Chapter 4, Problem 4.47FU

(a)

Interpretation Introduction

Interpretation:

The group number and name of the group that contains potassium should be identified.

Concept Introduction:

In the modern periodic table, the vertical columns are known as groups and the horizontal rows are known as periods. The group of an element is determined by the number of its valence electrons and the period of an element is based on the principal quantum number of the valence shell of the element.

Answer to Problem 4.47FU

The group number is 1 and the name is alkali metals group that contains potassium.

Explanation of Solution

The group number of an element is determined by the number of its valence electrons.

The electron configuration of K (potassium) is $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^1$ .

Potassium contains 1 electron in the valence shell. For this reason, the group number of potassium is 1.

The name of group 1 of the periodic table is alkali metals group.

(b)

Interpretation Introduction

Interpretation:

Whether potassium is a metal, a nonmetal, or a metalloid should be determined.

Concept Introduction:

Elements that easily lose electron(s) due to which they conduct electricity are said to be metals. Metals are shiny, ductile, and malleable and conduct heat.

Answer to Problem 4.47FU

Potassium is a metal.

Explanation of Solution

The electron configuration of K (potassium) is $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^1$ .

Potassium readily loses valence electron (4s¹) and attains stability due to easy loss of electron potassium is a metal also it is a good conductor of heat and electricity, shiny, malleable and ductile.

(c)

Interpretation Introduction

Interpretation:

The number of protons in a potassium atom should be determined.

Concept Introduction:

The atomic number of an element is the number of protons present in the nucleus of one atom of the element. It is also equal to the number of electrons revolving around the nucleus of a neutral atom.

Answer to Problem 4.47FU

There are 19 protons in an atom of potassium.

Explanation of Solution

The atomic number of potassium is 19. This means, one atom of potassium contains 19 protons in its nucleus. For this reason, there are 19 protons in an atom of potassium.

(d)

Interpretation Introduction

Interpretation:

The most prevalent isotope of potassium should be identified.

Concept Introduction:

Most of the elements have two or more than two isotopes. Isotopes are the atoms that have different mass number for an element which is due to presence of different number of neutrons in their nuclei. The relative abundance of isotopes varies in nature.

Answer to Problem 4.47FU

The most prevalent isotope of potassium is $K$ .

Explanation of Solution

The percent abundance of the isotope $K$ of potassium is 93.26% which is the highest percent abundance value for potassium. For this reason, the most prevalent isotope of potassium is $K$ .

(e)

Interpretation Introduction

Interpretation:

The atomic mass of potassium should be calculated from the naturally occurring isotopes and their abundance by using the weighted average mass method.

Concept Introduction:

Most of the elements have two or more than two isotopes. Isotopes are the atoms that have different mass number for an element which is due to presence of different number of neutrons in their nuclei. The relative abundance of isotopes varies in nature. For this reason, the atomic mass of an element is calculated by multiplying the mass of each isotope by its percentage abundance value and then adding all those values for all isotopes of the element.

Answer to Problem 4.47FU

The atomic mass of potassium is 39.09 amu.

Explanation of Solution

The percent abundance values and mass for each isotope of potassium are as follows:

  $K$ = 93.26%, 38.964 amu

  $K$ = 0.0117%, 39.964 amu

  $K$ = 6.73%, 40.962 amu

Therefore, the atomic mass of potassium

  $\begin{array}{l}=\frac{\left(93.26\times 38.964\right)+\left(0.0117\times 39.964\right)+\left(6.73\times 40.962\right)}{100}\\ =39.09\end{array}$

Therefore, the atomic mass of potassium is 39.09 amu.