The osmotic pressure of a solution containing \(4.0 \mathrm{~g}\) of solute (molar mass 246 ) per litre at \(27^{\circ} \mathrm{C}\) is \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\) (a) \(0.1 \mathrm{~atm}\) (b) \(0.3 \mathrm{~atm}\) (c) \(0.4 \mathrm{~atm}\) (d) \(0.9 \mathrm{~atm}\)

Colligative properties are characteristics of solutions that depend on the concentration of the solute particles but not on their identity. Essentially, these properties are influenced by the number of particles in a solution. One of the classic examples of a colligative property is osmotic pressure, which is the pressure required to prevent the flow of solvent into the solution through a semipermeable membrane.

Other colligative properties include boiling point elevation, freezing point depression, and vapor pressure lowering. For a given solvent, the magnitude of these changes is proportional to the solute concentration, which in dilute solutions is often represented as the number of moles of solute particles per kilogram of solvent. In the context of osmotic pressure, understanding this relationship underscores why it serves as a tool for determining molar masses of solutes by examining their effect on the solvent.

Molar mass is a critical concept in chemistry that represents the mass of one mole of a substance, usually expressed in grams per mole (\text{g/mol}). It is the bridge between the macroscopic world (grams) and the microscopic world (number of particles). As mole is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles, the molar mass tells us the mass of these entities when we have Avogadro's number of them—one mole, which is approximately \(6.022 \times 10^{23}\) particles.

In osmotic pressure calculations, knowledge of the molar mass allows us to convert a known mass of solute into moles which can then be used in the formula to calculate osmotic pressure.

The ideal gas constant (R) is a fundamental constant in physics and chemistry that links the amount of gas, temperature, and pressure in the ideal gas law (\text{PV=nRT}), where \text{P} is pressure, \text{V} is volume, \text{n} is the number of moles, and \text{T} is temperature. Its value is \(0.0821 \text{ L atm mol}^{-1} \text{K}^{-1}\) when expressed in units of liters, atmospheres, moles, and Kelvin.

This constant becomes paramount in osmotic pressure calculations as it essentially quantifies the relationship between the variables involved. Since osmotic pressure is a colligative property, which can be analogous to the pressure exerted by gases, \text{R} facilitates the translation of concentration data into pressure values provided by the osmotic pressure formula derived from the ideal gas law.

The Kelvin temperature scale is an absolute thermodynamic temperature scale, widely used in the sciences, and is critical in calculations that involve temperature, such as those dealing with gas laws and colligative properties. The Kelvin scale starts at absolute zero, the theoretical temperature where particles have minimal vibrational movement. Unlike Celsius, it does not use degrees but is simply denoted as \text{K}.

To convert Celsius to Kelvin, one adds \(273.15\) to the Celsius temperature. This is imperative in calculations concerning osmotic pressure because the value of the ideal gas constant \text{R} assumes that the temperature is measured in Kelvin, thus ensuring the proper unit consistency within the calculation.