Question

You have two distinct gaseous compounds made from element X and element Y. The mass percents are as follows:

Compound I:$\mathbf{30}.\mathbf{43}\%\mathbf{X},\mathbf{69}.\mathbf{57}\%\mathbf{Y}$

Compound II:$\mathbf{63}.\mathbf{64}\%\mathbf{X},\mathbf{36}.\mathbf{36}\%\mathbf{Y}$

In their natural standard states, element X and element Y exist as gases. (Monoatomic?Diatomic?Triatomic? That is for you to determine.) When you react "gas Y" to make the products, you get the following data (all at standard pressure and temperature):

1.$\mathbf{volume}\mathbf{}\mathbf{"}\mathbf{gas}\mathbf{}\mathbf{X}\mathbf{"}\mathbf{+}\mathbf{2}\mathbf{}\mathbf{volume}\mathbf{}\mathbf{"}\mathbf{gas}\mathbf{}\mathbf{Y}\mathbf{"}\to \mathbf{2}\mathbf{}\mathbf{volume}\mathbf{}\mathbf{compound}\mathbf{}\mathbf{I}$

2.$\mathbf{volume}\mathbf{}\mathbf{"}\mathbf{gas}\mathbf{X}\mathbf{"}+\mathbf{1}\mathbf{volume}\text{"}\mathbf{gas}\mathbf{Y}\mathbf{"}\to \mathbf{2}\mathbf{volume}\mathbf{compound}\mathbf{II}$

Assume the simplest possible formulas for reactants and products in these chemical equations. Then determine the relative atomic masses of element X and element Y.

Short answer

The relative mass is$\text{X = 39.38g,} \text{Y = 70.62g}$.

Step-by-step solution

Composition of compounds

Assume 100g of each compound, by giving the mass percent of each compound.

Compound 1:$\text{30.43\% X ,69.57\% Y}$

Compound 2:$\text{63.64\% X, 36.36\% Y}$

Relation between compounds

The following two relations are summed mathematically.

$$\begin{gathered} \text{X + 2Y}\to \text{2}\left[\text{Compound1}\right] \\ \text{2X + Y}\to \text{2}\left[\text{Compound2}\right] \end{gathered}$$

Calculations of relative atomic masses

As assumed, there is 100g of each compound. Substitute the values of compounds 1 and 2 in the respective equations as follows:

$$\begin{gathered} \text{X + 2Y}\to \text{2}\left[\text{30.43g} \text{X + 69.57g} \text{Y}\right] \\ \text{2X + Y}\to \text{2}\left[\text{63.6} \text{X+ 36.36g} \text{Y}\right] \end{gathered}$$

Add the equations to obtain,

$\text{3X + 3Y = 118.14X + 211.86gY}$

Divide the equation by 3 to obtain,

$\text{X + Y = 39.38gX + 70.62gY}$

Conclusion

Hence, the relative mass is$\text{X = 39.38g,Y = 70.62g}$