Question
How to calculate the molecular weight of an unknown non-electrolyte using vapor pressure lowering
Answers
GPT-4o mini
To calculate the molecular weight of an unknown non-electrolyte using vapor pressure lowering, you can use Raoult's Law and the concept of colligative properties. The following steps outline the procedure:
### Materials Needed
1. The unknown non-electrolyte solute.
2. A pure solvent (typically a volatile liquid such as water).
3. A barometer or a way to measure vapor pressure.
4. A balance for weighing.
5. A thermometer for measuring temperature.
### Steps
1. **Measure the Vapor Pressure of Pure Solvent**:
- Measure the vapor pressure of the pure solvent at a specific temperature. This value will be denoted as \( P_{\text{solvent}}^0 \).
2. **Prepare a Solution**:
- Weigh a known mass of solvent \( (m_{\text{solvent}}) \). Commonly used solvents include water or another non-volatile solvent.
- Dissolve a known mass of the unknown non-electrolyte solute \( (m_{\text{solute}}) \) in the solvent.
3. **Measure the Vapor Pressure of the Solution**:
- Measure the vapor pressure of the solution \( (P_{\text{solution}}) \) at the same temperature.
4. **Calculate the Vapor Pressure Lowering**:
- The change in vapor pressure can be calculated using:
\[
\Delta P = P_{\text{solvent}}^0 - P_{\text{solution}}
\]
5. **Apply Raoult’s Law**:
- According to Raoult's Law, the lowering of vapor pressure is related to the mole fraction of the solute. The mole fraction of the solute \( (X_{\text{solute}}) \) is given by:
\[
X_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}}
\]
where \( n_{\text{solute}} \) is the number of moles of the solute and \( n_{\text{solvent}} \) is the number of moles of the solvent.
6. **Calculate the Moles of Solvent**:
- The number of moles of the solvent can be calculated using its mass and molar mass \( (M_{\text{solvent}}) \):
\[
n_{\text{solvent}} = \frac{m_{\text{solvent}}}{M_{\text{solvent}}}
\]
7. **Relate Vapor Pressure Lowering to Mole Fraction**:
- The mole fraction can also be expressed in terms of vapor pressure lowering using:
\[
\Delta P = X_{\text{solute}} \cdot P_{\text{solvent}}^0
\]
- Rearranging gives:
\[
X_{\text{solute}} = \frac{\Delta P}{P_{\text{solvent}}^0}
\]
8. **Calculate the Moles of the Solute**:
- Rearranging the mole fraction equation:
\[
n_{\text{solute}} = X_{\text{solute}} \cdot (n_{\text{solute}} + n_{\text{solvent}})
\]
- Assuming \((n_{\text{solute}} << n_{\text{solvent}})\), this can be simplified further to approximate:
\[
n_{\text{solute}} \approx X_{\text{solute}} \cdot n_{\text{solvent}}
\]
9. **Substituting Values**:
- Substitute \( X_{\text{solute}} \) with \(\frac{\Delta P}{P_{\text{solvent}}^0}\) into the above formula for \( n_{\text{solute}} \):
\[
n_{\text{solute}} = \left( \frac{\Delta P}{P_{\text{solvent}}^0} \right) n_{\text{solvent}}
\]
10. **Calculate the Molar Mass of the Solute**:
- The molar mass \( M_{\text{solute}} \) can now be calculated using the mass of the solute and the number of moles you just calculated:
\[
M_{\text{solute}} = \frac{m_{\text{solute}}}{n_{\text{solute}}}
\]
### Conclusion
By following these steps, you can calculate the molecular weight of an unknown non-electrolyte solute from the vapor pressure lowering observed when it is dissolved in a solvent. Make sure to carry out the experiment at a controlled temperature to ensure accurate measurements.
### Materials Needed
1. The unknown non-electrolyte solute.
2. A pure solvent (typically a volatile liquid such as water).
3. A barometer or a way to measure vapor pressure.
4. A balance for weighing.
5. A thermometer for measuring temperature.
### Steps
1. **Measure the Vapor Pressure of Pure Solvent**:
- Measure the vapor pressure of the pure solvent at a specific temperature. This value will be denoted as \( P_{\text{solvent}}^0 \).
2. **Prepare a Solution**:
- Weigh a known mass of solvent \( (m_{\text{solvent}}) \). Commonly used solvents include water or another non-volatile solvent.
- Dissolve a known mass of the unknown non-electrolyte solute \( (m_{\text{solute}}) \) in the solvent.
3. **Measure the Vapor Pressure of the Solution**:
- Measure the vapor pressure of the solution \( (P_{\text{solution}}) \) at the same temperature.
4. **Calculate the Vapor Pressure Lowering**:
- The change in vapor pressure can be calculated using:
\[
\Delta P = P_{\text{solvent}}^0 - P_{\text{solution}}
\]
5. **Apply Raoult’s Law**:
- According to Raoult's Law, the lowering of vapor pressure is related to the mole fraction of the solute. The mole fraction of the solute \( (X_{\text{solute}}) \) is given by:
\[
X_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}}
\]
where \( n_{\text{solute}} \) is the number of moles of the solute and \( n_{\text{solvent}} \) is the number of moles of the solvent.
6. **Calculate the Moles of Solvent**:
- The number of moles of the solvent can be calculated using its mass and molar mass \( (M_{\text{solvent}}) \):
\[
n_{\text{solvent}} = \frac{m_{\text{solvent}}}{M_{\text{solvent}}}
\]
7. **Relate Vapor Pressure Lowering to Mole Fraction**:
- The mole fraction can also be expressed in terms of vapor pressure lowering using:
\[
\Delta P = X_{\text{solute}} \cdot P_{\text{solvent}}^0
\]
- Rearranging gives:
\[
X_{\text{solute}} = \frac{\Delta P}{P_{\text{solvent}}^0}
\]
8. **Calculate the Moles of the Solute**:
- Rearranging the mole fraction equation:
\[
n_{\text{solute}} = X_{\text{solute}} \cdot (n_{\text{solute}} + n_{\text{solvent}})
\]
- Assuming \((n_{\text{solute}} << n_{\text{solvent}})\), this can be simplified further to approximate:
\[
n_{\text{solute}} \approx X_{\text{solute}} \cdot n_{\text{solvent}}
\]
9. **Substituting Values**:
- Substitute \( X_{\text{solute}} \) with \(\frac{\Delta P}{P_{\text{solvent}}^0}\) into the above formula for \( n_{\text{solute}} \):
\[
n_{\text{solute}} = \left( \frac{\Delta P}{P_{\text{solvent}}^0} \right) n_{\text{solvent}}
\]
10. **Calculate the Molar Mass of the Solute**:
- The molar mass \( M_{\text{solute}} \) can now be calculated using the mass of the solute and the number of moles you just calculated:
\[
M_{\text{solute}} = \frac{m_{\text{solute}}}{n_{\text{solute}}}
\]
### Conclusion
By following these steps, you can calculate the molecular weight of an unknown non-electrolyte solute from the vapor pressure lowering observed when it is dissolved in a solvent. Make sure to carry out the experiment at a controlled temperature to ensure accurate measurements.