Consider the three mercury manometers shown here. One of...

Consider the three mercury manometers shown here. One of them has 1 mL of water on top of the mercury, another has $1 \mathrm{mL}$ of a $1 \mathrm{m}$ urea solution on top of the mercury, and the third one has $1 \mathrm{mL}$ of a 1 $m$ NaCl solution placed on top of the mercury. Which of these solutions is in the tube labeled X, which is in $Y,$ and which is in $Z ?$

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity acting on the fluid’s mass. In any vertical column of liquid, the pressure at the bottom is calculated as the product of the liquid’s density, the gravitational acceleration, and the height of the liquid column. This concept is key when comparing fluid columns of the same volume but different densities, as the height of the column needed to exert a given pressure will vary inversely with the density.

Density of Solutions

The density of a solution determines how much mass is contained in a given volume. When comparing different solutions in a manometer, even if the volume is the same, variations in the solution’s density will change the weight of the solution and consequently the hydrostatic pressure it exerts. This concept is central in understanding why liquids with different solute contents might shift interfaces by different amounts in a manometer setting.

Electrolyte Dissociation and Colligative Effects

In solutions containing electrolytes, such as salts, the solute dissociates into multiple ions, effectively increasing the number of particles in solution relative to a non?electrolyte at the same molal concentration. This increase in particle number not only affects colligative properties like boiling point elevation or freezing point depression but can also influence the overall density of the solution. Recognizing how dissociation alters physical properties is essential when comparing the behavior of different solutions in fluid statics applications.

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