Royal Society of Chemistry

Table 1.8

Other quantities used in analytical chemistry.

Quantity or constant	Symbol	Definition (relating to specified component B, C)	SI unit	Note
1. Non-SI units of time accepted for use with the SI are minute (min = 60 s), hour (h = 3600 s), and day (d = 86 400 s); while week, month, year are not accepted for use with SI units. 2. Time between identical events in periodic phenomena. 3. The unit Hz is not to be used for angular frequency. 4. The plane angle is often given in degree (°) where 1° = (π/180) rad; the degree can be divided decimally or in minute (1′ = (1/60)°) and second (1″=(1/60)′). 5. A denotes (surface) area. 6. The rcf ratio is used to characterize the effect of centrifuging a sample (frequency ν, radius r) in comparison to the gravitational acceleration g: f_rel : = ω²r/g = 4π²ν²r/g ≈ (4 s²/m)ν²r. In practice, the rotational frequency ν of the centrifuge is often given in “revolutions per minute” (rpm) and r is in the order of millimeters, then rcf can be re-written as f_rel ≈ 1.12{r}_mm({ν}_rpm/1000)², where the braces indicate the numerical value of the quantity when measured in the unit stated as subscript. 7. Pressure is often expressed in the non-SI unit bar, where 1 bar = 10⁵ Pa and 1 mbar = 10⁻³ bar = 100 Pa = 1 hPa; further 1 atm = 1.01325 bar and 1 atm = 760 Torr. 1 Torr ≈ 1 mmHg and 1 psi ≈ 68.95 mbar. 8. The fixed constants defining the SI are given in Table 1.9 of Section 1.8.5. They do not carry any measurement uncertainty. 9. The electronvolt, symbol “eV”, is a non-SI unit accepted for use with the SI and may be combined with the SI prefixes given in Table 1.3. 10. Degree Celsius is an SI-derived unit with special name and term (see Table 1.10). 11. a_H⁺ is the activity of the hydrogen ion in solution. 12. The reactance Im(Z) = X = (U/I) sin δ where δ is the loss angle. 13. This quantity should not be termed “magnetic field”. 14. N_B denotes the number of decaying entities. 15. Activity referred to a radio nuclide is sometimes incorrectly termed radioactivity. 16. The term “massic activity” is also used. 17. Since all isotopes of the given element are known n(E) ≡ Σn(ⁱE) and N(E) ≡ ΣN(ⁱE) 18. Half-lives of long-lived isotopes are commonly given in the non-SI unit years. 19. In infrared and Raman spectroscopy wavenumbers ṽ are typically given in cm⁻¹. 20. The speed of light within the medium is denoted by c. 21. The symbols for the quantities such as radiant energy are also used for the corresponding quantities concerning visible radiation, i.e. luminous quantities and photon quantities. Subscripts e for energetic, v for visible and p for photon may be added. The units used for luminous quantities are derived from the base unit candela (cd). 22. Radiant intensity is the radiant power per solid angle in the direction of the point from which the source is being observed. 23. The intensity or irradiance I is the radiation power per area that is received at a surface. This quantity must be distinguished from radiant intensity I_e which characterizes the source. 24. The correct definition of resolution depends on the line shape, but usually resolution is taken as the full line width at half maximum intensity (FWHM). 25. The unit depends on whether mass concentration or amount-of-substance concentration is used, the numerical value depends also on the base of the logarithm. 26. θ denotes Celsius temperature, ρ mass density.
