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The problem involves the Antoine equation:

\[
\log_{10} P_{\text{sat}} = A - \frac{B}{T + C}
\]

where:
- \( P_{\text{sat}} \) is the saturated vapor pressure in bar.
- \( A \), \( B \), and \( C \) are Antoine constants.
- \( T \) is the temperature in Kelvin.

Given Antoine constants for liquid water:
- \( A = 4.6543 \)
- \( B = 1435.264 \)
- \( C = -64.848 \)

You are asked to find the temperature \( T \) at which the saturated vapor pressure \( P_{\text{sat}} \) equals 1 atmosphere, which corresponds to \( P_{\text{sat}} = 1.01325 \) bar.

### Steps to solve using the Antoine equation:
1. The objective is to find \( T \) such that the right-hand side of the equation equals \( \log_{10}(1.01325) \).
2. First, calculate \( \log_{10}(1.01325) \):
   \[
   \log_{10}(1.01325) \approx 0.0057
   \]

3. Set up the equation:
   \[
   0.0057 = 4.6543 - \frac{1435.264}{T - 64.848}
   \]
4. Rearrange the equation to solve for \( T \):
   \[
   \frac{1435.264}{T - 64.848} = 4.6543 - 0.0057
   \]
   \[
   \frac{1435.264}{T - 64.848} = 4.6486
   \]
   \[
   T - 64.848 = \frac{1435.264}{4.6486}
   \]
   \[
   T = \frac{1435.264}{4.6486} + 64.848
   \]
   \[
   T \approx 373.2 \text{ K}
   \]

So, the temperature at which the saturated vapor pressure equals 1 atmosphere is approximately 373.2 K.

You can verify this using the Solver tool in Excel by setting \( T \) as the variable and aiming for the right-hand side of the Antoine equation to equal 0.0057.

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Do you have any questions or would you like further clarification?

Here are 5 related questions for further exploration:
1. How is the Antoine equation used to determine boiling points at different pressures?
2. What are the typical ranges of validity for the Antoine equation for different liquids?
3. How does the Antoine equation differ from other vapor pressure models?
4. What units must be used consistently when applying the Antoine equation?
5. How does changing the value of \( A \), \( B \), or \( C \) constants affect the solution?

**Tip**: When using Excel Solver, make sure your target cell and variable cell are correctly set up to automate the iteration process.

Use the Antoine equation to find the temperature at which the vapor pressure of water equals 1 atmosphere, using the given Antoine constants.

Learn how to use the Antoine equation to determine the temperature at which the vapor pressure of water equals 1 atmosphere, with a detailed step-by-step solution. Suitable for engineering students.

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