In the 'gas saturation method' for the measurement of vapour pressure, a volume \(V\) of gas (as measured at a temperature \(T\) and a pressure \(\mathrm{p}\) ) is bubbled slowly through the liquid that is maintained at the temperature \(T\), and a mass loss \(m\) is measured. Show that the vapour pressure, \(p\), of the liquid is related to its molar mass, \(\mathrm{M}\), by \(p=A m P /(1+A m)\), where \(\mathrm{A}=R T / M P V\). The vapour pressure of geraniol \(\left(M=154.2 \mathrm{~g} \mathrm{~mol}^{-1}\right)\), which is a component of oil of roses, was measured at \(110^{\circ} \mathrm{C}\). It was found that, when \(5.00 \mathrm{dm}^{3}\) of nitrogen at 760 Torr was passed slowly through the heated liquid, the loss of mass was \(0.32 \mathrm{~g}\). Calculate the vapour pressure of geraniol.

The gas saturation method is a laboratory technique utilized to measure the vapour pressure of a liquid. Vapour pressure is an indication of a liquid’s volatility—the higher the vapour pressure, the more readily the liquid turns into gas. In this method, a known volume of gas, measured at specific temperature and pressure, is bubbled through the liquid we are testing, which is also kept at the same temperature.
During this process, the gas becomes saturated with the vapour of the liquid. Any change in the mass of the gas can be associated with the absorption of the liquid's vapour. The mass lost by the liquid, due to the gas carrying away its vapour, can then be used to calculate the vapour pressure of the liquid using a mathematical relationship.
This technique is advantageous for determining volatile compound vapour pressures at various temperatures. By understanding the principles behind this technique, students can learn how to apply it to practical scientific problems, such as determining the vapour pressures of essential oils or fragrances, which often require accurate measurements of their volatile components.

Molar mass, denoted by M, is defined as the mass of one mole of a substance. It is a physical property that is particularly important in the realm of chemistry, as it directly relates the mass of a substance to the number of particles present in a sample. The unit for molar mass is grams per mole (\(g/mol\)).
In the context of the gas saturation method, the molar mass of the liquid plays a significant role in the calculation of the vapour pressure. Since the gas's mass loss after saturation is measurably related to the molar quantity of the vapour absorbed, the molar mass allows us to distinguish how many moles of vapour were responsible for the lost mass. Knowing the molar mass of a substance can assist in a variety of calculations and is crucial for the correct determination of vapour pressure in the given exercise.
Being such a key aspect of many scientific calculations, understanding how to use molar mass in different scenarios, such as in calculating the number of moles in a given mass of substance or determining the density of a gas, is an essential skill for students studying chemistry.

The ideal gas constant, represented as R, is a fundamental constant in chemistry that appears in the ideal gas law equation: \(PV = nRT\), where P is the pressure, V is the volume, n is the number of moles of gas, T is the temperature in Kelvin, and R is the ideal gas constant.
Its value is determined to be 0.0821 Liter atmospheres per mole Kelvin (\(L \text{ atm mol}^{-1} \text{ K}^{-1}\)), and it serves as a bridge between the macroscopic and microscopic properties of gases, linking pressure, volume, temperature, and the amount of substance. In the provided exercise, R is used in the derivation of the constant A and is instrumental in determining the vapour pressure of the liquid being tested.
Since the ideal gas constant is the same for all gases under ideal conditions, it is a crucial element for students to comprehend when performing calculations involving gases. Understanding how R is used in context and being able to recognize its role in various gas-related equations prepares students for a wide range of problem-solving situations in physics and engineering as well as chemistry.