Mass of Mole of Substance

Theorem

Let $S$ be a substance with molecular weight $W_S$.

Then one mole of $S$ has a mass of $W_S$ grams.

Let $m_S$ grams be the mean mass of one molecule of $S$.

Let $m_C$ grams be the mass of one atom of carbon-12.

Let $M_S$ grams be the mass of one mole of $S$.

Let $M_C$ grams be the mass of one mole of carbon-12.

Then:

$\ds W_S$

$=$

$\ds m_S \times \dfrac {12} {m_C}$

$\ds $

$=$

$\ds M_S \times \dfrac {12} {M_C}$

$\text {(1)}: \quad$

$\ds \leadsto \ \ $

$\ds M_S$

$=$

$\ds W_S \times \dfrac {M_C} {12}$

Before $2018$, the mole was defined as the number of atoms in $12$ grams of carbon-12.

While the mole is no longer so defined, the mass of $1$ mole of carbon-12 is still $12$ grams, for all practical purposes.

Thus we have:

$\ds M_C$

$=$

$\ds 12 \ \mathrm g$

$\ds \leadsto \ \ $

$\ds M_S$

$=$

$\ds W_S \dfrac {12 \ \mathrm g} {12}$

substituting for $M_C$ in $(1)$

$\ds \leadsto \ \ $

$\ds M_S$

$=$

$\ds W_S \ \mathrm g$

$\blacksquare$