Definition and conversion of volume mixing ratio

Definition

The volume mixing ratio, or simply mixing ratio, of a gas is defined as the ratio of the number density of the gas to the total number density of the atmosphere. In other words, ozone volume mixing ratio is the density of ozone divided by the density of all constituents in a unit volume (i.e. number of molecules per unit volume).

Therefore, an ozone mixing ratio of 10^-6 means that the number density of ozone is 10^-6 times the total number density of air in a unit volume. Following the standard convention for the Earth's troposphere and stratosphere, this mixing ratio equals 1 ppmv (parts per million by volume).

Conversion of volume mixing ratio

Below conversions of ozone volume mixing ratio (vmr) into common units are listed.
The volume mixing ratio is given in ppmv (parts per million, 10^-6), pressure in hPa and temperature in K.

• Ozone partial pressure p_O3 [nbar]:

p_O3 = vmr_O3 * pressure

• Ozone density ρ_O3[μg/m3]:

ρ_O3 = vmr_O3 * 577.3 * pressure / temperature

• Ozone mass mixing ratio m_O3 [μg/g]:

m_O3 = vmr_O3 * 1.66

• Ozone number density N_O3 [molecules/cm³]:

N_O3 = vmr_O3 * pressure / (1.38 10^-19 * temperature)

Conversion into volume mixing ratio

Below conversions of common units into ozone volume mixing ratio (vmr) are outlined.
The volume mixing ratio is given in ppmv, pressure in hPa and temperature in K.

• Ozone partial pressure pO3 [nbar]:

vmr_O3 = p_O3 / pressure

• Ozone density ρO3 [μg/m3]:

vmr_O3 = ρ_O3 * 1.7322 * 10^-3 * temperature / pressure

• Ozone mass mixing ratio m_O3 [μg/g]:

vmr_O3 = m_O3 * 0.602

• Ozone number density N_O3 [molecules/cm³]:

vmr_O3 = N_O3 * 1.38 10^-19 * temperature / pressure

Thilo Erbertseder, Frank Baier, last modified: October 2005