Vapor Pressure of Water Calculator

What is Vapor Pressure?

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (liquid or solid) at a given temperature. For water, it represents the pressure at which water vapor is in equilibrium with liquid water or ice at a specific temperature. This concept is crucial in various fields, including meteorology, chemistry, and engineering.

How to Calculate Vapor Pressure of Water

To calculate the vapor pressure of water, follow these steps:

1. Determine the temperature of the water or ice
2. Choose the appropriate form of the Antoine equation (for water or ice)
3. Apply the Antoine equation to find the vapor pressure
4. Convert the result to the desired pressure unit if necessary

Formula

The Antoine equation for calculating vapor pressure is:

\[ \log_{10}P = A - \frac{B}{C + T} \]

Where:

• \(P\) is the vapor pressure in mmHg
• \(T\) is the temperature in °C
• \(A\), \(B\), and \(C\) are constants that depend on the substance and temperature range

For water (0 to 100°C):

• \(A = 8.07131\)
• \(B = 1730.63\)
• \(C = 233.426\)

For ice (-50 to 0°C):

• \(A = 9.55484\)
• \(B = 2667.0\)
• \(C = 230.454\)

Calculation Steps

Let's calculate the vapor pressure of water at 25°C:

1. Identify known values: \(T = 25\text{ °C}\), \(A = 8.07131\), \(B = 1730.63\), \(C = 233.426\)
2. Apply the Antoine equation: \[ \log_{10}P = 8.07131 - \frac{1730.63}{233.426 + 25} \]
3. Solve for P: \[ \log_{10}P = 8.07131 - \frac{1730.63}{258.426} = 1.3998 \] \[ P = 10^{1.3998} = 25.09 \text{ mmHg} \]
4. Convert to kPa if needed: \[ 25.09 \text{ mmHg} \times \frac{0.133322 \text{ kPa}}{1 \text{ mmHg}} = 3.34 \text{ kPa} \]

Example and Visual Representation

Let's visualize the vapor pressure of water at different temperatures:

This graph illustrates:

• The non-linear relationship between temperature and vapor pressure
• At 0°C, the vapor pressure is about 0.61 kPa
• At 100°C, the vapor pressure reaches 101.325 kPa (1 atm), which is the boiling point of water at standard pressure
• The vapor pressure increases more rapidly at higher temperatures