Question
A 17.44-g sample of a hydrate of zinc sulfate is heated strongly in a crucible to drive off all water of hydration. After heating, the sample has a mass of 9.79g. calculate the molecular formula for this hydrate.
Answers
GPT-4o mini
To determine the molecular formula of the hydrate, we need to calculate the mass of the water lost during the heating process and then find the ratio of the moles of zinc sulfate to the moles of water.
1. **Calculate the mass of water lost.**
Mass of the hydrate before heating: 17.44 g
Mass of the anhydrous zinc sulfate after heating: 9.79 g
Mass of water lost = Mass of hydrate - Mass of anhydrous salt
\[
\text{Mass of water lost} = 17.44\, \text{g} - 9.79\, \text{g} = 7.65\, \text{g}
\]
2. **Determine the moles of anhydrous zinc sulfate (ZnSO₄).**
The molar mass of ZnSO₄ is calculated as follows:
- Zinc (Zn): \( 65.38\, \text{g/mol} \)
- Sulfur (S): \( 32.07\, \text{g/mol} \)
- Oxygen (O): \( 16.00\, \text{g/mol} \times 4 = 64.00\, \text{g/mol} \)
Molar mass of ZnSO₄ = \( 65.38 + 32.07 + 64.00 = 161.45\, \text{g/mol} \)
Now, calculate the moles of ZnSO₄:
\[
\text{Moles of ZnSO₄} = \frac{9.79\, \text{g}}{161.45\, \text{g/mol}} \approx 0.0607\, \text{mol}
\]
3. **Determine the moles of water (H₂O) lost.**
The molar mass of water (H₂O) is:
- Hydrogen (H): \( 1.01\, \text{g/mol} \times 2 = 2.02\, \text{g/mol} \)
- Oxygen (O): \( 16.00\, \text{g/mol} \)
Molar mass of H₂O = \( 2.02 + 16.00 = 18.02\, \text{g/mol} \)
Now, calculate the moles of water lost:
\[
\text{Moles of H₂O} = \frac{7.65\, \text{g}}{18.02\, \text{g/mol}} \approx 0.424\, \text{mol}
\]
4. **Find the mole ratio of ZnSO₄ to H₂O.**
Now we can find the ratio of moles of ZnSO₄ to moles of H₂O:
\[
\text{Ratio} = \frac{\text{Moles of H₂O}}{\text{Moles of ZnSO₄}} = \frac{0.424\, \text{mol}}{0.0607\, \text{mol}} \approx 6.99
\]
Since we want the simplest whole number ratio, we round 6.99 to 7. Thus, for every mole of ZnSO₄, there are about 7 moles of H₂O.
5. **Write the empirical formula for the hydrate.**
The formula of the hydrated compound is:
\[
\text{ZnSO₄} \cdot 7\text{H₂O}
\]
Thus, the molecular formula for the hydrate is **ZnSO₄ · 7H₂O**.
1. **Calculate the mass of water lost.**
Mass of the hydrate before heating: 17.44 g
Mass of the anhydrous zinc sulfate after heating: 9.79 g
Mass of water lost = Mass of hydrate - Mass of anhydrous salt
\[
\text{Mass of water lost} = 17.44\, \text{g} - 9.79\, \text{g} = 7.65\, \text{g}
\]
2. **Determine the moles of anhydrous zinc sulfate (ZnSO₄).**
The molar mass of ZnSO₄ is calculated as follows:
- Zinc (Zn): \( 65.38\, \text{g/mol} \)
- Sulfur (S): \( 32.07\, \text{g/mol} \)
- Oxygen (O): \( 16.00\, \text{g/mol} \times 4 = 64.00\, \text{g/mol} \)
Molar mass of ZnSO₄ = \( 65.38 + 32.07 + 64.00 = 161.45\, \text{g/mol} \)
Now, calculate the moles of ZnSO₄:
\[
\text{Moles of ZnSO₄} = \frac{9.79\, \text{g}}{161.45\, \text{g/mol}} \approx 0.0607\, \text{mol}
\]
3. **Determine the moles of water (H₂O) lost.**
The molar mass of water (H₂O) is:
- Hydrogen (H): \( 1.01\, \text{g/mol} \times 2 = 2.02\, \text{g/mol} \)
- Oxygen (O): \( 16.00\, \text{g/mol} \)
Molar mass of H₂O = \( 2.02 + 16.00 = 18.02\, \text{g/mol} \)
Now, calculate the moles of water lost:
\[
\text{Moles of H₂O} = \frac{7.65\, \text{g}}{18.02\, \text{g/mol}} \approx 0.424\, \text{mol}
\]
4. **Find the mole ratio of ZnSO₄ to H₂O.**
Now we can find the ratio of moles of ZnSO₄ to moles of H₂O:
\[
\text{Ratio} = \frac{\text{Moles of H₂O}}{\text{Moles of ZnSO₄}} = \frac{0.424\, \text{mol}}{0.0607\, \text{mol}} \approx 6.99
\]
Since we want the simplest whole number ratio, we round 6.99 to 7. Thus, for every mole of ZnSO₄, there are about 7 moles of H₂O.
5. **Write the empirical formula for the hydrate.**
The formula of the hydrated compound is:
\[
\text{ZnSO₄} \cdot 7\text{H₂O}
\]
Thus, the molecular formula for the hydrate is **ZnSO₄ · 7H₂O**.