I was told that the number of moles is ‘dimensionless’.
According to the official definition, mole is a unit that has a dimension. This is counterintutitive perhaps given its definition ("the amount containing $\pu{6.02214076E23}$ particles"), but is has a dimension nonetheless.
Does this mean that the dimension of molar mass is simply mass and hence the unit g/mol can be expressed as equal or proportional to the dalton?
The dalton is set as 1/12 of the mass of the 12-carbon isotope, so it has dimensions of a mass. As measurements get more accurate, the value will change a bit over time. The mass of a particle and the molar mass of the pure substance made of those particles is proportional. The ratio of g/mol to Da, using current measurements, is 0.99999999965(30) times the Avogadro constant. So g/mol and dalton have different dimensions and can not be equal.
To say they are proportional does not make sense because both of them are units, not measurements. So while it makes sense to say that the mass and volume of samples of gold are proportional (at certain temperature and pressure), and call the proportionality factor the density of gold, it makes no sense to say that the units mL and g are proportional.
I was told that the number of moles is ‘dimensionless’.
According to the official definition, mole is a unit that has a dimension. This is counterintutitive perhaps given its definition ("the amount containing $\pu{6.02214076E23}$ particles"), but is has a dimension nonetheless.
Does this mean that the dimension of molar mass is simply mass and hence the unit g/mol can be expressed as equal or proportional to the dalton?
The dalton is set as 1/12 of the mass of the 12-carbon isotope, so it has dimensions of a mass. As measurements get more accurate, the value will change a bit over time. The mass of a particle and the molar mass of the pure substance made of those particles is proportional. The ratio of g/mol to Da, using current measurements, is 0.99999999965(30) times the Avogadro constant. So g/mol and dalton have different dimensions and can not be equal.
To say they are proportional does not make sense because both of them are units, not measurements. So while it makes sense to say that the mass and volume of samples of gold are proportional (at certain temperature and pressure), and call the proportionality factor the density of gold, it makes no sense to say that the units mL and g are proportional.
Yes, I acknowledge that your and @Loongs answer follow the current official interpretation of the definition of the mole, and mine does not. Anyway, the paper you linked by Klaus Schmidt-Rohr is a very good treatise on this issue (thank you for sharing) and I fully agree with his reasoning.More
I should have said differ by a factor of a pure number such as 1kg = 1000kg, they need to have the same dimension on each side for this to be true.More
The mole, symbol $\pu{mol},$ is the SI unit of amount of substance. One mole contains exactly $\pu{6.02214076E23}$ elementary entities. This number is the fixed numerical value of the Avogadro constant, $N_\mathrm{A}$, when expressed in the unit $\pu{mol^-1}$ and is called the Avogadro number.
So a mole is a short notation for a certain amount of molecules/atoms etc. In this respect, it is similar to a e.g. a dozen which is equal to 12 elementary entities.
The mole, symbol $\pu{mol},$ is the SI unit of amount of substance. One mole contains exactly $\pu{6.02214076E23}$ elementary entities. This number is the fixed numerical value of the Avogadro constant, $N_\mathrm{A}$, when expressed in the unit $\pu{mol^-1}$ and is called the Avogadro number.
So a mole is a short notation for a certain amount of molecules/atoms etc. In this respect, it is similar to a e.g. a dozen which is equal to 12 elementary entities.
Using the current official definition, you should not substitute a dimensionless number for the unit mole. A dozen is equal to 12, but a mole is not equal to the Avogadro number in the SI unit system. Thus, g/mol and Da are not equal in the SI system, and the given equation is incorrect. However, anyone is free to switch to another unit system; they just have to explicitly state it. (Quantum physicists for example like using the Hartree atomic units, which are all dimensionless.)More
drop the unit altogether also in chemistry, you then would have to work with very small numbers (masses) or large numbers (amounts). The unit is a very handy helper. Between $\ce{Da}$ and $\ce{g mol^{-1}}$, the latter spells out more explicitly how the mass is normalized.More
would we consider the dimension of g/mol to have equal dimension to mass in that case? I understand the idea of using dozen but a mole is specifically a unit of molecules or atoms, where a dozen is similar to just saying a grouping of 12 of any objects.More
According to ISO ISO/IEC 80000 Quantities and units, BIPM The International System of Units (SI), IUPAC Quantities, Units and Symbols in Physical Chemistry (Green Book), NIST Guide for the Use of the International System of Units (SI) etc., the quantity amount of substance is not dimensionless. Amount of substance and mass are two of the seven ISQ base quantities; the corresponding SI base units are the mole and the kilogram, respectively.
The quantity molar mass (quantity symbol: $M$) for a pure sample is defined as
$$M = m/n$$
where $m$ is mass and $n$ is amount of substance.
The dimension of the molar mass is
$$\dim M = \mathsf{M}\;\mathsf{N}^{-1}$$
The coherent SI unit for molar mass is ‘kilogram per mole’ (unit symbol: $\mathrm{kg/mol}$).
(The usually used unit is gram per mole ($\mathrm{g/mol}$) rather than kilogram per mole ($\mathrm{kg/mol}$).)
According to ISO ISO/IEC 80000 Quantities and units, BIPM The International System of Units (SI), IUPAC Quantities, Units and Symbols in Physical Chemistry (Green Book), NIST Guide for the Use of the International System of Units (SI) etc., the quantity amount of substance is not dimensionless. Amount of substance and mass are two of the seven ISQ base quantities; the corresponding SI base units are the mole and the kilogram, respectively.
