Question

A substancehas X₂Z the composition (by mass) of 40.0% X and 60.0% Z. What is the composition (by mass) of the compound XZ₂ ?

Short answer

Thecomposition (by mass) of the compound XZ₂is 85.7%.

Step-by-step solution

Definition

The mass percent of an atomin a compound is equal to the ratio of the atom's total mass to the complex's total mass multiplied by 100. As a result, it may be stated as follows:

Mass percent of an atom =$\left(\frac{totalmassofthatom}{totalmassofthesubs\tan ce}\right)100$

Determination of mass of 1 molecule of Z

Here the composition of X₂Z is,

X - 40.0% and Z - 60.0%

Thus the mass ofX in 100.0g of X₂Z - 40.0g

Mass ofZ in 100.0 ofX₂Z - 40.0g

From the given, the compound X₂Z has 2 moles of X for each moles of Z.

Thus the ratio of moles of X to Z in the compoundX₂Z is given below,

$$\begin{gathered} \frac{MolX}{MolZ}=\frac{2}{1} \\ =\frac{{\displaystyle \frac{40.0gX}{massof1milofX}}}{{\displaystyle \frac{60.0gZ}{massof1MolofZ}}} \end{gathered}$$

Let’s rearrange as,

$$\begin{gathered} \Rightarrow \frac{{\displaystyle \frac{40.0gX}{massof1molofX}}}{{\displaystyle \frac{60.0gZ}{massof1molofZ}}}=2 \\ massof1molofZ=3(massof1molofX)-----\left(1\right) \end{gathered}$$

Determination of composition of XZ2 by mass

Let’s compute the composition ofXZ₂,

mass of 1 mol ofXZ₂ = (mass of 1 mol of X) + 2(mass of 1 mol of Z)

From equation (1),

= (mass of 1 mol of X) + 2{3(mass of 1 mol of X)}

= 7 (mass of 1 mol of X) -----(2)

Mass percent of$X=\left(\frac{massofX1molX{Z}_2}{massof1molX{Z}_2}\right)100\%$

$$\begin{gathered} =\left(\frac{massofX1molX{Z}_2}{7massof1molX{Z}_2}\right)100\% \\ =\left(\frac{1}{7}\right)\times 100\% \\ =14.3\% \end{gathered}$$

Mass percent of Z = (100.0-14.3)%

Therefore the mass percent of Zis 85.7%.