# An unknown compound was found to have a percent composition as follows: 47.0% potassium, 14.5% carbon, and 38.5% oxygen. What is empirical formula? If the true molar mass of the compound is 166.22 g/mol, what is its molecular formula?

Mar 31, 2017

The $\text{empirical formula}$ is $K C {O}_{2}$

#### Explanation:

As with all these problems, we assume a $100 \cdot g$ mass of unknown compound, and then we work out the molar quantity:

$\text{Moles of potassium} = \frac{47.0 \cdot g}{39.10 \cdot g \cdot m o {l}^{-} 1} = 1.20 \cdot m o l$

$\text{Moles of carbon} = \frac{14.5 \cdot g}{12.011 \cdot g \cdot m o {l}^{-} 1} = 1.21 \cdot m o l$

$\text{Moles of oxygen} = \frac{38.5 \cdot g}{16.0 \cdot g \cdot m o {l}^{-} 1} = 2.41 \cdot m o l$

We divide thru by the smallest molar quantity to give the empirical formula:

$K C {O}_{2}$.

Now the molecular formula is always a whole number of the empirical formula:

i.e. $\text{molecular formula"=nxx"empirical formula}$

And thus with the molecular mass, we can solve for $n$.

$166.2 \cdot g \cdot m o {l}^{-} 1 = n \times \left(39.1 + 12.011 + 2 \times 16.00\right) \cdot g \cdot m o {l}^{-} 1$

$166.2 \cdot g \cdot m o {l}^{-} 1 = n \times \left(83.1\right) \cdot g \cdot m o {l}^{-} 1$

Clearly, $n = 2$, and the $\text{molecular formula} = {K}_{2} {C}_{2} {O}_{4}$

The compound is LIKELY the potassium salt of oxalic acid, K^(+)""^(-)O(O=)C-C(=O)O^(-)K^+, i.e. $\text{potassium oxalate.}$