time, duration	t		s	1
frequency (of periodic phenomenon)	ν, f	ν = 1/T	s⁻¹ = Hz
period	T		s	2
angular frequency, angular velocity	ω	ω = 2π ν	s⁻¹ rad s⁻¹	3
speed	v	v = dl/dt	m s⁻¹
plane angle	α, β, γ, ⋯		rad, 1	4
solid angle	Ω	Ω = A/r²	sr, 1	5
force	F		N = m kg s⁻²
weight	G	G = m g	N
standard acceleration of gravity g_n = 9.80665 m s⁻² (defined)⁶	g_n		m s⁻²
relative centrifugal force (rcf)	f_rel	f_rel = m ω²r/G	1	6
moment of force, torque	M	M = F × l	N m
surface tension	γ	γ = dW/dA	N/m	5
pressure, stress	p	p = F/A	Pa = N m⁻²	5, 7
viscosity (dynamic)	η		Pa s
energy, work, heat	E, W, Q		J = N m
electronvolt eV = 1.602176634 × 10⁻¹⁹ J (constant usable as unit)	eV	eV = (1 V) e	J = C V	8, 9
power	P		W = J s⁻¹
Planck constant h = 6.62607015 × 10⁻³⁴ J s	h		J s	8
molar gas constant R ≈ 8.314462618 J K⁻¹ mol⁻¹	R	R = k N_A	J K⁻¹ mol⁻¹	8
Celsius temperature zero point at 273.15 K (defined)⁶	θ, t		°C	10
thermodynamic temperature	T		K
standard temperature and pressure for gases (STP)		θ = 0 °C, P = 10⁵ Pa
pH	pH, pa_H⁺	pH = −log₁₀ (a_H⁺)	1	11
elementary charge e = 1.602176634 × 10⁻¹⁹ C	e		C	8
Faraday constant F ≈ 96485.33212 C mol⁻¹	F	F = e N_A	C mol⁻¹	8
electric charge	Q		C = A s
electric current	I, i		A
electric current density	J, j		A m⁻²
electric potential	V, Φ		V = J C⁻¹
electric potential difference, tension	U		V
electric field strength	E	E = U/l	V m⁻¹
electric resistance	R	R = U/I	Ω = V A⁻¹
electric impedance	Z	Z = R + iX	Ω	12
electric resistivity	ρ		Ω m
electric conductance	G		S = Ω⁻¹
electric conductivity	σ		S m⁻¹
electric capacitance	C		F = C V⁻¹
magnetic field strength	H		A m⁻¹
magnetic flux density, magnetic induction	B		T = V s m⁻²	13
activity of a radioactive material, activity	A	A = −dN_B/dt	Bq = s⁻¹	14, 15
decay (rate) constant	λ	λ = A/N_B	s⁻¹	14
specific activity	a	a = A/m	Bq kg⁻¹	16
isotopic ratio	R	R = N_B/N_C	1
abundance of isotope ⁱE in element E:				17
isotope mole fraction.	x(ⁱE)	x(ⁱE) = n(ⁱE)/n(E)	1
isotope number fraction	X(ⁱE)	X(ⁱE) = N(ⁱE)/N(E)	1
half-life	t_1/2, T_1/2		s	18
absorbed dose	D		Gy = J kg⁻¹
dose equivalent	H		Sv = J kg⁻¹
speed of light	c		m s⁻¹
speed of light in vacuum c₀ = 2.99792458 × 10⁸ m s⁻¹	c, c₀		m s⁻¹	8
wavelength	λ		m
wavenumber	, σ	 = λ⁻¹	m⁻¹	19
frequency (of electromagnetic radiation)	ν	ν = c λ⁻¹	Hz
refractive index	n	n = c₀/c	1	20
radiant energy	Q, W		J	21
radiant power, (radiant energy per time)	P	P	W = J s⁻¹	22
radiant intensity	I_e	I_e = dP/dΩ	W sr⁻¹	23
irradiance, intensity	I	I = dP/dA	W m⁻²	21, 23
luminous intensity	I_v		cd	20
luminous flux	Φ_v		lm = cd sr	21
illuminance	E_v	E_v = dΦ_v/dA	lx = lm m⁻²	5, 21
resolution	δ		m⁻¹	24
transmittance	T	T = P_transmitted/P₀	1
reflectance	R	R = P_reflected/P₀	1
absorptance	α	α = 1 – T	1
absorbance	A	A = ε c l	1
decadic absorbance	A₁₀	A₁₀ = −log₁₀ T	1
Naperian absorbance	A_e	A_e = −ln T	1
absorption coefficient	ε	ε = A/cl		25
absorption index	k	k = A_e/(4πlṽ)	1
complex refractive index	n̂	n̂ = n + ik	1
angle of optical rotation	α		1, rad	3
specific optical rotatory power	[α] $_{λ}^{θ}$	[α] $_{λ}^{θ}$ = α/ρl	rad m² kg⁻¹	4, 26
catalytic activity	z_E		kat = mol s⁻¹
mass flux	q_m	q_m = dm/dt	kg s⁻¹

Quantity or constant	Symbol	Definition (relating to specified component B, C)	SI unit	Note