The quantity molar mass (quantity symbol: $M$) for a pure sample is defined as$$M = m/n$$where $m$ is mass and $n$ is amount of substance. The dimension of the molar mass is$$\dim M = \mathsf{M}\;\mathsf{N}^{-1}$$The coherent SI unit for molar mass is ‘kilogram per mole’ (unit symbol: $\mathrm{kg/mol}$). (The usually used unit is gram per mole ($\mathrm{g/mol}$) rather than kilogram per mole ($\mathrm{kg/mol}$).)
According to the official definition, mole is a unit that has a dimension. This is counterintutitive perhaps given its definition ("the amount containing $\pu{6.02214076E23}$ particles"), but is has a dimension nonetheless.
The dalton is set as 1/12 of the mass of the 12-carbon isotope, so it has dimensions of a mass. As measurements get more accurate, the value will change a bit over time. The mass of a particle and the molar mass of the pure substance made of those particles is proportional. The ratio of g/mol to Da, using current measurements, is 0.99999999965(30) times the Avogadro constant. So g/mol and dalton have different dimensions and can not be equal.
To say they are proportional does not make sense because both of them are units, not measurements. So while it makes sense to say that the mass and volume of samples of gold are proportional (at certain temperature and pressure), and call the proportionality factor the density of gold, it makes no sense to say that the units mL and g are proportional.
According to the official definition, mole is a unit that has a dimension. This is counterintutitive perhaps given its definition ("the amount containing $\pu{6.02214076E23}$ particles"), but is has a dimension nonetheless.
The dalton is set as 1/12 of the mass of the 12-carbon isotope, so it has dimensions of a mass. As measurements get more accurate, the value will change a bit over time. The mass of a particle and the molar mass of the pure substance made of those particles is proportional. The ratio of g/mol to Da, using current measurements, is 0.99999999965(30) times the Avogadro constant. So g/mol and dalton have different dimensions and can not be equal.
To say they are proportional does not make sense because both of them are units, not measurements. So while it makes sense to say that the mass and volume of samples of gold are proportional (at certain temperature and pressure), and call the proportionality factor the density of gold, it makes no sense to say that the units mL and g are proportional.
More
VOTE
VOTE
VOTE
From the IUPAC Gold Book:
So a mole is a short notation for a certain amount of molecules/atoms etc. In this respect, it is similar to a e.g. a dozen which is equal to 12 elementary entities.
The unit of the molar mass is $\pu{g mol^-1}$. So, one could argue that indeed the unit Dalton, for which you also find a definition in the Gold Book, and $\pu{g mol^-1}$ are equal:
$$\frac{\pu{g mol^-1}}{\pu{Da}}=\frac{\pu{g}}{\pu{6.022E23}\times\pu{1.661E-24 g}}=1$$
From the IUPAC Gold Book:
So a mole is a short notation for a certain amount of molecules/atoms etc. In this respect, it is similar to a e.g. a dozen which is equal to 12 elementary entities.
The unit of the molar mass is $\pu{g mol^-1}$. So, one could argue that indeed the unit Dalton, for which you also find a definition in the Gold Book, and $\pu{g mol^-1}$ are equal:
$$\frac{\pu{g mol^-1}}{\pu{Da}}=\frac{\pu{g}}{\pu{6.022E23}\times\pu{1.661E-24 g}}=1$$
More
VOTE
VOTE
VOTE
VOTE
VOTE
VOTE
According to ISO ISO/IEC 80000 Quantities and units, BIPM The International System of Units (SI), IUPAC Quantities, Units and Symbols in Physical Chemistry (Green Book), NIST Guide for the Use of the International System of Units (SI) etc., the quantity amount of substance is not dimensionless. Amount of substance and mass are two of the seven ISQ base quantities; the corresponding SI base units are the mole and the kilogram, respectively.
The quantity molar mass (quantity symbol: $M$) for a pure sample is defined as $$M = m/n$$ where $m$ is mass and $n$ is amount of substance.
The dimension of the molar mass is $$\dim M = \mathsf{M}\;\mathsf{N}^{-1}$$ The coherent SI unit for molar mass is ‘kilogram per mole’ (unit symbol: $\mathrm{kg/mol}$).
(The usually used unit is gram per mole ($\mathrm{g/mol}$) rather than kilogram per mole ($\mathrm{kg/mol}$).)
According to ISO ISO/IEC 80000 Quantities and units, BIPM The International System of Units (SI), IUPAC Quantities, Units and Symbols in Physical Chemistry (Green Book), NIST Guide for the Use of the International System of Units (SI) etc., the quantity amount of substance is not dimensionless. Amount of substance and mass are two of the seven ISQ base quantities; the corresponding SI base units are the mole and the kilogram, respectively.
The quantity molar mass (quantity symbol: $M$) for a pure sample is defined as$$M = m/n$$where $m$ is mass and $n$ is amount of substance.
The dimension of the molar mass is$$\dim M = \mathsf{M}\;\mathsf{N}^{-1}$$The coherent SI unit for molar mass is ‘kilogram per mole’ (unit symbol: $\mathrm{kg/mol}$).
(The usually used unit is gram per mole ($\mathrm{g/mol}$) rather than kilogram per mole ($\mathrm{kg/mol}$).)
More
VOTE