Question

Cobalt(II) nitrate (Co(NO3)2) is used in ceramic glazes and produces a blue color when the ceramic is fired. This compound exists as a hydrate whose composition is 37.1% water and 62.9% Co(NO3)2 by mass. Write the molecular formula

Answer 1

To determine the molecular formula of the hydrate of cobalt(II) nitrate (Co(NO₃)₂·xH₂O), we need to calculate the value of \( x \), which represents the number of water molecules in the hydrate.

1. **Calculate the molar mass of Co(NO₃)₂:**
- Cobalt (Co): 58.93 g/mol
- Nitrogen (N): 14.01 g/mol (2 nitrogen atoms in Co(NO₃)₂)
- Oxygen (O): 16.00 g/mol (6 oxygen atoms in Co(NO₃)₂, since there are 3 oxygen atoms per nitrate and there are 2 nitrates)

Molar mass calculation:
\[
\text{Molar mass of Co(NO}_3\text{)}_2 = 58.93 + (2 \times 14.01) + (6 \times 16.00)
\]
\[
= 58.93 + 28.02 + 96.00 = 182.95 \, \text{g/mol}
\]

2. **Calculate the molar mass of water (H₂O):**
- Hydrogen (H): 1.01 g/mol (2 hydrogen atoms)
- Oxygen (O): 16.00 g/mol (1 oxygen atom)

Molar mass of water:
\[
\text{Molar mass of H}_2\text{O} = (2 \times 1.01) + 16.00 = 2.02 + 16.00 = 18.02 \, \text{g/mol}
\]

3. **Set up equations based on the mass percentages:**
The hydrate consists of \( x \) moles of water and 1 mole of Co(NO₃)₂. The total mass of the hydrate can be expressed as:
\[
\text{Total mass} = \text{mass of Co(NO}_3\text{)}_2 + \text{mass of water}
\]
\[
= 182.95 \, \text{g/mol} + x \cdot 18.02 \, \text{g/mol}
\]

4. **Determine mass percentages:**
Given that the hydrate is 37.1% water and 62.9% Co(NO₃)₂ by mass, you can set up the following equations using mass percentages:
\[
\frac{x \cdot 18.02}{182.95 + x \cdot 18.02} = 0.371
\]

5. **Cross multiply and solve for \( x \):**
\[
x \cdot 18.02 = 0.371(182.95 + x \cdot 18.02)
\]
\[
x \cdot 18.02 = 68.00365 + 0.371x \cdot 18.02
\]
\[
x \cdot 18.02 - 0.371x \cdot 18.02 = 68.00365
\]
\[
x \cdot (18.02 - 0.371 \cdot 18.02) = 68.00365
\]
\[
x \cdot (18.02 \cdot (1 - 0.371)) = 68.00365
\]
\[
x \cdot (18.02 \cdot 0.629) = 68.00365
\]
\[
x \cdot 11.32 = 68.00365
\]
\[
x = \frac{68.00365}{11.32} \approx 6.0
\]

6. **Final formula:**
Thus, the hydrate is cobalt(II) nitrate hexahydrate:
\[
\text{Molecular formula} = \text{Co(NO}_3\text{)}_2 \cdot 6\text{H}_2\text{O}
\]

So, the molecular formula is \( \text{Co(NO}_3\text{)}_2 \cdot 6\text{H}_2\text{O} \).