In air pollution literature ppm applied to a gas, always means parts per million by volume or by mole. These are identical for an ideal gas, and practically identical for most gases of air pollution interest at 1 atm. Another way of expressing this value is ppmv. 
One part per million (by volume) is equal to a volume of a given gas mixed in a million volumes of air:
A micro liter volume of gas in one liter of air would therefore be equal to 1 ppm:
Today's more and more there is an interest to express gas concentrations in metric units, i.e. µg/m3. Although expressing gaseous concentrations in µg/m3 units, has the advantage of metric expression, it has the disadvantage of being greatly influenced by changes in temperature and pressure. Additionally, because of difference in molecular weight, comparisons of concentrations of different gases are difficult. 
To convert ppmv to a metric expression like µg/m3, the density of the concerning gas is needed. The density of gas can be calculated by the Law of Avogadro's, which says: equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This law implies that 1 mole of gas at STP a volume of 22.71108 liters (dm3) enfolds, also mentioned as the molar volume of ideal gas. Standard Temperature and Pressure (STP) is defined as a condition of 100.00 kPa (1 bar) and 273.15 K (0°C), which is a standard of IUPAC.  The amount of moles of the concerning gas can be calculated with the molecular weight.
||standard molar volume of ideal gas (at 1 bar and 273.15 K) 
||molecular weight of gas
For converting ppm by mole, the same equation can be used. This can be made clear by the following notation:
By checking the dimensions of the most right part of the equation, there will be found a dimensionless value, like the concentration in ppm is.
To calculate the concentration in metric dimensions, with other temperature and pressure conditions the Ideal Gas Law comes in handy. The volume (V) divided by the number of molecules (n) represents the molar volume (Vn) of the gas with a temperature (T) and pressure (P).
||specific molar volume of ideal gas (at pressure P and temperature T)
||volume of the gas
||amount of molecules
||universal gas law constant 
||[8.314510 J K-1 mol-1] or [m3 Pa K-1 mol-1]
With this equation it comes clear that the percentage notation by ppm is much more useful, because the independency of the temperature and pressure.
Parts per Million by Weight in Water
The concentration in ppm of gas in water is meanly meant by weight. To express this concentration with metric units the density of water is needed.
The density of pure water has to be by definition 1000.0000 kg/m3 at a temperature of 3.98°C and standard atmospheric pressure, till 1969. Till then this was mean definition for the kilogram. Today's the kilo is defined as being equal to the mass of the international prototype of the kilogram . Water with a high purity (VSMOW) at a temperature of 4°C (IPTS-68) and standard atmospheric pressure has a density of 999.9750 kg/m3. 
The density of water is effected by the temperature, pressure and impurities, i.e. dissolved gasses or the salinity of the water. Even the concerning concentration of gas dissolved in the water is affecting the density of the solution. By nature there's a chance that water contains a certain concentration of Deuterium which influences the density of the water. This concentration is also called the isotopic composition .
Accurate calculations on these conversions are only possible when the density of the water is measured. In practice the density of water is therefore set to 1.0 ·103 kg/m3. When calculating the conversion with this value you gets:
||density of water
||[1.0 ·103 kg/m3]
 Never, N. , Air Pollution Control Engineering. McGraw-HILL, Singapore 1995.
 Godish, T. , Air Quality. Lewis Publishers, Michigan 1991.
 Cohen, E.R. and Taylor, B.N., J. Res. Nat. Bur. Stand. 92 (1987) 85-95. (International Union of Pure and Applied Chemistry (IUPAC))