Determine Boiling Point Of Water At 672 Mm Hg

Let's explore how to accurately determine the boiling point of water at a specific pressure, in this case, 672 mm Hg. Understanding this concept involves delving into the relationship between vapor pressure, atmospheric pressure, and the fascinating physics behind phase transitions.

Understanding Boiling Point and Vapor Pressure

The boiling point of a liquid isn't a fixed temperature. It's the temperature at which the vapor pressure of the liquid equals the surrounding pressure. This surrounding pressure is typically atmospheric pressure. Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. In simpler terms, it's the tendency of a liquid to evaporate.

When the vapor pressure of a liquid reaches the external pressure, bubbles of vapor can form throughout the liquid and rise to the surface – this is boiling. At standard atmospheric pressure (760 mm Hg or 1 atm), water boils at 100°C (212°F). However, if the pressure is lower, the water will boil at a lower temperature, and if the pressure is higher, the water will boil at a higher temperature.

The Relationship Between Pressure and Boiling Point

The relationship between pressure and boiling point is governed by the Clausius-Clapeyron equation, a fundamental equation in thermodynamics. This equation provides a mathematical relationship between the vapor pressure of a substance and temperature. A simplified version useful for our purpose is:

ln(P1/P2) = -ΔHvap/R * (1/T1 - 1/T2)

Where:

• P1 and P2 are the vapor pressures at temperatures T1 and T2, respectively.
• ΔHvap is the enthalpy of vaporization (the amount of energy required to vaporize one mole of the liquid at its boiling point). For water, ΔHvap is approximately 40.7 kJ/mol.
• R is the ideal gas constant (8.314 J/mol·K).

This equation tells us that the vapor pressure of a liquid increases exponentially with temperature. It also allows us to calculate the boiling point at a different pressure if we know the boiling point at one pressure and the enthalpy of vaporization.

Determining the Boiling Point of Water at 672 mm Hg: Methods

There are two primary methods to determine the boiling point of water at 672 mm Hg:

1. Using the Clausius-Clapeyron Equation: This is a calculation-based approach.
2. Using a Vapor Pressure of Water Table or Chart: This is a reference-based approach.

Let's explore each method in detail.

Method 1: Using the Clausius-Clapeyron Equation

This method involves using the Clausius-Clapeyron equation to calculate the new boiling point.

Steps:

1. Identify the known values:

   • P1 = 760 mm Hg (standard atmospheric pressure)
   • T1 = 100°C = 373.15 K (boiling point of water at standard pressure)
   • P2 = 672 mm Hg (the pressure at which we want to find the boiling point)
   • ΔHvap = 40.7 kJ/mol = 40700 J/mol (enthalpy of vaporization of water)
   • R = 8.314 J/mol·K (ideal gas constant)
   • T2 = ? (the boiling point we want to find)

2. Rearrange the Clausius-Clapeyron equation to solve for T2:

   First, let's isolate the (1/T1 - 1/T2) term:

   ln(P1/P2) / (-ΔHvap/R) = (1/T1 - 1/T2)

   Then, rearrange to solve for 1/T2:

   1/T2 = 1/T1 - ln(P1/P2) / (ΔHvap/R)

   Finally, take the reciprocal to solve for T2:

   T2 = 1 / [1/T1 - ln(P1/P2) / (ΔHvap/R)]

3. Plug in the values and calculate:

   T2 = 1 / [1/373.15 - ln(760/672) / (40700/8.314)]

   T2 = 1 / [0.00268 - ln(1.131) / 4895.82]

   T2 = 1 / [0.00268 - 0.123/ 4895.82]

   T2 = 1 / [0.00268 - 0.000025]

   T2 = 1 / 0.002655

   T2 ≈ 376.65 K

4. Convert back to Celsius:

   T2 (°C) = T2 (K) - 273.15

   T2 (°C) = 376.65 - 273.15

   T2 (°C) ≈ 96.5°C

Therefore, the calculated boiling point of water at 672 mm Hg is approximately 96.5°C.

Advantages of this method:

• It's a fundamental, physics-based approach.
• It provides a good approximation, especially when a vapor pressure table isn't readily available.

Disadvantages of this method:

• It relies on approximations in the Clausius-Clapeyron equation.
• The accuracy depends on the accuracy of the enthalpy of vaporization value.
• It requires calculations and familiarity with thermodynamics concepts.

Method 2: Using a Vapor Pressure of Water Table or Chart

This method involves referencing a table or chart that lists the vapor pressure of water at various temperatures. These tables are typically generated experimentally and are considered highly accurate.

Steps:

1. Find a reliable vapor pressure of water table or chart. Many scientific and engineering handbooks contain this information. Online resources like the Engineering Toolbox or Kaye and Laby Tables are also excellent sources.
2. Locate the pressure closest to 672 mm Hg in the vapor pressure column. Since the table might not have an exact entry for 672 mm Hg, you might need to interpolate between two values.
3. Read the corresponding temperature value. This temperature is the approximate boiling point of water at 672 mm Hg.