1. Non-SI units of time accepted for use with the SI are minute (min = 60 s), hour (h = 3600 s), and day (d = 86 400 s); while week, month, year are not accepted for use with SI units. 2. Time between identical events in periodic phenomena. 3. The unit Hz is not to be used for angular frequency. 4. The plane angle is often given in degree (°) where 1° = (π/180) rad; the degree can be divided decimally or in minute (1′ = (1/60)°) and second (1″=(1/60)′). 5. A denotes (surface) area. 6. The rcf ratio is used to characterize the effect of centrifuging a sample (frequency ν, radius r) in comparison to the gravitational acceleration g: f_rel : = ω²r/g = 4π²ν²r/g ≈ (4 s²/m)ν²r. In practice, the rotational frequency ν of the centrifuge is often given in “revolutions per minute” (rpm) and r is in the order of millimeters, then rcf can be re-written as f_rel ≈ 1.12{r}_mm({ν}_rpm/1000)², where the braces indicate the numerical value of the quantity when measured in the unit stated as subscript. 7. Pressure is often expressed in the non-SI unit bar, where 1 bar = 10⁵ Pa and 1 mbar = 10⁻³ bar = 100 Pa = 1 hPa; further 1 atm = 1.01325 bar and 1 atm = 760 Torr. 1 Torr ≈ 1 mmHg and 1 psi ≈ 68.95 mbar. 8. The fixed constants defining the SI are given in Table 1.9 of Section 1.8.5. They do not carry any measurement uncertainty. 9. The electronvolt, symbol “eV”, is a non-SI unit accepted for use with the SI and may be combined with the SI prefixes given in Table 1.3. 10. Degree Celsius is an SI-derived unit with special name and term (see Table 1.10). 11. a_H⁺ is the activity of the hydrogen ion in solution. 12. The reactance Im(Z) = X = (U/I) sin δ where δ is the loss angle. 13. This quantity should not be termed “magnetic field”. 14. N_B denotes the number of decaying entities. 15. Activity referred to a radio nuclide is sometimes incorrectly termed radioactivity. 16. The term “massic activity” is also used. 17. Since all isotopes of the given element are known n(E) ≡ Σn(ⁱE) and N(E) ≡ ΣN(ⁱE) 18. Half-lives of long-lived isotopes are commonly given in the non-SI unit years. 19. In infrared and Raman spectroscopy wavenumbers ṽ are typically given in cm⁻¹. 20. The speed of light within the medium is denoted by c. 21. The symbols for the quantities such as radiant energy are also used for the corresponding quantities concerning visible radiation, i.e. luminous quantities and photon quantities. Subscripts e for energetic, v for visible and p for photon may be added. The units used for luminous quantities are derived from the base unit candela (cd). 22. Radiant intensity is the radiant power per solid angle in the direction of the point from which the source is being observed. 23. The intensity or irradiance I is the radiation power per area that is received at a surface. This quantity must be distinguished from radiant intensity I_e which characterizes the source. 24. The correct definition of resolution depends on the line shape, but usually resolution is taken as the full line width at half maximum intensity (FWHM). 25. The unit depends on whether mass concentration or amount-of-substance concentration is used, the numerical value depends also on the base of the logarithm. 26. θ denotes Celsius temperature, ρ mass density.
