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I ran into the following problem, wherein I'm asked to find the simplest formula of a compound containing $50 \%$ of element $X$ (atomic wt. 10) and $50\%$ of element $Y$ (atomic wt. 20).

I know about few laws of chemical combinations. I think Law of Definite Proportions may come into play.

$$\text{atomic wt. }X:\text{atomic wt. } Y=1:2\implies XY_2$$

Am I correct in my reasoning? If not kindly point out the flaws, if any? Thanks

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    $\begingroup$ The first thing to ask is % of what? If this is mass percent you will get a different answer than you would get if the percentage is expressed in moles. $\endgroup$
    – matt_black
    Commented Apr 11, 2019 at 9:01
  • $\begingroup$ Could you tell me what the answer would be in each case. The solution is given to be $X_2Y$ $\endgroup$
    – Paras Khosla
    Commented Apr 11, 2019 at 15:56

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$$M=\frac{m}{n}\ \curvearrowright\ m=M\cdot n$$

$$M_X=10\ g\ mol^{-1},\ M_Y=20\ g\ mol^{-1}$$

$$\frac{m_X}{m_X+m_Y}=50\ \%,\ \frac{m_Y}{m_X+m_Y}=50\ \%:$$

$$m_X=m_Y$$

$$M_X\cdot n_X=M_Y\cdot n_Y$$

$$\frac{n_X}{n_Y}=\frac{M_Y}{M_X}=\frac{20\ g\ mol^{-1}}{10\ g\ mol^{-1}}=2$$

$$n_X=2\ n_Y$$

$$\curvearrowright\ X_2Y$$

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