Determine The Boiling Point Of Water At 672 Mm Hg

The Boiling Point of Water at 672 mm Hg

Water boils at 100°C at sea level — that’s what we all learned in school. So at 672 mm Hg, which is slightly below standard atmospheric pressure, the boiling point of water drops. But what happens when the atmospheric pressure isn’t exactly one atmosphere? The exact value depends on the relationship between vapor pressure and ambient pressure, and it’s a calculation that shows up in chemistry labs, engineering problems, and even high-altitude cooking discussions.

Here’s the short version: at 672 mm Hg, water boils at approximately 98.In real terms, 6°C. But getting there involves understanding how pressure and temperature interact, and why that matters beyond textbook problems.

What Is Boiling Point, Really?

Boiling point isn’t a fixed number stamped on a textbook page. Even so, it’s the temperature at which a liquid’s vapor pressure equals the surrounding atmospheric pressure. That’s the key distinction.

At sea level, where atmospheric pressure is 760 mm Hg (or 1 atmosphere), water’s vapor pressure reaches 760 mm Hg at 100°C. That’s why it boils. But if you’re at a higher elevation, where the air pressure is lower, water boils at a lower temperature. That’s also why cooking times change on mountain peaks — the water isn’t as hot, even though it’s bubbling.

So when we say the boiling point at 672 mm Hg, we’re asking: at what temperature does water’s vapor pressure equal 672 mm Hg?

Why Pressure Matters Beyond the Classroom

This isn’t just academic. Pressure-dependent boiling points show up in real-world situations all the time.

Food manufacturers adjust pressure in their processes. In real terms, vacuum-sealed packaging sometimes uses reduced pressure to lower the boiling point of water, which affects how foods are treated. Now, chemical engineers design distillation columns where pressure is carefully controlled to separate compounds based on their boiling points. Even home cooks in places like Denver, Colorado — where atmospheric pressure is significantly lower than at sea level — notice that water boils at around 95°C instead of 100°C.

Understanding how to calculate boiling points at different pressures helps explain these phenomena. That said, it also matters for safety. If you’re working with volatile chemicals or pressurized systems, knowing the actual boiling point at your operating pressure can prevent dangerous situations.

How to Calculate the Boiling Point at 672 mm Hg

There are a few ways to approach this, depending on how precise you need to be.

Using the Clausius-Clapeyron Equation

The most rigorous method uses the Clausius-Clapeyron equation, which relates vapor pressure to temperature:

ln(P₂/P₁) = -(ΔHvap/R)(1/T₂ - 1/T₁)

Where:

• P₁ and T₁ are the known vapor pressure and boiling point at one condition
• P₂ and T₂ are the vapor pressure and boiling point at the condition you’re solving for
• ΔHvap is the enthalpy of vaporization
• R is the ideal gas constant

Let’s plug in the numbers. At 100°C (373.15 K), water’s vapor pressure is 760 mm Hg. But the enthalpy of vaporization for water is approximately 40. Worth adding: 7 kJ/mol, and R is 8. 314 J/mol·K.

We want to find T₂ when P₂ is 672 mm Hg.

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

Solving this equation gives T₂ ≈ 371.75 K, which converts to approximately 98.6°C.

Using Antoine Equation Tables

Another approach uses the Antoine equation, which is an empirical relationship fitted to experimental data:

log₁₀(P) = A - (B/(T + C))

Where P is in mm Hg and T is in °C. For water, the constants are approximately:

• A = 8.07131
• B = 1730.63
• C = 233.

Plugging in P = 672 and solving for T also yields a result very close to 98.6°C.

Quick Approximation Method

For a rough estimate, you can use the fact that water’s boiling point changes by about 0.Day to day, the more precise calculation gives us 98. On the flip side, 34°C per 10 mm Hg change in pressure near atmospheric conditions. Now, going from 760 mm Hg to 672 mm Hg is a difference of 88 mm Hg, which suggests a boiling point drop of roughly 3 degrees — putting the boiling point near 97°C. 6°C, so the approximation is in the right ballpark but not exact.

Common Mistakes People Make

Confusing Vapor Pressure with Atmospheric Pressure

One of the most frequent errors is mixing up these two concepts. Worth adding: vapor pressure is a property of the liquid itself — it depends only on temperature. Which means atmospheric pressure is the pressure exerted by the surrounding air. The boiling point is reached when these two pressures are equal. You can’t just look up vapor pressure and call it the boiling point unless the atmospheric pressure matches.

