Mercury's Essential Properties for Barometers

Mercury is a unique liquid metal widely used in barometers due to several advantageous physical properties. A barometer is an instrument designed to measure atmospheric pressure. For accurate and practical measurement, the liquid used in a barometer must possess specific characteristics. The question asks why mercury is used, specifically highlighting its high density and very low vapor pressure.

High Density and Barometer Design

One of the primary reasons mercury is chosen for barometers is its high density.

• Density is defined as mass per unit volume. Mercury has a density of approximately $\text{13600 kg/m}^3$ ($\text{13.6 g/cm}^3$) at standard conditions, which is significantly higher than other common liquids like water ($\text{1000 kg/m}^3$).
• Atmospheric pressure is balanced by the weight of the liquid column in the barometer. The pressure exerted by a liquid column is given by the formula $\text{P} = \rho \text{gh}$, where $\text{P}$ is pressure, $\rho$ is density, $\text{g}$ is acceleration due to gravity, and $\text{h}$ is the height of the column.
• Since atmospheric pressure is relatively constant at a given location, if the density ($\rho$) is high, the required height ($\text{h}$) of the liquid column to balance this pressure will be less.
• For example, if water were used in a barometer, the column height needed to balance standard atmospheric pressure would be approximately $\text{10.3 meters}$ (or about $\text{34 feet}$). This would make the instrument impractically tall and difficult to use.
• With mercury's high density, a much shorter, more manageable column height of about $\text{760 mm}$ (or $\text{0.76 meters}$) is sufficient to measure standard atmospheric pressure. This makes mercury barometers compact and practical for everyday use.

Low Vapor Pressure and Accurate Readings

Another crucial property of mercury that makes it suitable for barometers is its very low vapor pressure.

• Vapor pressure refers to the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature.
• In a mercury barometer, above the mercury column, there is a space known as the Torricellian vacuum. This space should ideally be a perfect vacuum to ensure that only the atmospheric pressure is balancing the mercury column.
• If the liquid used has a significant vapor pressure, its vapor would fill the space above the liquid column, exerting its own pressure. This vapor pressure would then contribute to the total pressure above the mercury column, making the measured height of the mercury column less than it should be, thus providing an inaccurate reading of the true atmospheric pressure.
• Mercury has a very low vapor pressure at room temperature. This means that very few mercury atoms evaporate into the Torricellian vacuum, and the pressure they exert is negligible.
• This negligible vapor pressure ensures that the height of the mercury column directly and accurately reflects the atmospheric pressure without any significant interference from the vapor above the column. Liquids like water have much higher vapor pressure, which would lead to inaccurate readings.

Conclusion on Mercury Barometers

Both the high density and very low vapor pressure of mercury are essential characteristics that contribute to its effectiveness as a fluid in barometers. High density allows for a compact instrument, while low vapor pressure ensures accurate and reliable atmospheric pressure measurements. Therefore, both statements (i) and (ii) are correct reasons for mercury's use in barometers.