What do you predict for the height of a barometer column based on 1-iodododecane, when the atmospheric pressure is 749 torr ?
The correct answer and explanation is:
To predict the height of a barometer column based on 1-iodododecane when the atmospheric pressure is 749 torr, we need to understand the relationship between pressure, liquid density, and column height in a barometer.
Step-by-Step Solution:
The barometric formula relates pressure to height and density: P=ρghP = \rho g h
Where:
- PP = pressure (in pascals, Pa)
- ρ\rho = density of the liquid (kg/m³)
- gg = acceleration due to gravity (9.81 m/s²)
- hh = height of the column (m)
Step 1: Convert Pressure to Pascals
Since 1 torr=133.322 Pa1 \, \text{torr} = 133.322 \, \text{Pa}: P=749 torr×133.322 Patorr=99,838.2 PaP = 749 \, \text{torr} \times 133.322 \, \frac{\text{Pa}}{\text{torr}} = 99,838.2 \, \text{Pa}
Step 2: Find the Density of 1-iodododecane
The density of 1-iodododecane is approximately: ρ≈1.198 g/cm3=1198 kg/m3\rho \approx 1.198 \, \text{g/cm}^3 = 1198 \, \text{kg/m}^3
Step 3: Solve for Height
Rearranging the formula: h=Pρg=99,838.21198×9.81≈99,838.211,751.38≈8.5 mh = \frac{P}{\rho g} = \frac{99,838.2}{1198 \times 9.81} \approx \frac{99,838.2}{11,751.38} \approx 8.5 \, \text{m}
✅ Final Answer:
The predicted height of a barometer column based on 1-iodododecane at 749 torr is approximately 8.5 meters.
Explanation (300 words):
Barometers operate on the principle of balancing the atmospheric pressure with the weight of a liquid column. When a liquid is placed in a closed tube and exposed to atmospheric pressure, the liquid rises until the weight of the column balances the external pressure.
The height a liquid reaches depends on its density—denser liquids rise to shorter heights, while less dense ones rise higher to balance the same pressure.
In this problem, we use 1-iodododecane, an organic compound with a relatively high density (~1.198 g/cm³), but still much less dense than mercury (13.6 g/cm³), which is typically used in barometers. Because 1-iodododecane is less dense, the column must be much taller than a mercury column to balance the same atmospheric pressure.
We convert atmospheric pressure from torr to pascals, ensuring all units are SI-compatible. Using the barometric formula P=ρghP = \rho g h, we isolate hh, plug in the known pressure, density, and gravitational constant, and solve. The result (about 8.5 meters) is significantly taller than a mercury barometer column (typically ~0.76 m at sea level), illustrating how fluid density impacts barometer design.
In real-world applications, this is why mercury is preferred despite its toxicity—it allows for compact, manageable devices. However, understanding how other fluids behave helps in designing safer or specialized instruments.