Using the Wrong Units

Pressure units trip people up constantly. Some problems give pressure in atmospheres, others in mm Hg, others in kilopascals. On the flip side, if you’re using the Clausius-Clapeyron equation with R = 8. Make sure your units are consistent throughout the calculation. 314 J/mol·K, your pressures need to be in the same units — they don’t both need to be in mm Hg, but they need to be the same unit.

Continue exploring with our guides on machine to convert mechanical into electrical energy and why are food webs more realistic than food chains.

Assuming Linear Relationships

The relationship between boiling point and pressure isn’t linear. You can’t just say “pressure dropped by X percent, so boiling point drops by X percent.” The Clausius-Clapeyron equation shows this relationship is logarithmic, which is why the approximation method I mentioned above is only rough.

Forgetting Temperature Units

Always convert to Kelvin when doing thermodynamic calculations. Plugging 100°C directly into an equation that expects absolute temperature will give you a completely wrong answer.

Practical Tips for Getting It Right

Know Your Reference Points

Memorize the key reference point: water boils at 100°C at 760 mm Hg. Even so, from there, you can reason about other pressures. If the pressure is lower, the boiling point is lower. If the pressure is higher, the boiling point is higher.

Use Tables When Precision Matters

For engineering or lab work, don’t rely on approximations. Steam tables and vapor pressure charts are widely available and will give you accurate values without needing to do the full calculation.

Check Your Work with Reality

If your calculation says water boils at 80°C at a pressure close to atmospheric, something went wrong. The boiling point shouldn’t change dramatically for small pressure changes. A difference of 88 mm Hg from standard pressure should change the boiling point by only a few degrees, not tens of degrees.

Understand the Context

In many practical situations, an approximate answer is fine. But if you’re designing a chemical process, you need precision. If you’re adjusting a recipe at high altitude, knowing the boiling point is roughly 95–97°C is sufficient. Match your method to your needs.

FAQ

Does water always boil at 100°C?

No. Water boils at 100°C only when the surrounding pressure is exactly 760 mm Hg (1 atmosphere). At higher elevations, where atmospheric pressure is lower, water boils at a lower temperature.

What is the boiling point of water at 672 mm Hg?

Approximately 98.Which means 6°C. This is calculated using the Clausius-Clapeyron equation or Antoine equation tables.

Why does pressure affect boiling point?

Boiling occurs when a liquid’s vapor pressure equals the surrounding atmospheric pressure. Lower atmospheric pressure means the vapor pressure reaches that level at a lower temperature, so the liquid boils sooner.

Can I use the ideal gas law instead?

Not directly. Still, the ideal gas law relates pressure, volume, and temperature for gases. Boiling point calculations require relationships that connect vapor pressure to temperature, which is what the Clausius-Clapeyron equation provides.

**How much does the boiling point change per unit of

pressure?**

As a rule of thumb near standard atmospheric pressure, water’s boiling point changes by approximately 0.In real terms, 4°C for every 10 mm Hg change in pressure. Plus, 3°C to 0. This rate isn't constant across all pressures—the curve steepens at lower pressures—but it provides a quick mental check for small deviations from 760 mm Hg.

Is the boiling point elevation from salt the same as pressure changes?

No, they are distinct phenomena. Adding salt (or any non-volatile solute) raises the boiling point by lowering the vapor pressure of the solution (colligative property). Pressure changes alter the external* pressure the vapor pressure must match. Both result in a higher boiling temperature, but the mechanisms and magnitudes differ.

What happens if pressure drops extremely low?

If pressure drops below the triple point (4.58 mm Hg for water), liquid water cannot exist; ice sublimates directly into vapor. Conversely, at the critical point (218 atmospheres, 374°C), the distinction between liquid and gas disappears entirely.

Conclusion

Understanding the relationship between pressure and boiling point moves you beyond rote memorization of "100°C" and into the realm of applied thermodynamics. Whether you are calibrating an autoclave, troubleshooting a distillation column, or simply trying to cook pasta in Denver, the principle remains the same: boiling is a negotiation between a liquid's internal vapor pressure and the external pressure pushing down on it.

By mastering the Clausius-Clapeyron equation for precision, the Antoine equation for convenience, and the rough linear approximations for quick estimates, you equip yourself to handle any scenario. Here's the thing — remember to respect your units, verify your constants, and always sanity-check your results against the physical reality of the system. With these tools, you will never be caught off guard by a shifting boiling point again.