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Chapter 9: Problem 8

What is the vapor pressure of water at \(100^{\circ} \mathrm{C} ?\) How do you know?

Short Answer

Expert verified
The vapor pressure of water at \(100^{\circ} \mathrm{C}\) is \(760~\mathrm{mm}~\mathrm{Hg}\) (1 atm). We know this by looking up the value in a vapor pressure table or using empirical formulas. At this temperature, water is boiling, as the vapor pressure equals the atmospheric pressure, meaning the water is in equilibrium between its liquid and gaseous phases.

Step by step solution

01

Understand Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its condensed phases (solid or liquid) at a specific temperature. The higher the temperature, the higher the vapor pressure, as more molecules in the liquid or solid phase have enough energy to break into the gaseous phase.
02

Find the Vapor Pressure of Water at 100°C

We can use a vapor pressure table to find the vapor pressure of water at 100°C. Alternatively, you can use the Antoine equation or other empirical formulas to calculate the vapor pressure. According to the most common vapor pressure table, the vapor pressure of water at 100°C is \(760~ \mathrm{mm}~ \mathrm{Hg}\), which is also equivalent to \(1~ \mathrm{atm}\) (atmosphere), as these are standard conditions.
03

Determine the State of Water at 100°C and 760 mm Hg

At 100°C and a vapor pressure of \(760~\mathrm{mm}~\mathrm{Hg}\), we can conclude that water is boiling, as it is at the point where the vapor pressure of the liquid equals the atmospheric pressure. This means that the water is in equilibrium between its liquid and gaseous phases at this temperature and pressure. So, the vapor pressure of water at \(100^{\circ} \mathrm{C}\) is \(760~\mathrm{mm}~\mathrm{Hg}\). We know this because the vapor pressure table or empirical formulas show that at this temperature, water is in equilibrium between its liquid and gaseous phases, and the vapor pressure equals the atmospheric pressure of \(760~\mathrm{mm}~\mathrm{Hg}\) or \(1~\mathrm{atm}\).

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