What is the approximate mass of one formula unit of silver nitrate, AgNO3?
The Correct Answer and Explanation is:
To calculate the approximate mass of one formula unit of silver nitrate (AgNO₃), we need to determine the molar mass of the compound. Silver nitrate is composed of silver (Ag), nitrogen (N), and oxygen (O). Each of these elements contributes a certain amount to the total mass.
Step-by-step Calculation:
- Silver (Ag):
- The atomic mass of silver (Ag) is approximately 107.87 g/mol.
- There is 1 silver atom in AgNO₃, so the contribution of silver to the total mass is 107.87 g/mol.
- Nitrogen (N):
- The atomic mass of nitrogen (N) is approximately 14.01 g/mol.
- There is 1 nitrogen atom in AgNO₃, so the contribution of nitrogen to the total mass is 14.01 g/mol.
- Oxygen (O):
- The atomic mass of oxygen (O) is approximately 16.00 g/mol.
- There are 3 oxygen atoms in AgNO₃, so the contribution of oxygen is (3 \times 16.00 = 48.00) g/mol.
Total Molar Mass of AgNO₃:
- The molar mass of AgNO₃ is the sum of the masses of all the atoms:
[
107.87\ \text{(Ag)} + 14.01\ \text{(N)} + 48.00\ \text{(O)} = 169.88\ \text{g/mol}.
]
This means that the molar mass of one mole of AgNO₃ is approximately 169.88 g. Since a mole contains (6.022 \times 10^{23}) formula units (Avogadro’s number), the mass of one formula unit of AgNO₃ can be found by dividing the molar mass by Avogadro’s number:
[
\text{Mass of one formula unit} = \frac{169.88\ \text{g/mol}}{6.022 \times 10^{23}\ \text{units/mol}} \approx 2.82 \times 10^{-22}\ \text{g}.
]
Explanation:
The approximate mass of one formula unit of AgNO₃ is (2.82 \times 10^{-22}) grams. This extremely small value reflects the fact that a single formula unit is a very tiny amount of matter. In chemistry, we often work with large quantities of molecules or formula units, which is why molar mass (grams per mole) is a useful measure for practical purposes. By using atomic masses from the periodic table and Avogadro’s number, we can determine the mass of individual formula units, giving us insight into the scale of atoms and molecules.