Question

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

Short answer

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

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.

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.

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 $1\mathrm{atm}$.

Key concepts

Equilibrium

In the context of vapor pressure and boiling points, equilibrium is a crucial concept to understand. Equilibrium in this setting refers to a state where the rate of evaporation of a liquid equals the rate of condensation of its vapor. This balance means the amounts of gas and liquid remain constant over time.
When water reaches its boiling point, that is, at 100°C under standard atmospheric pressure of 760 mm Hg, it is in equilibrium between its liquid and gaseous states. This condition is crucial for determining when boiling occurs. - The pressure exerted by the vapor is exactly what is needed to cause bubbles to form within the liquid and rise to the surface, which is boiling. - If the atmospheric pressure was lower, such as at higher altitudes, water would boil at a lower temperature because equilibrium would be reached sooner. Understanding these principles is key to grasping how vapor pressure and external conditions like atmospheric pressure influence the physical state of a substance.

Boiling Point

The boiling point of a liquid is the temperature at which its vapor pressure becomes equal to the external pressure surrounding the liquid. For water, this is typically 100°C under standard atmospheric pressure (1 atm or 760 mm Hg).
At the boiling point, molecules throughout the liquid have sufficient energy to form vapor bubbles, which rise and escape into the air. The boiling point can change depending on the surrounding atmospheric pressure. - At higher altitudes where the atmospheric pressure is lower, water boils at a temperature less than 100°C. - Conversely, in a pressure cooker where the pressure is increased, water boils at a temperature higher than 100°C. Hence, the boiling point is not just a fixed property, but is dependent on environmental pressure conditions. This makes it essential for understanding processes like cooking at high altitudes or using pressure cookers for faster cooking.

Antoine Equation

The Antoine equation is a mathematical formula that relates the vapor pressure of a substance to its temperature. It is often expressed as:$${\log }_{10}(P)=A-\frac{B}{C+T}$$where $P$ is the vapor pressure, $T$ is the temperature in degrees Celsius, and $A$, $B$, $C$ are constants specific to each substance. This equation allows for accurate calculations of vapor pressure over a range of temperatures.Using the Antoine equation, scientists can predict how substances behave under various thermal conditions without needing to consult a table. The constants $A$, $B$, and $C$ are determined experimentally for each substance and reflect its unique characteristics. - This equation is particularly useful for calculating vapor pressures of substances at temperatures for which no measured data exists.- It serves as an empirical tool to help understand the relationship between temperature and pressure, making it a valuable resource in thermodynamics and physical chemistry.With the Antoine equation, you can more deeply explore the nature of phase changes and the interplay between temperature and vapor pressure without relying solely on standard tables.