Question

The relative lowering of vapour pressure produced by dissolving $71.5g$ of a substance in $1000g$ of water is $0.00713$ . The molecular weight of the substance will be

Answer 1

Hint : Mixtures can be of two types. One is a homogeneous mixture of substances that are soluble and inseparable while the heterogeneous mixture of substances that are not soluble and the both substances can be easily seen differently.

Complete Step By Step Answer:
Raoult’s law states that vapour pressure of a volatile component in a given solution is given by ${p_i} = {p_ \circ }{x_i}$ . In the solution of gas and liquids, one of the components is so volatile that it cant exist as a solution and exists as a gas. We can say that the partial pressure of the volatile component in the solution is equal to the mole fraction of that component in the solution.
${p_ \circ }$ can be defined as the total pressure of the gas when it and only it is present in the container.
By Raoult’s law we can say that a graph starting at zero can be drawn to represent this principle where when the mole fraction is zero the partial pressure above the solution is zero and when the partial pressure ${p_ \circ }$ , gas and only that gas is present in the container.
Now for a solution to actually obey all these laws, the enthalpy of mixing the pure components to form a solution has to be zero and the change in the volume of the mixing has to be zero. These are the conditions that are always obeyed by an ideal solution.
Now the molecular weight of water is
$2H + O$
$= 2 \times 1 + 16$
$= 18\dfrac{g}{{mol}}$
Given mass of water is $1000g$
Given mass of substance is $71.5g$
Mole fraction of the substance is equal to the moles of the substances divided by the moles of substance and the moles of water
$\chi = \dfrac{{moles\,of \; substance}}{{moles\,of\,subs\tan ce + moles\,of\,water\,or\,solvent}}$
Putting the values, knowing mole is equal given mass divided by the molecular weight
Let's say molecular weight of substance be $x$
$\chi = \dfrac{{moles\,of\;substance}}{{moles\,of\,subs\tan ce + moles\,of\,water\,or\,solvent}} \\\ \Rightarrow 0.00713 = \dfrac{{\dfrac{{71.5}}{x}}}{{\dfrac{{71.5}}{x} + \dfrac{{1000}}{{18}}}} \\\ \Rightarrow x = 180 \\\$
The molar mass of the substance is $180\dfrac{g}{{mol}}$ .

Note :
There are few mixtures which when mixed with each other release heat or sometimes some solutions need energy to get mixed with each other. These solutions or mixtures are called non-ideal solutions. Non ideal solutions have their own specific laws with changes.