Chapter 10, Problem 90A

(a)

Interpretation Introduction

Interpretation: The atomic mass of element E needs to be determined.

Concept introduction: The relation between the number of moles and the atomic mass of an element is as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is atomic mass,

Explanation of Solution

According to the question, there are 15 boron atoms on the left-hand side of the balance are balanced by 6 atoms of an unknown element E on the right side. Thus, the mass of both elements is the same. Now, 1 mol of any substance contains the same number of atoms that is $6.022\times {10}^{23}$ . Thus, the ratio of the number of moles and the number of atoms will be the same.

This can be taken as if the number of moles of boron atom is 15, the number of moles of unknown element E will be 6 mol. Also, the mass of 15 mol of boron is equal to the mass of 6 mol of element E.

Now, the atomic mass of boron is 10.81 g/mol thus, the atomic mass of element E can be calculated as follows:

  $n=\frac{m}{M}$

Or,

  $m=n\times M$

Here, n is the number of moles, m is mass and M is molar mass. In the case of elements, M is the atomic mass.

Since the mass of both the elements is same, thus,

  $n_{\text{B}}\times M_{\text{B}}=n_{\text{E}}\times M_{\text{E}}$

Substitute the values,

  $\left(15\text{ mol}\right)\left(10.81\text{ g/mol}\right)=\left(6\text{ mol}\right)\times M_{\text{E}}$

Or,

  $\begin{array}{c}{M}_{\text{B}}=\frac{\left(15\text{ mol}\right)\left(10.81\text{ g/mol}\right)}{\left(6\text{ mol}\right)}\\ =27.025\text{ g/mol}\end{array}$

Therefore, the atomic mass of element E is $27.025\text{ g/mol}$ .

(b)

Interpretation Introduction

Interpretation: The element E needs to be identified.

Concept Introduction: All the elements in the periodic table have unique atomic numbers thus, the identity of an element can be easily determined if its atomic number is known. Atomic mass is approximately equal to twice the atomic number of an element. Thus, an idea of the identity of the element can also be given by knowing its atomic mass.

Explanation of Solution

The atomic mass of unknown element E is calculated as 27.025 g/mol. From the periodic table, this value corresponds to the element aluminum. Thus, the unknown element E is aluminum.