Question

At high altitudes water boils at above $100^{ o }{ C }$.
(A) True
(B) False

Answer 1

In order to solve this question we first need to understand Boyle's law which states that the volume of a given mass of a gas is inversely proportional to its pressure. By using this law we will get to know that the air is less dense at higher altitudes because the atmospheric pressure is low. The boiling point for a liquid is the temperature at which the vapour pressure of the liquid becomes equal to the atmospheric pressure.

Complete step by step answer:
To solve this question we need to first understand one of the gas laws namely Boyle’s law:
According to Boyle’s law, the volume of a given mass of a gas is inversely proportional to its pressure. That is:
$V\propto \cfrac { 1 }{ P }$
Where V is the volume of the gas and P is the pressure exerted by the gas. Therefore:
$V=k\times \cfrac { 1 }{ P }$
Where k is the proportionality constant. Hence,
$PV=k$
This means the product of the pressure and volume for a given amount of a gas is a constant at constant temperature.
Boyle’s law proves that gases are compressible. If we increase the pressure, the gases will become denser. Hence we can say that at a constant temperature, the density of a gas is directly proportional to its pressure for a fixed mass of a gas.
So, if m is the mass of a gas, V is its volume and P is its pressure, then its density d will be:
$d=\cfrac { m }{ V }$

Now, according to Boyle’s law, $PV=k$ or $V=k\times \cfrac { 1 }{ P }$
Putting this value of V in the density formula,
$d=\cfrac { m }{ \cfrac { k }{ P } }$
$\Rightarrow d=\cfrac { m }{ k } \times P={ k }^{ \prime }P$
Where ${ k }^{ \prime }=\cfrac { m }{ k }$, another constant.

Therefore at higher altitudes the air is less dense since at higher altitudes the pressure is very low. This results in altitude sickness.
When the vapour pressure of a liquid becomes equal to the atmospheric pressure at a particular temperature, then that temperature is called the boiling point of the liquid. Since at high altitudes the atmosphere is less dense and the atmospheric pressure is low, therefore the boiling point for a particular liquid will decrease at high altitudes.
So, the correct answer is “Option B”.

Note: The elevation in boiling point for a particular liquid is observed if a non-volatile solute is added to the liquid. This is because when we add a non-volatile solute to a solvent, it displaces some solvent molecules at the surface of the solution and hence reduces the vapour pressure of the solvent.