Problem 3 - Chemistry The Molecular Nature of Matter

Question

At \(20^{\circ} \mathrm{C}\) the density of mercury is \(13.6 \mathrm{~g} \mathrm{~mL}^{-1}\) and that of water is \(1.00 \mathrm{~g} \mathrm{~mL}^{-1}\). At \(20^{\circ} \mathrm{C}\), the vapor pressure of mercury is 0.0012 torr and that of water is 18 torr. Give and explain two reasons why water would be an inconvenient fluid to use in a Torricelli barometer.

Step-by-Step Solution

Answer

Water is inconvenient for use in a Torricelli barometer because it has a significantly lower density than mercury, requiring an impractically tall barometer, and it has a much higher vapor pressure, which would affect the barometer's accuracy due to evaporation into the vacuum.

Step 1: Compare Densities

The density of a fluid used in a barometer is critical for the instrument's functionality. A higher density fluid allows the barometer to be more compact, whereas a lower density fluid would require a taller structure to measure the same atmospheric pressure. The density of mercury is significantly higher (\(13.6 \text{ g/mL}\)) compared to that of water (\(1.00 \text{ g/mL}\)). Therefore, using water in a Torricelli barometer would result in a barometer that is impractically tall.

Step 2: Evaluate Vapor Pressure

Vapor pressure is another important characteristic for a fluid in a barometer. It indicates how much of the fluid will evaporate into the vacuum space above the fluid column. A high vapor pressure means more fluid will evaporate, which affects the pressure reading. The vapor pressure of water (\(18 \text{ torr}\)) is vastly higher than that of mercury (\(0.0012 \text{ torr}\)). Therefore, water would evaporate significantly into the vacuum of the barometer, affecting its accuracy.

Key Concepts

Density in Barometers

Understanding the role of density in a barometer is essential for comprehending how these devices measure atmospheric pressure. Barometers function by balancing the weight of a column of fluid against the pressure exerted by the atmosphere. The density of the fluid, thereby, has a direct impact on the height of the fluid column.

High-density fluids such as mercury, which has a density of around \(13.6 \text{ g/mL}\) at room temperature, are preferred because they allow the barometer to be relatively short and manageable. In comparison, if a low-density fluid like water were used, with a density of \(1.00 \text{ g/mL}\) at the same temperature, the column would need to be significantly taller — potentially over ten times the height — to measure atmospheric pressure accurately. Therefore, for practical and space-saving reasons, mercury's high density makes it an ideal choice for use in barometers.

Vapor Pressure

Vapor pressure is indicative of a fluid's tendency to evaporate. In the context of a barometer, it's crucial because any fluid that evaporates into the top of the barometer (the space above the fluid column that's supposed to be a vacuum) can result in incorrect atmospheric pressure readings. Ideally, the chosen fluid should have minimal vapor pressure.

In the case of mercury, its vapor pressure at room temperature is merely \(0.0012 \text{ torr}\), which is negligible. This feature is one reason why mercury is ideal for barometric measurements. On the contrary, water carries a vapor pressure of \(18 \text{ torr}\) at the same conditions, which is significantly higher. As a result, water would evaporate and collect in the space at the top of the barometer, interfering with the measurement and yielding unreliable results. This distinction in vapor pressures provides a strong case against using water as the working liquid in a Torricelli barometer.

Measurement of Atmospheric Pressure

The Torricelli barometer is a classic instrument for measuring atmospheric pressure, which is an essential parameter in weather forecasting, altimetry, and for various scientific researches. The device consists of a sealed tube filled with mercury and inverted into a dish containing the same liquid.

The atmospheric pressure pushes on the surface of the mercury in the dish, and the height of the mercury column in the tube is a direct measurement of this pressure. As the atmospheric pressure changes, the mercury level adjusts accordingly, rising when pressure increases and falling when it decreases. This concept hinges on a consistent relationship between the fluid's height and the atmospheric pressure, so fluctuations due to inappropriate density or vapor pressure from the fluid, as would be the case with water, would lead to inaccurate readings.