Question

How many electrons are transferred when: a) one \(\mathrm{Zn}\) atom reacts with one \(\mathrm{Cu}^{2+}\) ion? b) one mole of \(\mathrm{Zn}\) reacts with one mole of \(\mathrm{Cu}^{2+}\) ?

Short answer

a) Two electrons are transferred when one \(\mathrm{Zn}\) atom reacts with one \(\mathrm{Cu^{2+}}\) ion. b) 1.2044 x \(10^{24}\) electrons are transferred when one mole of \(\mathrm{Zn}\) reacts with one mole of \(\mathrm{Cu^{2+}}\).

Step-by-step solution

Determine the Number of Electrons Transferred in Atom-level Reaction

Identify the oxidation states of both \(\mathrm{Zn}\) and \(\mathrm{Cu^{2+}}\) before and after the reaction. \(\mathrm{Zn}\) has an oxidation state of 0, and \(\mathrm{Cu^{2+}}\) has an oxidation state of +2. During the reaction, \(\mathrm{Zn}\) loses two electrons (oxidation) and becomes \(\mathrm{Zn^{2+}}\) while \(\mathrm{Cu^{2+}}\) gains the two electrons (reduction) lost by \(\mathrm{Zn}\), becoming \(\mathrm{Cu}\). Thus, two electrons are transferred.

Determine the Number of Electrons Transferred in a Mole-level Reaction

Using Avogadro's number (6.022 x \(10^{23}\) atoms/mole), find the total number of \(\mathrm{Zn}\) atoms and \(\mathrm{Cu^{2+}}\) ions in one mole. One mole of \(\mathrm{Zn}\) atoms or \(\mathrm{Cu^{2+}}\) ions contains 6.022 x \(10^{23}\) entities. Each \(\mathrm{Zn}\) atom transfers 2 electrons, so the total number of electrons transferred when one mole of \(\mathrm{Zn}\) reacts with one mole of \(\mathrm{Cu^{2+}}\) is 2x 6.022 x \(10^{23}\) = 1.2044 x \(10^{24}\).

Key concepts

Oxidation State

Understanding oxidation states is crucial in determining how elements interact in chemical reactions. The oxidation state, often referred to as oxidation number, indicates the degree of oxidation of an atom in a compound. It represents the number of electrons an atom can gain, lose, or share to form a chemical bond.

In the example reaction, zinc (\(\mathrm{Zn}\)) starts with an oxidation state of 0 because it is in its elemental form. On the other hand, copper (\(\mathrm{Cu^{2+}}\)) has an oxidation state of +2, meaning it has lost two electrons. This difference in oxidation states reveals which atoms will undergo oxidation or reduction during the reaction.

When \(\mathrm{Zn}\) reacts with \(\mathrm{Cu^{2+}}\), \(\mathrm{Zn}\) loses two electrons, increasing its oxidation state to +2. Meanwhile, \(\mathrm{Cu^{2+}}\) gains those two electrons, reducing its oxidation state to 0. Identifying these changes helps predict the flow of electrons between reactants.

Redox Reaction

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between substances. They are central to understanding chemical processes, such as reactions in batteries and biological systems.

In a redox reaction, one substance loses electrons (oxidation) while another gains electrons (reduction). It's important to remember:

• Oxidation involves the loss of electrons.
• Reduction involves the gain of electrons.
• The number of electrons lost equals the number of electrons gained.

In the zinc and copper reaction, zinc gets oxidized as it loses two electrons, while copper ions are reduced by gaining those same electrons. This electron exchange forms the basis of many essential chemical processes.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, representing the number of atoms, molecules, or ions in one mole of a substance. This number is approximately \(6.022 \times 10^{23}\), allowing chemists to relate macroscopic quantities of materials to their molecular scales.

In the context of electron transfer, Avogadro's number helps determine the total number of electrons exchanged in reactions involving moles of substances. For example, when one mole of zinc reacts with one mole of copper ions, each zinc atom transfers two electrons. Given one mole comprises \(6.022 \times 10^{23}\) atoms, the total electron transfer amounts to \(2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{24}\) electrons.

Understanding Avogadro’s number is essential for converting between atomic and macroscopic scales, ensuring precise calculations in chemical reactions.