Consider liquid water in equilibrium with its vapor at 100 ^∘ C. Estimate the number of water mo

step 1 Given that the density of liquid water at 100 degree centigrade is 0 .958 gram per centimeter cu

Consider liquid water in equilibrium with its vapor at 100...

Consider liquid water in equilibrium with its vapor at $100{ }^{\circ} \mathrm{C}$. Estimate the number of water molecules per $\mathrm{cm}^{3}$ in (a) the liquid (density $=0.958 \mathrm{~g} / \mathrm{cm}^{3}$ at $\left.100{ }^{\circ} \mathrm{C}\right)$; (b) the vapor.

Key Concepts

Molar Mass

The molar mass links the mass of a substance to the number of moles it contains. It is essential for converting measurements of mass (such as density in g/cm³) into moles, which can then be related to the number of molecules via Avogadro's number.

Avogadro's Number

Avogadro's number defines the number of particles, typically atoms or molecules, in one mole of a substance. It is a key constant used to convert between moles and the actual number of individual molecules, thereby enabling the calculation of molecular density.

Density

Density is the mass per unit volume of a substance and is crucial for estimating the number of molecules in a given volume. It connects macroscopic measurements with microscopic quantities such as moles and individual molecular counts.

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and the number of moles of a gas. It is used to estimate the number density of a vapor phase by connecting these macroscopic state variables, thereby calculating the number of molecules present per unit volume.

Phase Equilibrium

Phase equilibrium refers to the state in which different phases of a substance, such as liquid water and its vapor, coexist under equilibrium conditions. Understanding phase equilibrium is important for knowing that the properties of each phase (like density for liquid and behavior as a gas for vapor) can differ significantly, impacting how molecular counts are estimated.

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