Example (using hypothetical data):

Let's say our vapor pressure table looks something like this:

In this case, 672 mm Hg falls very close to the vapor pressure at 96.5°C. Therefore, we can conclude that the boiling point of water at 672 mm Hg is approximately 96.5°C. If a more precise value is needed, linear interpolation can be used.

Linear Interpolation (if required):

If the exact pressure isn't in the table, we can use linear interpolation to estimate the boiling point. Using the values from our hypothetical table above:

T = T1 + (P - P1) * (T2 - T1) / (P2 - P1)

Where:

• P = 672 mm Hg (the pressure we're interested in)
• P1 = 671.8 mm Hg (vapor pressure at T1)
• P2 = 686.4 mm Hg (vapor pressure at T2)
• T1 = 96.5 °C
• T2 = 97.0 °C

T = 96.5 + (672 - 671.8) * (97.0 - 96.5) / (686.4 - 671.8)

T = 96.5 + (0.2) * (0.5) / (14.6)

T = 96.5 + 0.0068

T ≈ 96.51 °C

In this case, the interpolated value is extremely close to 96.5°C, further validating our earlier conclusion.

Advantages of this method:

• It's generally more accurate than using the Clausius-Clapeyron equation directly, as the table values are based on experimental data.
• It's quicker and easier to use than calculations.

Disadvantages of this method:

• It relies on having access to a reliable vapor pressure table or chart.
• Interpolation might be necessary, introducing a small amount of error.

Factors Affecting Boiling Point Determination

Several factors can influence the accuracy of boiling point determination in practical settings:

• Impurities: The presence of impurities in the water will affect its boiling point. Dissolved salts, for instance, will generally raise the boiling point (boiling point elevation).
• Dissolved Gases: Dissolved gases can also influence the boiling point. Deaerated water (water with dissolved gases removed) will boil more smoothly and predictably.
• Superheating: Under certain conditions, water can be heated slightly above its boiling point without actually boiling. This phenomenon, called superheating, can lead to bumping (sudden, violent boiling) and inaccurate temperature readings. Using boiling chips or stirring the water can prevent superheating.
• Accuracy of Pressure Measurement: The accuracy of the pressure measurement is critical. If the pressure reading is inaccurate, the determined boiling point will also be inaccurate. Use a calibrated barometer or pressure sensor.
• Altitude: The boiling point of water decreases with increasing altitude because atmospheric pressure decreases. Therefore, altitude must be considered when determining boiling points.
• Surface Tension: Surface tension can affect bubble formation during boiling. Substances that lower the surface tension can promote smoother boiling.
• Calibration of Thermometer: Ensure the thermometer used to measure the temperature is properly calibrated. An inaccurate thermometer will lead to an incorrect boiling point determination.

Practical Applications

Understanding the boiling point of water at different pressures has numerous practical applications in various fields:

• Cooking and Food Processing: At higher altitudes where atmospheric pressure is lower, water boils at a lower temperature, which can affect cooking times and methods. Chefs and food processors need to adjust recipes and techniques accordingly.
• Industrial Processes: Many industrial processes, such as distillation, evaporation, and sterilization, rely on precise control of boiling points. Understanding the pressure-temperature relationship is crucial for optimizing these processes.
• Chemical Engineering: Chemical engineers use boiling point data for designing and operating chemical plants, particularly in processes involving separation and purification of liquids.
• Meteorology: Atmospheric pressure and temperature influence the formation of clouds and precipitation. Understanding the boiling point of water at different pressures helps meteorologists model atmospheric processes.
• Sterilization: Autoclaves use high pressure to increase the boiling point of water, allowing for sterilization at temperatures above 100°C, which is more effective at killing microorganisms.
• Heating and Cooling Systems: Understanding the boiling point of water and other fluids at different pressures is essential for designing efficient heating and cooling systems, such as steam turbines and refrigeration systems.
• Laboratory Research: In research laboratories, controlling the boiling point of solvents is essential for various experiments and reactions. Reduced pressure distillation, for example, allows for the purification of compounds that decompose at high temperatures.

Conclusion

Determining the boiling point of water at a specific pressure, such as 672 mm Hg, involves understanding the fundamental relationship between vapor pressure, temperature, and external pressure. While the Clausius-Clapeyron equation provides a theoretical framework, using a reliable vapor pressure table or chart is often the most accurate and practical approach. Factors such as impurities, dissolved gases, and pressure measurement accuracy can influence the results in real-world scenarios. This knowledge is essential in diverse fields, from cooking to chemical engineering, highlighting the importance of this fundamental scientific concept. By using the correct methods and considering the potential sources of error, accurate determination of boiling points at different pressures can be achieved, enabling a variety of applications.