Question

Calculate the molecular mass or formula mass (in amu) of each of the following substances: (a) \(\mathrm{Li}_{2} \mathrm{CO}_{3},\) (b) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (c) \(\mathrm{NF}_{2}\), (d) \(\mathrm{Al}_{2} \mathrm{O}_{3}\) (e) \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) (f) \(\mathrm{PCl}_{5}\) (g) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}\)

Short answer

(a) 73.89 amu, (b) 30.08 amu, (c) 52.01 amu, (d) 101.96 amu, (e) 241.88 amu, (f) 208.22 amu, (g) 100.95 amu.

Step-by-step solution

List Atomic Masses

To begin, list the atomic masses of all elements involved in the compounds based on the periodic table: - Lithium (Li): 6.94 amu - Carbon (C): 12.01 amu - Oxygen (O): 16.00 amu - Hydrogen (H): 1.01 amu - Nitrogen (N): 14.01 amu - Fluorine (F): 19.00 amu - Aluminum (Al): 26.98 amu - Iron (Fe): 55.85 amu - Phosphorus (P): 30.97 amu - Chlorine (Cl): 35.45 amu - Magnesium (Mg): 24.31 amu.

Calculate for Li2CO3

Use the formula for lithium carbonate: - Two lithium atoms: \(2 \times 6.94 = 13.88\) amu - One carbon atom: \(1 \times 12.01 = 12.01\) amu - Three oxygen atoms: \(3 \times 16.00 = 48.00\) amu - Total: \(13.88 + 12.01 + 48.00 = 73.89\) amu.

Calculate for C2H6

For ethane, use its chemical formula: - Two carbon atoms: \(2 \times 12.01 = 24.02\) amu - Six hydrogen atoms: \(6 \times 1.01 = 6.06\) amu - Total: \(24.02 + 6.06 = 30.08\) amu.

Calculate for NF2

Finding the formula mass of nitrogen difluoride: - One nitrogen atom: \(1 \times 14.01 = 14.01\) amu - Two fluorine atoms: \(2 \times 19.00 = 38.00\) amu - Total: \(14.01 + 38.00 = 52.01\) amu.

Calculate for Al2O3

Use the formula for aluminium oxide: - Two aluminium atoms: \(2 \times 26.98 = 53.96\) amu - Three oxygen atoms: \(3 \times 16.00 = 48.00\) amu - Total: \(53.96 + 48.00 = 101.96\) amu.

Calculate for Fe(NO3)3

For iron(III) nitrate, calculate as follows: - One iron atom: \(1 \times 55.85 = 55.85\) amu - Three nitrogen atoms: \(3 \times 14.01 = 42.03\) amu - Nine oxygen atoms: \(9 \times 16.00 = 144.00\) amu - Total: \(55.85 + 42.03 + 144.00 = 241.88\) amu.

Calculate for PCl5

For phosphorus pentachloride: - One phosphorus atom: \(1 \times 30.97 = 30.97\) amu - Five chlorine atoms: \(5 \times 35.45 = 177.25\) amu - Total: \(30.97 + 177.25 = 208.22\) amu.

Calculate for Mg3N2

For magnesium nitride, use its composition: - Three magnesium atoms: \(3 \times 24.31 = 72.93\) amu - Two nitrogen atoms: \(2 \times 14.01 = 28.02\) amu - Total: \(72.93 + 28.02 = 100.95\) amu.

Key concepts

Atomic Mass

The concept of atomic mass is foundational in chemistry. It's the mass of a single atom of a chemical element measured in atomic mass units (amu). This value is approximately equivalent to the total number of protons and neutrons in the atom's nucleus.
Understanding atomic mass helps chemists determine the mass of molecules and compounds, which are fundamental in stoichiometry calculations. For instance, the atomic mass of lithium is 6.94 amu, meaning this is the average mass of one lithium atom based on the isotopic distribution in nature. Such precise measurements are crucial when adding up the mass contributions from each element to find the molecular mass.

Periodic Table

The periodic table is a chart where all known elements are organized based on their chemical properties. Each element's position provides important information, including its atomic number and atomic mass.
The atomic number, found above the element symbol, tells how many protons are in an atom of the element, while the number right below the symbol is the atomic mass. This table is indispensable for chemists as it not only gives quick access to atomic masses for molecular mass calculations, but it also highlights relationships between different elements.
For example, elements in the same column (group) often have similar chemical properties such as reactivity.

Chemical Formula

A chemical formula is a symbolic way to represent the composition of a chemical compound. It shows the elements present and their respective proportions. The subscripts in a chemical formula indicate how many atoms of each element are in a molecule.
For example, \( \text{Li}_2\text{CO}_3 \) indicates the presence of two lithium atoms, one carbon atom, and three oxygen atoms in lithium carbonate. Calculating molecular mass requires analyzing these formulas to sum the atomic masses based on subscripts in the formula.
Understanding chemical formulas is crucial for predicting chemical reactions and stoichiometry calculations.

Stoichiometry

Stoichiometry involves the calculations of reactants and products in chemical reactions. It is based on the conservation of mass, where the total mass of reactants equals the total mass of products.
This concept is heavily reliant on chemical formulas and requires a clear understanding of the amounts of each substance involved in a reaction.
Using stoichiometry enables chemists to predict the amount of products that can be formed given a certain amount of reactants, or vice versa.
Molecular mass calculations are the starting point for stoichiometric calculations, ensuring accuracy in quantifying elements and compounds.