphere or 101.325 kPa).

Concentration - Mass percentage

Mass percentage denotes the mass of a substance in a mixture as a percentage of the mass of the entire mixture. For instance: if a bottle contains 40 grams of ethanol and 60 grams of water, then it contains 40% ethanol by mass. Commercial concentrated aqueous reagents such as acid and bases are often labeled in concentrations of weight percentage with the specific gravity also listed. In older texts and references this is sometimes referred to as weight-weight percentage (abbreviated as w/w).

Concentration - Mass-volume percentage

Mass-volume percentage, (sometimes referred to as weight-volume percentage and often abbreviated as % m/v or % w/v) denotes the mass of a substance in a mixture as a percentage of the volume of the entire mixture. Mass-volume percentage is often used for solutions made from solid reagents. It is the mass of the solute in grams multiplied by one hundred divided by the volume of solution in milliliters.

Concentration - Volume-volume percentage

Volume-volume percentage or % (v/v) describes the volume of the solute in mL per 100 mL of the resulting solution. This is most useful when a liquid - liquid solution is being prepared. For example, beer is about 5% ethanol by volume. This means every 100 mL beer contains 5 mL ethanol (ethyl alcohol).

Concentration - Molarity

Molarity (M) denotes the number of moles of a given substance per litre of solution. For instance: 4.0 litres of liquid, containing 2.0 moles of dissolved particles, constitutes a solution of 0.5 M. Such a solution may be described as "0.5 molar." (Working with moles can be highly advantageous, as they enable measurement of the absolute number of particles in a solution, irrespective of their weight and volume. This is often more useful when performing stoichiometric calculations.). See molar solution for further information.

Concentration - Molality

Molality (m) denotes the number of moles of a given substance per kilogram of solvent. For instance: 2.0 kilograms of solvent, containing 1.0 moles of dissolved particles, constitutes a molality of 0.5 mol/kg. Such a solution may be described as "0.5 molal."

The advantage of molality is that it does not change with the temperature as it deals with the mass of solvent, rather than the volume of solution. Volume typically increases with increase in temperature resulting in decrease in molarity. Molality of a solution is always constant irrespective of the physical conditions like temperature and pressure.

Concentration - Molinity

Molinity is a rarely-used term that denotes the number of moles of a given substance per kilogram of solution. For instance: imagine 2.0 kg of solvent, plus 1.0 mol of dissolved particles, weighs a total of 2.5 kg. The molinity of the solution is therefore 1 mol / 2.5 kg = 0.4 mol/kg.

Note: molarity and molinity are calculated using the volume of the entire solution, but molality is calculated using the mass of solvent only. Warning: There may be confusion between above terms, which look and sound very similar; also, the abbreviations 'M' (denoting molarity) and 'm' (denoting molality) can be ambiguous. Special care should be exercised; if there is any risk of confusion, one should fully describe the measure being used.

Concentration - Normality

Normality is a concept related to molarity, usually applied to acid-base solutions and reactions. For acid-base reactions, the equivalent is the mass of acid or base that can accept or donate exactly one mole of protons (H⁺ ions). Normality is also used for redox reactions. In this case the equivalent is the quantity of oxidizing or reducing agent that can accept or furnish one mole of electrons.

Whereas molarity measures the number of particles per litre of solution, normality measures the number of equivalents per litre of solution.

In practice, this simply means one multiplies the molarity of a solution by the valence of the ionic solute. A bit more complex for redox reactions.

Note: The normality is always equal to, or greater than the molarity for acid-base reactions. However, for redox reactions the normality is typically equal to or less than the molarity.

Concentration - Mole fraction

The mole fraction χ, chi (also called molar fraction) denotes the number of moles of solute as a proportion of the total number of moles in a solution. For instance: 1 mole of solute dissolved in 9 moles of solvent would have a mole fraction of 1/10 or 0.1.

Concentration - Formal

The formal (F) is yet another measure of concentration similar to molarity. It is used rarely. It is calculated based on the formula weights of chemicals per litre of solution. The difference between formal and molar concentrations is that the formal concentration indicates moles of the original chemical formula in solution, without regard for the species that actually exist in solution. Molar concentration, on the other hand, is the concentration of species in solution.

For example: if one dissolves sodium carbonate (Na₂CO₃) in a litre of water, the compound dissociates into the Na⁺ and CO₃^2- ions. Some of the CO₃^2- reacts with the water to form HCO₃^- and H₂CO₃. If the pH of the solution is low, there is practically no Na₂CO₃ left in the solution. So, although we have added 1 mol of Na₂CO₃ to the solution, it does not contain 1 M of that substance. (Rather, it contains a molarity based on the other constituents of the solution.) However, one can still say that the solution contains 1 F of Na₂CO₃.

Concentration - Parts-per notation

The parts-per notation is used for extremely low concentrations. This is often used to denote the relative abundance of trace elements in the Earth's crust, trace elements in forensics or other analyses, or levels of pollutants in the environment.

Parts per hundred (denoted by '%' and very rarely 'pph') - denotes one particle of a given substance for every 99 other particles. This is the common percent. 1 part in 10².
Parts per thousand (denoted by '‰' [the per mil symbol], and occasionally 'ppt') denotes one particle of a given substance for every 999 other particles. This is roughly equivalent to one drop of ink in a cup of water, or one second per 17 minutes. 'Parts per thousand' is often used to record the salinity of seawater. 1 part in 10³.
Parts per million ('ppm') denotes one particle of a given substance for every 999,999 other particles. This is roughly equivalent to one drop of ink in a 40 gallon drum of water, or one second per 280 hours. 1 part in 10⁶.
Parts per billion ('ppb') denotes one particle of a given substance for every 999,999,999 other particles. This is roughly equivalent to one drop of ink in a canal lock full of water, or one second per 32 years. 1 part in 10⁹.
Parts per trillion ('ppt') denotes one particle of a given substance for every 999,999,999,999 other particles. This is roughly equivalent to one drop of ink in an Olympic-sized swimming pool, or one second every 320 centuries. 1 part in 10¹².
Parts per quadrillion ('ppq') denotes one particle of a given substance for every 999,999,999,999,999 other particles. This is roughly equivalent to a drop of ink in a medium-sized lake, or one second every 32,000 millennia. There are a few analytical techniques that can measure ppq concentrations; and it is used in some mathematical models of toxicology and epidemiology. 1 part in 10¹⁵. Some contaminants such as methylmercury can be present in lakes at ppq concentrations and are biomagnified such that fish contain ppm concentrations of mercury.

Warning: although 'ppt' is usually used to denote 'parts per trillion', it is also on occasion used to denote 'parts per thousand'. If there is any chance of ambiguity, one should describe the abbreviation in full.

According to the U.S. National Institute of Standards and Technology (NIST) Guide for the Use of the International System of Units (SI), "the language-dependent terms part per million, part per billion, and part per trillion ... are not acceptable for use with the SI to express the values of quantities." [1] which lists examples of alternative expressions.

Notes for clarity:

The indication given above is that parts per notation refers to numbers of particles (equivalent to moles), whereas in the last column of the chart below it is given by mass (grams per kilogram). Those using the notation need to state their usage to avoid confusion. In atmospheric chemistry the parts per notation is commonly expressed with a v following, such as ppmv (or ppvm is some usages), to indicate parts per million by volume. In gases ppmv is equivalent to ppm by particles (Avogadro's law). This works fine for gases, but may have problems with cloud droplets and smoke or other atmospheric particulate matter.