The vapours pressure of water at \(23^{\circ} \mathrm{C}\) is \(19.8 \mathrm{~mm}\). of Hg. \(0.1\) mole of glucose is dissolved in \(178.2 \mathrm{~g}\) of water. What is the vapour pressure (in \(\mathrm{mm}\) of \(\mathrm{Hg}\) ) of the resultant solution? (a) \(19.0\) (b) \(19.602\) (c) \(19.402\) (d) \(19.202\)

When a liquid is in a closed container, it tends to evaporate by releasing molecules into the space above the liquid surface. Over time, these molecules exert a force on the container's walls, known as vapor pressure. It's a measure of a liquid's tendency to evaporate and is influenced by the substance's temperature.

At a given temperature, each substance has its characteristic vapor pressure. When a liquid reaches the temperature at which its vapor pressure equals the external pressure, boiling occurs. In the exercise provided, the vapor pressure of pure water at 23°C is given as 19.8 mmHg. This is a crucial piece of information when using Raoult's Law to determine changes in vapor pressure in the presence of a solute, such as glucose.

The mole fraction is a way of expressing the proportion of a component in a mixture and is defined as the moles of that component divided by the total moles of all components present. When dealing with solutions, the mole fraction helps comprehend how much of the solution is made up of a specific component, be it a solute or solvent.

Mathematically, the mole fraction, X, can be represented by the equation \[X = \frac{n_{component}}{n_{total}}\], where n_{component} represents the number of moles of the component of interest, and n_{total} is the sum of moles of all components in the mixture. In our exercise, the mole fraction is critical for applying Raoult's Law to determine the vapor pressure of the solution.

Certain properties of solutions that depend on the number of solute particles but not their identity are known as colligative properties. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

In this context, Raoult's Law connects directly to the colligative property of vapor pressure lowering. According to the law, adding a non-volatile solute to a solution decreases the solution's vapor pressure proportionally to the solute's mole fraction. The exercise we're looking at demonstrates this property by calculating how much the vapor pressure of water is decreased due to the addition of glucose.

The study of solution chemistry involves the mixtures of substances and how they interact, dissolve, and affect each other's properties. Solutions can be solids, liquids, or gases, and the components are classified as solutes (the substances being dissolved) and solvents (the substances doing the dissolving).

With our exercising problem, water acts as the solvent and the glucose as the solute. Understanding the respective roles of solute and solvent, as well as other factors like temperature and pressure, is fundamental in solving problems in solution chemistry. By dissolving glucose in water, we're able to observe real-time changes in properties such as vapor pressure, highlighting the practical applications of solution chemistry principles.