Ever tried to boil a pot of water on a mountain cabin, only to watch the bubbles crawl slower than usual?
Day to day, or maybe you’ve seen a science‑fair experiment where the water “boils” at a temperature that looks more like a warm bath than a rolling boil. The culprit isn’t a broken stove—it’s the pressure around the water Which is the point..
When the atmospheric pressure is 672 mm Hg, water’s boiling point isn’t the textbook 100 °C. It’s lower, and figuring it out is a mix of simple math, a dash of chemistry, and a pinch of good old‑fashioned curiosity.
What Is the Boiling Point of Water at 672 mm Hg
In everyday talk, “boiling point” means the temperature where liquid water turns to vapor at the pressure you’re standing in. At sea level that pressure is about 760 mm Hg (1 atm), and the boiling point lands nicely at 100 °C The details matter here..
Drop the pressure to 672 mm Hg—roughly what you’d find at 2,000 feet above sea level—and the water doesn’t need as much heat to escape. It will start bubbling vigorously at a temperature somewhere in the 90s °C range And it works..
The physics behind it
Water molecules are constantly jostling. Now, when they have enough kinetic energy to overcome the surrounding atmospheric pressure, they break free as steam. Lower the pressure, and the energy threshold drops. That’s why water boils sooner on a high‑altitude trek than in a kitchen at sea level.
The math you need
The relationship between pressure and boiling temperature is captured by the Clausius–Clapeyron equation. You don’t have to be a thermodynamics professor to use it; a rearranged, simplified version does the trick:
[ \ln!\left(\frac{P_2}{P_1}\right)=\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right) ]
- (P_1) = reference pressure (760 mm Hg)
- (P_2) = new pressure (672 mm Hg)
- (T_1) = boiling point at (P_1) (373.15 K)
- (\Delta H_{vap}) = enthalpy of vaporisation for water (≈ 40.7 kJ mol⁻¹)
- (R) = universal gas constant (8.314 J mol⁻¹ K⁻¹)
Solve for (T_2) and you’ll have the boiling point at 672 mm Hg Simple as that..
Why It Matters
Cooking at altitude
Ever tried making pasta in Denver and found it taking forever? The lower boiling point means the water is cooler, so the pasta cooks slower. Knowing the exact temperature helps you adjust cooking times or add a pressure cooker to the mix It's one of those things that adds up..
Laboratory precision
In a chemistry lab, reactions that require a “boiling water bath” assume 100 °C. If you’re on a high‑altitude campus and you don’t correct for pressure, you could be under‑heating a reaction and getting weird yields Still holds up..
Safety in industrial settings
Many processes—distillation, sterilization, steam generation—rely on water’s phase change. A miscalculated boiling point can lead to under‑pressurised equipment, which is a recipe for failure or even an accident.
How to Determine the Boiling Point at 672 mm Hg
Below is a step‑by‑step guide that works with a calculator, a thermometer, and a pressure gauge. No need for fancy software.
1. Gather the constants
| Symbol | Value | Units |
|---|---|---|
| (P_1) | 760 | mm Hg |
| (P_2) | 672 | mm Hg |
| (T_1) | 373.15 | K (100 °C) |
| (\Delta H_{vap}) | 40,700 | J mol⁻¹ |
| (R) | 8.314 | J mol⁻¹ K⁻¹ |
If you’re using a source that lists (\Delta H_{vap}) in kJ mol⁻¹, just remember to convert to joules Not complicated — just consistent. Simple as that..
2. Plug into the rearranged equation
First isolate the temperature term:
[ \frac{1}{T_2}= \frac{1}{T_1} - \frac{R}{\Delta H_{vap}} \ln!\left(\frac{P_2}{P_1}\right) ]
Now compute each piece.
- (\ln(P_2/P_1) = \ln(672/760) \approx \ln(0.8842) \approx -0.123)
- (\frac{R}{\Delta H_{vap}} = \frac{8.314}{40,700} \approx 0.000204)
Multiply them:
- (-0.123 \times 0.000204 \approx -2.51 \times 10^{-5})
Subtract from (1/T_1):
- (1/T_1 = 1/373.15 \approx 0.00268)
- (0.00268 - (-2.51 \times 10^{-5}) = 0.002705)
Finally invert:
- (T_2 = 1 / 0.002705 \approx 369.6) K
Convert to Celsius:
- (369.6 K - 273.15 = 96.5 °C)
Result: At 672 mm Hg, water boils at roughly 96.5 °C Still holds up..