time, duration	t		s	1
frequency (of periodic phenomenon)	ν, f	ν = 1/T	s⁻¹ = Hz
period	T		s	2
angular frequency, angular velocity	ω	ω = 2π ν	s⁻¹ rad s⁻¹	3
speed	v	v = dl/dt	m s⁻¹
plane angle	α, β, γ, ⋯		rad, 1	4
solid angle	Ω	Ω = A/r²	sr, 1	5
force	F		N = m kg s⁻²
weight	G	G = m g	N
standard acceleration of gravity g_n = 9.80665 m s⁻² (defined)⁶	g_n		m s⁻²
relative centrifugal force (rcf)	f_rel	f_rel = m ω²r/G	1	6
moment of force, torque	M	M = F × l	N m
surface tension	γ	γ = dW/dA	N/m	5
pressure, stress	p	p = F/A	Pa = N m⁻²	5, 7
viscosity (dynamic)	η		Pa s
energy, work, heat	E, W, Q		J = N m
electronvolt eV = 1.602176634 × 10⁻¹⁹ J (constant usable as unit)	eV	eV = (1 V) e	J = C V	8, 9
power	P		W = J s⁻¹
Planck constant h = 6.62607015 × 10⁻³⁴ J s	h		J s	8
molar gas constant R ≈ 8.314462618 J K⁻¹ mol⁻¹	R	R = k N_A	J K⁻¹ mol⁻¹	8
Celsius temperature zero point at 273.15 K (defined)⁶	θ, t		°C	10
thermodynamic temperature	T		K
standard temperature and pressure for gases (STP)		θ = 0 °C, P = 10⁵ Pa
pH	pH, pa_H⁺	pH = −log₁₀ (a_H⁺)	1	11
elementary charge e = 1.602176634 × 10⁻¹⁹ C	e		C	8
Faraday constant F ≈ 96485.33212 C mol⁻¹	F	F = e N_A	C mol⁻¹	8
electric charge	Q		C = A s
electric current	I, i		A
electric current density	J, j		A m⁻²
electric potential	V, Φ		V = J C⁻¹
electric potential difference, tension	U		V
electric field strength	E	E = U/l	V m⁻¹
electric resistance	R	R = U/I	Ω = V A⁻¹
electric impedance	Z	Z = R + iX	Ω	12
electric resistivity	ρ		Ω m
electric conductance	G		S = Ω⁻¹
electric conductivity	σ		S m⁻¹
electric capacitance	C		F = C V⁻¹
magnetic field strength	H		A m⁻¹
magnetic flux density, magnetic induction	B		T = V s m⁻²	13
activity of a radioactive material, activity	A	A = −dN_B/dt	Bq = s⁻¹	14, 15
decay (rate) constant	λ	λ = A/N_B	s⁻¹	14
specific activity	a	a = A/m	Bq kg⁻¹	16
isotopic ratio	R	R = N_B/N_C	1
abundance of isotope ⁱE in element E:				17
isotope mole fraction.	x(ⁱE)	x(ⁱE) = n(ⁱE)/n(E)	1
isotope number fraction	X(ⁱE)	X(ⁱE) = N(ⁱE)/N(E)	1
half-life	t_1/2, T_1/2		s	18
absorbed dose	D		Gy = J kg⁻¹
dose equivalent	H		Sv = J kg⁻¹
speed of light	c		m s⁻¹
speed of light in vacuum c₀ = 2.99792458 × 10⁸ m s⁻¹	c, c₀		m s⁻¹	8
wavelength	λ		m
wavenumber	, σ	 = λ⁻¹	m⁻¹	19
frequency (of electromagnetic radiation)	ν	ν = c λ⁻¹	Hz
refractive index	n	n = c₀/c	1	20
radiant energy	Q, W		J	21
radiant power, (radiant energy per time)	P	P	W = J s⁻¹	22
radiant intensity	I_e	I_e = dP/dΩ	W sr⁻¹	23
irradiance, intensity	I	I = dP/dA	W m⁻²	21, 23
luminous intensity	I_v		cd	20
luminous flux	Φ_v		lm = cd sr	21
illuminance	E_v	E_v = dΦ_v/dA	lx = lm m⁻²	5, 21
resolution	δ		m⁻¹	24
transmittance	T	T = P_transmitted/P₀	1
reflectance	R	R = P_reflected/P₀	1
absorptance	α	α = 1 – T	1
absorbance	A	A = ε c l	1
decadic absorbance	A₁₀	A₁₀ = −log₁₀ T	1
Naperian absorbance	A_e	A_e = −ln T	1
absorption coefficient	ε	ε = A/cl		25
absorption index	k	k = A_e/(4πlṽ)	1
complex refractive index	n̂	n̂ = n + ik	1
angle of optical rotation	α		1, rad	3
specific optical rotatory power	[α] $_{λ}^{θ}$	[α] $_{λ}^{θ}$ = α/ρl	rad m² kg⁻¹	4, 26
catalytic activity	z_E		kat = mol s⁻¹
mass flux	q_m	q_m = dm/dt	kg s⁻¹

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