Question

A $2\cdot 38$g of uranium is strongly heated in a current of air. The resulting oxide will weigh $2\cdot 806$g. Determine the empirical formula of compound.

Answer 1

Hint:First find the mass of oxygen present in the resulting oxide by subtracting the given mass of uranium from the oxide. Then find the no. of moles for uranium and oxygen by dividing their given masses in oxide by their atomic masses. Obtain the simple whole no. ratio to get the empirical formula.

Complete step by step answer:
The given mass of uranium in the oxide is $2\cdot 38$g and the mass of oxide is $2\cdot 806$g. So, the mass of oxygen in this resulting oxide = mass of oxide – mass of uranium
 $\begin {align}
  &\text{Mass of oxygen in oxide} =2\cdot 806-2\cdot 38 \\
 & =0\cdot 426 \\
\end{align}$
Finding the no. of moles for uranium we have, no. of moles = given mass/molar mass
No. of moles of uranium in oxide $=\dfrac{2\cdot 38}{238}=0\cdot 01$ (atomic mass of uranium $=238$)
 No. of moles of oxygen in oxide $=\dfrac{0\cdot 426}{16}=0\cdot 027$ (atomic mass of oxygen is$=16$)
Converting these ratios into simple ratios by dividing both the ratios with the smallest ratio between the two i.e. with $0\cdot 01$
So, for uranium we get $\dfrac{0\cdot 01}{0\cdot 01}=1$
And for oxygen we get $\dfrac{0\cdot 027}{0\cdot 01}=2\cdot 7$
For empirical formula both the ratios should be the whole number ratio so multiplying $2\cdot 7$ with $3$ to get its nearest whole number ratio and correspondingly the ratio of uranium should also be multiplied by $3$
Therefore we get, simple whole no. ratio for uranium $=1\times 3=3$
And simple whole no. ratio for oxygen$=2\cdot 7\times 3=8$
So, the formula for resulting oxide includes $3$moles of uranium and $8$moles of oxygen i.e. ${{U} _{3}} {{O}_ {8}} $.

Additional Information:
 Empirical formula tells us about the simplest ratio of elements in the compound whereas molecular formula tells us about the total no. of atoms of an element present in the compound. The empirical formula for two compounds can be similar as it is the simplest ratio of its constituent elements but two different compounds can never have the same molecular formula.

Note:
The empirical formula should always be in the whole number values. The method to find empirical formula includes, finding the no. of moles of constituent elements and then converting them into simple whole number ratios. Molecular formula provides more information about a compound than empirical formula because it tells us about the exact no. of atoms of an element present in the compound. One should study about the atomic masses for different elements.