Question

Calculate the molar mass of each of the following: (a) \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}\) (b) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) (c) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{BrF}_{3}\)

Short answer

Molar masses: (a) 149.12 g/mol, (b) 84.93 g/mol, (c) 249.72 g/mol, (d) 136.90 g/mol.

Step-by-step solution

- Calculate the Molar Mass of \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}\)

First, find the atomic masses of nitrogen (N), hydrogen (H), phosphorus (P), and oxygen (O). Then, calculate the total molar mass by adding up the contributions of each element as follows: For \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}\): \(3\times(1\times\mathrm{N}+4\times \mathrm{H})\)+\(1\times \mathrm{P} + 4\times \mathrm{O})\) \[3\times(14.01 + 4\times1.01) + (30.97 + 4\times16.00)\] \[3\times18.05 + 30.97 + 64.00 \] \[54.15 + 30.97 + 64.00 = 149.12 \ \mathrm{g/mol}\]

- Calculate the Molar Mass of \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\)

Find the atomic masses of carbon (C), hydrogen (H), and chlorine (Cl). Then, calculate the molar mass by adding up the contributions of each element: For \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\): \(1 \times \mathrm{C} + 2 \times \mathrm{H} + 2 \times \mathrm{Cl} \) \[12.01 + 2\times 1.01 + 2\times35.45\] \[12.01 + 2.02 + 70.90 \] \[12.01 + 2.02 + 70.90 = 84.93 \ \mathrm{g/mol}\]

- Calculate the Molar Mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\)

Find the atomic masses of copper (Cu), sulfur (S), oxygen (O), and hydrogen (H). Then, calculate the molar mass by adding up the contributions of each element: For \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\): \(1 \times \mathrm{Cu} + 1 \times \mathrm{S} + 4 \times \mathrm{O} + 5 \times(2 \times \mathrm{H} + \mathrm{O})\) \[63.55 + 32.07 + 4\times16.00 + 5\times(2\times 1.01 + 16.00)\] \[63.55 + 32.07 + 64.00 + 5\times18.02\] \[63.55 + 32.07 + 64.00 + 90.10\] \[63.55 + 32.07 + 64.00 + 90.10 = 249.72 \ \mathrm{g/mol}\]

- Calculate the Molar Mass of \(\mathrm{BrF}_{3}\)

Find the atomic masses of bromine (Br) and fluorine (F). Then, calculate the molar mass by adding up the contributions of each element: For \(\mathrm{BrF}_{3}\): \(1 \times \mathrm{Br} + 3 \times \mathrm{F}\) \[79.90 + 3\times19.00\] \[79.90 + 57.00\] \[79.90 + 57.00 = 136.90 \ \mathrm{g/mol}\]

Key concepts

Atomic Mass

To calculate the molar mass of a compound, you first need to understand the concept of atomic mass. Atomic mass is the mass of an individual atom, usually expressed in atomic mass units (amu). Each element has a unique atomic mass which can be found on the periodic table. For example:
- Hydrogen (H) has an atomic mass of approximately 1.01 amu.
- Carbon (C) has an atomic mass of approximately 12.01 amu.
- Oxygen (O) has an atomic mass of approximately 16.00 amu.
When you calculate the molar mass, you sum up the atomic masses of all atoms present in the molecule.

Molecular Formula

The molecular formula shows the exact number of each type of atom in a molecule. This is key for calculating the molar mass of the compound. For instance, in the compound \( \left( \mathrm{NH}_{4} \right)_{3} \mathrm{PO}_{4} \), the molecular formula tells us that there are:
- 3 nitrogen (N) atoms
- 12 hydrogen (H) atoms (since 4 hydrogen atoms are bonded to each nitrogen, and there are 3 nitrogen)
- 1 phosphorus (P) atom
- 4 oxygen (O) atoms
Each of these counts should be multiplied by their respective atomic masses and then summed together to get the total molar mass.

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It also plays a role when calculating molar masses. For instance, water is often found in its hydrated form in many compounds (like \( \mathrm{CuSO}_{4} \cdot 5\mathrm{H}_{2} \mathrm{O} \)). The '5H2O' indicates that there are five water molecules for every formula unit of copper(II) sulfate. You need to account for these additional water molecules when calculating the molar mass of the hydrated compound.
In this example:
- Water (H2O) has a molar mass of approximately 18.02 amu (from 2 x H + 1 x O)
- This value needs to be multiplied by 5, the number of water molecules, and then added to the molar mass of anhydrous \( \mathrm{CuSO}_{4} \).

Chemical Compounds

Chemical compounds are made up of two or more elements chemically bonded together. Understanding the types of bonds and the way elements combine helps in calculating their molar mass. For example, in \( \mathrm{BrF}_{3} \) , bromine (Br) and fluorine (F) are bonded. The molecular formula lets you know there are one bromine and three fluorine atoms.
To calculate the molar mass:
- Find the atomic mass of bromine: 79.90
- Find the atomic mass of fluorine: 19.00
- Multiply the atomic mass of fluorine by 3, then add it to the atomic mass of bromine.This gives \[ 79.90\ + \ (3 \times 19.00) = 136.90 \ \text{g/mol} \]
Understanding these concepts ensures you correctly calculate the molar mass of any given chemical compound.