# XCl_3 contains 67.2% chlorine by mass. Calculate the molar mass of X and identity the element. ?

Oct 4, 2017

Element $X$ has a molar mass of approximately $52$ $g m o {l}^{-} 1$ and is chromium ($C r$).

#### Explanation:

We can proceed as though we have one mole of $X C {l}_{3}$.

The molar mass of chlorine is $35.5$ $g m o {l}^{-} 1$, and 3 mol of $C l$ will therefore have a mass of $3 \times 35.5 = 106.5$ $g$.

To find the mass of one mole of $X C {l}_{3}$, when this makes up $67.2$%, we multiply by $\frac{100}{67.2}$:

$106.5 \times \left(\frac{100}{67.2}\right) = 158.48$

This is the molar mass of one mole of $X C {l}_{3}$. To find the molar mass of $X$ we subtract the mass of the chlorine:

$158.48 - 106.5 = 51.98$

We need the element whose molar mass is closest to $52$. Looking at a periodic table, we find that that is chromium ($C r$).