Effect of redefining Avogadro's constant and kilogram on molar mass Avogadro's constant $N_\mathrm A$ is defined as the number of constituent particles (usually atoms or molecules) contained in the amount of substance given by one mole.

The value of Avogadro's constant $N_\mathrm A$ is going to be set to exactly $6.02214076\times 10^{23}\ \mathrm{mol}^{-1}$ in 2019. 

I might add that the kilogram is also going to be redefined in 2019 based on Planck's constant.

Will these changes result in the molar mass of a substance no longer being exactly equal to the molecular mass expressed in grams?
Will these changes result in the molar mass of a substance no longer being exactly equal to the molecular mass expressed in grams?


Yes. The ratio between the molar mass and the relative molecular mass is called the molar mass constant, and it used to be 1 g/mol exactly. Now that Avogadro's constant is set to a fixed value, it's value has to be determined experimentally.

NIST quotes its value as 0.999 999 999 65(30) x 10-3 kg mol-1 (CODATA 2018).

The relative molecular mass of the carbon-12 isotope is still exactly 12 and the atomic mass unit u (or dalton Da) is still defined as 1/12 of the mass of a carbon-12 atom, so the relationship between relative molecular mass and molecular mass still holds. However, its molar mass is no longer exactly 12 g/mol.

As @MaxW says in a comment, these changes are so minute that they have no practical implications outside of metrology (which was one of the goals of the International Bureau of Weights and Measures when they suggested the change).