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Chapter 2: Problem 36

Bromine has two naturally occurring isotopes, bromine- 79 (atomic mass \(=78.9183 \mathrm{u} ; \quad\) abundance \(=50.69 \%)\) a \(\mathrm{nd}\) bromine-81 \(\quad\) (atomic mass \(=80.9163 \mathrm{u} ;\) abundance \(=\) $49.31 \%) .$ Calculate the atomic weight of bromine.

Short Answer

Expert verified
The atomic weight of bromine can be calculated using the weighted average of its naturally occurring isotopes, bromine-79 and bromine-81. By multiplying the atomic masses of each isotope by their respective abundances in decimal form and then adding these contributions, we find that the atomic weight of bromine is approximately 79.8910 u.

Step by step solution

01

Determine the atomic mass of each isotope with its abundance.

First, we need to find the product of the atomic mass for bromine-79 and bromine-81 by their respective abundances provided in percentage. For bromine-79: Atomic mass = 78.9183 u Abundance = 50.69 % For bromine-81: Atomic mass = 80.9163 u Abundance = 49.31 %
02

Convert percentage abundance into decimal form.

To simplify calculations, we need to convert percentage abundance into decimal form. To do this, divide the percentage abundance by 100. For bromine-79: Abundance = 50.69 % / 100 = 0.5069 For bromine-81: Abundance = 49.31 % / 100 = 0.4931
03

Compute the contribution of each isotope's atomic mass to the atomic weight of bromine.

Multiply the atomic mass of each isotope by their corresponding abundance in decimal form. For bromine-79: Contribution = 78.9183 u * 0.5069 = 39.9943 u For bromine-81: Contribution = 80.9163 u * 0.4931 = 39.8967 u
04

Calculate the atomic weight of bromine.

Add the contributions of both isotopes to get the atomic weight of bromine. Atomic weight = Contribution of bromine-79 + Contribution of bromine-81 Atomic weight = 39.9943 u + 39.8967 u Atomic weight = 79.8910 u The atomic weight of bromine is approximately 79.8910 u.

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Most popular questions from this chapter

Using the periodic table to guide you, predict the chemical formula and name of the compound formed by the following elements: (a) Ga and F, (b) Li and H, (c) Al and I, \((\mathbf{d}) \mathrm{K}\) and S.

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of \(\mathrm{Br}_{2}\) molecules, and the mass of a \(\mathrm{Br}_{2}\) molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of \(\mathrm{Br}_{2}\) consists of three peaks: $$ \begin{array}{lc} \hline \text { Mass (u) } & \text { Relative Size } \\ \hline 157.836 & 0.2569 \\ 159.834 & 0.4999 \\ 161.832 & 0.2431 \\ \hline \end{array} $$ (a) What is the origin of each peak (of what isotopes does each consist)? (b) What is the mass of each isotope? (c) Determine the average molecular mass of a \(\mathrm{Br}_{2}\) molecule. (d) Determine the average atomic mass of a bromine atom. (e) Calculate the abundances of the two isotopes.

The diameter of a rubidium atom is \(495 \mathrm{pm}\) We will consider two different ways of placing the atoms on a surface. In arrangement A, all the atoms are lined up with one another to form a square grid. Arrangement B is called a close-packed arrangement because the atoms sit in the "depressions" formed by the previous row of atoms: (a) Using arrangement A, how many Rb atoms could be placed on a square surface that is \(1.0 \mathrm{~cm}\) on a side? \((\mathbf{b})\) How many \(\mathrm{Rb}\) atoms could be placed on a square surface that is \(1.0 \mathrm{~cm}\) on a side, using arrangement B? (c) By what factor has the number of atoms on the surface increased in going to arrangement \(\mathrm{B}\) from arrangement A? If extended to three dimensions, which arrangement would lead to a greater density for Rb metal?

Copper (Cu) consists of two naturally occurring isotopes with masses of 62.9296 and 64.9278 u. (a) How many protons and neutrons are in the nucleus of each isotope? Write the complete atomic symbol for each, showing the atomic number and mass number. (b) The average atomic mass of Cu is $63.55 \mathrm{u}$. Calculate the abundance of each isotope.

Write the chemical formula for each substance mentioned in the following word descriptions (use the front inside cover to find the symbols for the elements you do not know). (a) Zinc carbonate can be heated to form zinc oxide and carbon dioxide. (b) On treatment with hydrofluoric acid, silicon dioxide forms silicon tetrafluoride and water. (c) Sulfur dioxide reacts with water to form sulfurous acid. (d) The substance phosphorus trihydride, commonly called phosphine, is a toxic gas. (e) Perchloric acid reacts with cadmium to form cadmium(II) perchlorate. (f) Vanadium(III) bromide is a colored solid.
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