Chapter 6, Problem 3STP

Interpretation Introduction

Interpretation: The mystery metal needs to be identified, if 20.0 g of mystery metal contains 4 times as many atoms as there are in 20.0 g of silver metals.

Concept Introduction: The molecular mass of compound is the sum of atomic mass of all the atoms present in the given chemical compound. Mole concept is used to calculate the moles, mass, number of atoms and moles of a compound. The relation between these values can be shown as:

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ {\text{1 mole = N}}_{\text{a}}\text{ atoms}\\ {\text{N}}_{\text{a}}\text{ = 6}\text{.022 }\times {\text{ 10}}^{\text{23}}\end{array}$

Answer to Problem 3STP

Correct answer: Option (D)

Explanation of Solution

Reason for correct option:

Mass of silver metal = 20.0 g

Molar mass of silver = 108 g/mol

Mass of mystery metal = 20.0 g

Number of atoms of mystery metal = 4 x number of atoms of silver

Thus moles of mystery metal = 4 x moles of silver

Calculate moles of silver-

  $\begin{array}{l}\text{Moles = }\frac{\text{mass}}{\text{molar mass}}\\ \text{Moles = }\frac{\text{20}\text{.0 g}}{\text{108 g/mol }}\text{=0}\text{.185moles}\end{array}$

Calculate moles of mystery metal:

  $\begin{array}{l}\text{Number of atoms of mystery metal = 4 }\times \text{ number of atoms of silver}\\ \text{Moles of mystery metal = 4 }\times \text{ Moles of silver}\\ \text{Moles of mystery metal = 4 }\times \text{ 0}\text{.185moles}\\ \text{Moles of mystery metal = }0.741\text{moles}\end{array}$

Calculate molar mass of mystery metal:

  $\text{Molar mass of mystery metal = }\frac{\text{20}\text{.0g}}{\text{0}\text{.741moles}}\text{=27}\text{.0g/mol}$

The metal with molar mass 27.0 g/mol is Aluminium.

Conclusion

Reasons for incorrect options: Since the molar mass of iron is 55.8g/mol, platinum is 195 g/mol and lithium is 6.94 g/mol therefore they are not mystery metal.