Question

(a) What is the mass, in grams, of one mole of \({ }^{79} \mathrm{Br}\) ? (b) How many bromine atoms are present in one mole of \({ }^{79} \mathrm{Br}\) ?

Short answer

(a) The mass of one mole of bromine-79 is 79 g. (b) There are \(6.022 \times 10^{23}\) bromine atoms in one mole of bromine-79.

Step-by-step solution

(a) Determine the mass of one mole of bromine-79

To determine the mass of one mole of bromine-79, we need to know the atomic mass of bromine-79. The atomic mass of an isotope is approximately equal to its mass number, and the given isotope is \({ }^{79} \mathrm{Br}\) , which has a mass number of 79. Therefore, the atomic mass of bromine-79 is 79 atomic mass units (amu). To convert this to grams, we will use the definition of a mole, which states that one mole of a substance contains Avogadro's number (\(6.022 \times 10^{23}\)) of particles and has a mass in grams equal to the atomic mass in amu. So: Mass of one mole of bromine-79 = Atomic mass in amu × 1 g/mol = 79 amu × 1 g/mol

(a) Calculate the mass in grams

Now that we have the formula, we can calculate the mass of one mole of bromine-79: Mass of one mole of bromine-79 = 79 g/mol This means that one mole of bromine-79 has a mass of 79 grams.

(b) Determine the number of bromine atoms in one mole of bromine-79

We know that one mole of a substance contains Avogadro's number of particles. So, in our case, one mole of bromine-79 contains Avogadro's number of bromine atoms. This can be calculated as: Number of bromine atoms in one mole of bromine-79 = Avogadro's number = \(6.022 \times 10^{23}\) atoms This means that one mole of bromine-79 contains \(6.022 \times 10^{23}\) bromine atoms.

Key concepts

Atomic Mass

The atomic mass is a fundamental concept in chemistry that refers to the mass of an atom, typically expressed in atomic mass units (amu). For any given element, the atomic mass can be found on the Periodic Table and represents the weighted average of all naturally occurring isotopes of that element. However, when discussing a specific isotope, like bromine-79 \((^{79}\text{Br})\), the atomic mass is nearly equal to its mass number.

The mass number is the sum of protons and neutrons in an atom's nucleus. Bromine-79, for example, has a mass number of 79, meaning its atomic mass in amu is approximately 79. When calculating the mass of one mole of a substance, the atomic mass in amu can be converted directly to grams per mole. Therefore, the mass of one mole of bromine-79 is 79 grams, which correlates directly with the atomic mass of the isotope.

Avogadro's Number

Named after the scientist Amedeo Avogadro, Avogadro's number is a constant that is pivotal in the field of chemistry. It describes the number of atoms, ions, or molecules contained in one mole of a substance, which is exactly \(6.022 \times 10^{23}\) particles.



This incredibly large number helps bridge the gap between the macroscopic amounts of material we can see and the microscopic world of atoms and molecules. In essence, when you have one mole of any substance, whether it's an element like bromine or a compound like water, you have \(6.022 \times 10^{23}\) basic units of that substance.



For bromine-79, this means that one mole, which weighs 79 grams, contains \(6.022 \times 10^{23}\) bromine atoms. Avogadro's number allows chemists to count particles by weighing them, making it an extremely powerful tool for understanding chemical reactions and stoichiometry.

Isotopes

Isotopes are variants of a particular chemical element that share the same number of protons and, therefore, the same atomic number, but have different numbers of neutrons. This variance in neutron number means that isotopes of an element have different mass numbers.

For example, the element bromine has two stable isotopes: bromine-79 \((^{79}\text{Br})\) and bromine-81 \((^{81}\text{Br})\). Though they share the same atomic number of 35, bromine-79 has 44 neutrons while bromine-81 has 46 neutrons. Thus, their mass numbers are 79 and 81, respectively.



Isotopes are significant because they can exhibit different physical or chemical properties. In nuclear chemistry, isotopes can be especially important, as some may be stable while others are radioactive. When calculating atomic mass for elements with naturally occurring isotopes, the atomic mass is a weighted average in amu, reflecting the abundance of each isotope. This is why elements often have non-integer atomic masses on the periodic table.