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.

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 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.

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.