Chapter 9, Problem 59A

Interpretation Introduction

Interpretation: The balanced chemical equation and the element $\text{X}$ are to be stated.

Concept Introduction: The formula to calculate the number of moles is given as shown below:

  $\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Answer to Problem 59A

The element $\text{X}$ is $\text{P}$ .

Explanation of Solution

It is given that ${\text{X}}_4$ reacts with $\text{HCl}$ to form ${\text{XCl}}_3$ and hydrogen gas. Therefore, the complete balanced reaction is as follows.

  ${\text{X}}_4+\text{HCl}\to 4{\text{XCl}}_3+6{\text{H}}_{\text{2}}$

The given value of mass of hydrogen gas is $\text{24}\text{.0}\text{g}$ . The molar mass of hydrogen is $\text{2}\text{.01588}\text{g}/\text{mol}$ .

Substitute the given values in the above formula to calculate number of moles of hydrogen.

  $\begin{array}{c}\text{Number of moles}=\frac{24.0\text{g}}{2.01588\frac{\text{g}}{\text{mol}}}\\ =11.90\text{mol}\end{array}$

The balanced chemical reaction shows that one mole of ${\text{X}}_4$ form six moles of hydrogen. Therefore, the number of moles required for is,

  $\begin{array}{c}\text{1}\text{mol}{\text{X}}_4=6\text{mol}{\text{H}}_{\text{2}}\\ 1\text{mol}{\text{H}}_{\text{2}}=\frac{\text{1}}{6}\text{mol}{\text{X}}_4\\ 11.90\text{}\text{mol}{\text{H}}_{\text{2}}=11.90\times \frac{\text{1}}{6}\text{mol}{\text{X}}_4\\ =1.98\text{moles}\end{array}$

Therefore, the molar mass of ${\text{X}}_4$ is as follows.

  $\begin{array}{c}\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}\\ 1.98\text{mol}=\frac{248\text{g}}{\text{Molar mass}}\\ \text{Molar mass}=\frac{248\text{g}}{1.98\text{mol}}\\ =125.25\text{g}/\text{mol}\end{array}$

The calculated molar mass is similar to the molar mass of ${\text{P}}_4$ . Therefore, the element $\text{X}$ is $\text{P}$ .

Conclusion

Thus, the element $\text{X}$ is $\text{P}$ .