3. Verify with a thermometer
If you have a calibrated thermometer that reads Celsius, set up a simple experiment:
- Fill a pot with water and place it on a stove.
- Attach a pressure gauge to the pot’s lid (or use a barometer to read ambient pressure).
- Heat slowly and watch for the first steady stream of bubbles.
- Record the temperature when the bubbles become continuous.
You should see a reading close to the calculated 96–97 °C. Small deviations are normal—air currents, impurities, or gauge accuracy can shift the number by a degree or two.
4. Use an online steam‑table shortcut (optional)
Most engineering handbooks include a table that lists boiling temperature versus pressure. Look up 672 mm Hg and you’ll find a value around 96 °C, confirming the math Small thing, real impact..
Common Mistakes / What Most People Get Wrong
Assuming “boiling = 100 °C” everywhere
The biggest myth is that water always boils at 100 °C. Now, that’s a sea‑level convenience, not a universal law. When you see a recipe that says “boil for 10 minutes,” it’s really “boil at the temperature your local pressure gives you.
Mixing up units
Pressure can be reported in atm, kPa, or inches of mercury. Plugging 672 mm Hg directly into a formula that expects kPa will give nonsense. But convert first: 672 mm Hg ≈ 89. 5 kPa.
Forgetting the logarithm sign
The Clausius–Clapeyron equation uses a natural log. Using a base‑10 log will underestimate the temperature shift, often by a full degree.
Ignoring water purity
Mineral content raises the boiling point slightly (a phenomenon called boiling point elevation). If you’re using hard tap water, you might see a marginally higher temperature than the pure‑water calculation predicts Easy to understand, harder to ignore. Nothing fancy..
Over‑relying on a single data point
One thermometer reading at “first bubbles” isn’t always the true boiling point. That said, the water must reach a steady rolling boil. Otherwise you’re measuring the onset of nucleate boiling, not the equilibrium point Turns out it matters..
Practical Tips / What Actually Works
- Carry a portable barometer when you travel to high altitudes. A cheap aneroid model will give you the pressure you need for quick calculations.
- Use a digital thermometer with a quick‑response probe. The faster it reads, the less lag you have between the water actually boiling and the number you write down.
- Adjust cooking times by about 5 % for every 10 mm Hg drop in pressure. It’s a rule‑of‑thumb that works for most pasta, rice, and boiled vegetables.
- If you need a true 100 °C boil, use a pressure cooker. Raising the internal pressure above 760 mm Hg forces the water to reach the higher temperature you expect.
- Document your conditions. Jot down the altitude, ambient temperature, and pressure each time you run a critical experiment. Future you will thank you when a reaction “fails” and you realize the water was only 96 °C.
- Consider the psychrometric chart if you’re dealing with humid air. High humidity can slightly alter the effective pressure on the water surface, though the effect is usually under 0.2 °C.
FAQ
Q1: How much does the boiling point change per millimeter of mercury?
A: Roughly 0.03 °C for each 1 mm Hg change near sea level. So a drop from 760 to 672 mm Hg (88 mm Hg) reduces the boiling point by about 2.6 °C, landing near 96–97 °C.
Q2: Can I use the simple rule “boil at 1 °C lower for every 30 ft of elevation”?
A: That rule works as an approximation up to about 5,000 ft. It translates to about 1 °C per 300 ft, which aligns with the pressure‑temperature relationship we calculated.
Q3: Does the Clausius–Clapeyron equation work for all pressures?
A: It’s accurate for moderate pressures (roughly 300–1,000 mm Hg). At extreme low pressures (high vacuum) or very high pressures, the linear approximation breaks down and you need more complex steam‑table data.
Q4: My thermometer reads 95 °C when the water is bubbling. Is that wrong?
A: Not necessarily. Thermometer calibration error, local impurities, or a slight pressure variation can shift the reading a degree or two. As long as it’s within the 95–97 °C window, you’re good Most people skip this — try not to..
Q5: How does altitude affect other liquids?
A: The same principle applies—lower pressure reduces the boiling point of any liquid. For ethanol, for example, the boiling point drops from 78.4 °C at 760 mm Hg to about 73 °C at 672 mm Hg That's the whole idea..
So the next time you hear “water boils at 100 °C,” remember it’s a sea‑level shorthand, not a universal truth. In real terms, at 672 mm Hg, the water is content with a cozy 96. In practice, 5 °C, and with a quick calculation—or even a handheld barometer—you can predict exactly where that sweet spot lies. Happy boiling, wherever the pressure takes you Less friction, more output..
