Question

Consider the following data for three binary compounds of hydrogen and nitrogen:

When 1.00 L of each gaseous compound is decomposed to its elements, the following volumes of H₂(g) and N₂(g) are obtained

Use these data to determine the molecular formulas of compounds I, II, and III and to determine the relative values for the atomic masses of hydrogen and nitrogen.

Short answer

The molecular formulas of compounds I, II, and IIIand to determine the relative values for the atomic masses of hydrogen and nitrogenare NH₃, N₂H₄, HN₃.

Step-by-step solution

Definition

The molar mass of a materialis defined as the mass of the substancecontained in one moleof the substance, and it is equal to the total massof the component atoms. It may be stated mathematically as follows:
Molar mass =$\frac{Weighting}{numberofmoles}$

Determination of compound I

We know the mass percentageof each element and the atomic mass of each, and we want to figure out how many atoms are in each molecule. If x is the number of N atoms and y is the number of H atoms, then:

$$\begin{gathered} 82.25\%=\frac{x\times 14.01}{x\times 14.01+y\times 1.008} \\ 82.908y=248.68x \\ y=3x\to y \\ =1 \\ x=3 \end{gathered}$$

Thus the Formula of compoundis NH₃.

Determination of compound II

We know the mass percentageof each element and the atomic mass of each, and we want to figure out how many atoms are in each molecule. If x is the number of N atoms and y is the number of H atoms, then:

$$\begin{gathered} 87.42\%=\frac{x\times 14.01}{x\times 14.01+y\times 1.008} \\ 88.12y=176.25x \\ 2y=4x \end{gathered}$$

Thus the Formula of compoundis N₂H₄.

Determination of compound III

We know the mass percentageof each element and the atomic mass of each, and we want to figure out how many atoms are in each molecule. If x is the number of N atoms and y is the number of H atoms, then:

$$\begin{gathered} 97.66\%=\frac{x\times 14.01}{x14.01+y\times 1.008} \\ 98.44y=32.78x \\ 3y=4x \end{gathered}$$

Thus the Formula of compoundis. HN₃.

Therefore, molecularformula compound I,II,III areNH₃, N₂H₄, HN₃.