Question

Total number of electrons present in \(4.4 \mathrm{~g}\) oxalate ion \(\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right)\) is (a) \(0.05 N_{\mathrm{A}}\) (b) \(2.3 N_{\mathrm{A}}\) (c) \(2.2 N_{\mathrm{A}}\) (d) \(2.1 N_{\mathrm{A}}\)

Short answer

The total number of electrons present is approximately \(2.2 N_{\text{A}}\), making option (c) the correct answer.

Step-by-step solution

Determine Molar Mass

Calculate the molar mass of the oxalate ion (C2O4^2-). Carbon (C) has a molar mass of approximately 12.01 g/mol, and Oxygen (O) has a molar mass of 16.00 g/mol. The oxalate ion has 2 Carbons and 4 Oxygens, so its molar mass is (2*12.01)+(4*16.00) g/mol.

Calculate Moles of Oxalate Ion

Use the molar mass from Step 1 to convert the mass of oxalate ion to moles: moles = mass (4.4 g) / molar mass of C2O4^2-.

Count the Total Electrons in Oxalate Ion

Each Carbon contributes with 6 electrons and each Oxygen with 8 electrons. Adding the 2 extra electrons for the charge gives a total of (2*6) + (4*8) + 2 electrons per molecule of C2O4^2-.

Calculate Total Electrons in Moles of Oxalate Ion

Multiply the total number of electrons per molecule from Step 3 by Avogadro's number (NA) to find the number of electrons per mole, then multiply by the number of moles of C2O4^2- obtained in Step 2.

Determine the Correct Answer

Compare the calculated number of electrons to the given options. The closest value that corresponds to the calculated number will be the correct answer.

Key concepts

Molar Mass Calculation

Understanding the molar mass calculation is crucial in chemistry to relate the mass of a substance to the number of particles it contains. Start by recognizing that the molar mass of a compound is the sum of the atomic masses of its constituent elements. In the context of the given exercise, the oxalate ion, \(C_2O_4^{2-}\), consists of carbon and oxygen atoms. The atomic mass of carbon is approximately 12.01 g/mol, and for oxygen, it is about 16.00 g/mol. The total molar mass of the oxalate ion is calculated by the formula:
\[ \text{Molar Mass of } C_2O_4^{2-} = (2 \times \text{Molar Mass of Carbon}) + (4 \times \text{Molar Mass of Oxygen}) \]
By substituting the atomic masses, you get the molar mass of the oxalate ion, which plays a seminal role in converting grams to moles in subsequent steps of the solution.

Avogadro's Number

Avogadro's number, denoted as \(N_A\), is a constant that provides a link between the microscale and macroscale worlds of chemistry. Specifically, \(N_A\) is \(6.022 \times 10^{23}\) entities per mole, which serves as a bridge between the number of particles and the amount of substance in moles. When dealing with electrons in the oxalate ion, you not only count them individually but also relate their number to the mole concept. By multiplying the number of electrons in a single ion by Avogadro's number, you can establish the total number of electrons in one mole of ions, further applying this in real-world quantitative calculations, as seen in the exercise.

Stoichiometry

Stoichiometry is the quantifiable study of reactants and products in chemical reactions. It involves calculating quantities, such as mass or number of moles, often requiring an understanding of the balanced chemical equation. While the current exercise does not directly entail a reaction, the principle of stoichiometry is still applied. The calculation relies on the stoichiometry of the oxalate ion itself, considering the number of carbon and oxygen atoms it contains as well as the total charge, to determine the number of electrons involved. This familiarity with stoichiometric calculations aids in comprehensively interpreting the exercise and arriving at the correct answer.

Moles to Mass Conversion

The process of converting moles to mass is a frequent task in chemistry, essential for relating the measurable quantity of a substance to its number of particles or molecules. Based on the mole concept and the compound's molar mass, you can determine the mass from the number of moles or vice versa. In our exercise, we start with the known mass of oxalate ions and use the previously calculated molar mass to decipher the number of moles:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
By converting the mass of oxalate ions (4.4 g) to moles, you establish a foundation for the final calculation of the total number of electrons present. This straightforward yet fundamental conversion lays the groundwork for understanding more complex chemical scenarios.