Chapter 19, Problem 11A

Interpretation Introduction

Interpretation: The nuclear symbol of each isotope of sulfur has to be given. The number of neutrons present in each isotope has to be given and the consistency of the average atomic mass of sulfur with relative abundances of the isotopes has to be predicted.

Concept introduction: A different form of the same element is called an isotope. Isotopes of the same element contain the same number of protons and electrons but a different number of neutrons.

The atomic number of an element tells about the number of protons present.

  $\text{Atomic}\text{number}=\text{Number}\text{of}\text{protons}$

The number of protons present will be equal to the number of electrons.

  $\text{Number}\text{of}\text{protons}=\text{Number}\text{of}\text{electrons}$

The number of neutrons is the difference between the mass number and the atomic number.

  $\text{Number}\text{of}\text{neutrons}=\text{Mass}\text{number-Atomic}\text{number}$

The average atomic mass of a chemical element is calculated by multiplying the atomic masses of its natural isotopes with their respective abundance.

Answer to Problem 11A

The nuclear symbol of each isotope of sulfur is $\text{S},{}_{16}^{34}\text{S}$ and $\text{S}.$

The number of neutrons in sulfur-33 is $\text{17}\text{.}$

The number of neutrons in sulfur-34 is $\text{18}\text{.}$

The number of neutrons in sulfur-36 is $\text{20}\text{.}$

No, the average atomic mass of sulfur is in consistence with the relative abundances of the isotopes.

Explanation of Solution

The mass number is the sum of the protons and neutrons in the nucleus.

The atomic number is the number of protons present in the nucleus.

For an element $\text{E,}$ the top left number represents the mass number and the bottom-left number represents the atomic number.

  

The letter A represents the mass number.

The letter Z represents the atomic number.

Sulfur has an atomic number of 16 but the mass number varies.

For a mass number of 33, the nuclear symbol of the isotope is $\text{S}.$

For a mass number of 34, the nuclear symbol of the isotope is $\text{S}.$

For a mass number of 36, the nuclear symbol of the isotope is $\text{S}.$

The number of neutrons is the difference between the mass number and the atomic number.

  $\text{Number}\text{of}\text{neutrons=Mass}\text{number-Atomic}\text{number}$

For a mass number of 33, the neutrons is $33-16=17.$

For a mass number of 34, the neutrons is $34-16=18.$

For a mass number of 36, the neutrons is $36-16=20.$

The number of neutrons in sulfur-33 is $\text{17}\text{.}$

The number of neutrons in sulfur-34 is $\text{18}\text{.}$

The number of neutrons in sulfur-36 is $\text{20}\text{.}$

The average atomic mass of sulfur is $\text{32}\text{.07}\text{g}\text{.}$

The atomic mass of sulfur-33 and its relative abundance are $\text{32}\text{.971}\text{g}\text{\&}\text{0}\text{.76}\text{\%}$ respectively.

The atomic mass of sulfur-34 and its relative abundance are $\text{33}\text{.967}\text{g}\text{\&}4.22\text{\%}$ respectively.

The atomic mass of sulfur-36 and its relative abundance are $\text{35}\text{.967}\text{g}\text{\&}0.014\text{\%}$ respectively.

The average atomic mass can be calculated using the formula,

Average atomic mass= ${\sum }_i\left({\text{isotope}}_{\text{i}}\text{×abundance}\right)$

Average atomic mass=

  $\left(\text{32}\text{.971}\text{g×0}\text{.0076}\right)\text{+}\left(\text{33}\text{.967}\text{g×0}\text{.0422}\right)\text{+}\left(\text{35}\text{.967}\text{g+0}\text{.00014}\right)$

Average atomic mass= $\text{1}\text{.689}\text{g}$

Average atomic mass= $\text{1}\text{.7}\text{g}$

The average atomic mass of sulfur is not consistent with the relative abundances of the isotopes.

Conclusion

The nuclear symbol of each isotope of sulfur is $\text{S}{\text{, }}_{\text{16}}^{\text{34}}\text{S}$ and $\text{S}\text{.}$

The number of neutrons in sulfur-33 is $\text{17}\text{.}$

The number of neutrons in sulfur-34 is $\text{18}\text{.}$

The number of neutrons in sulfur-36 is $\text{20}\text{.}$

No, the average atomic mass of sulfur is in consistence with the relative abundances of the isotopes.