Question

Weight of 32 g hydrated magnesium sulphate when dissolved in 84 g of water, the solution freezes at $- 4.5836^\circ C$ .If ${K_f} = 1.86Kkgmol{e^{ - 1}}$ and magnesium sulphate is a strong electrolyte. What is the value of x?
A.7
B.6
C.8
D.5

Answer 1

Magnesium sulfate heptahydrate is a hydrated that is the heptahydrate form of magnesium sulfate. It has a role as laxative and cathartic. It is a magnesium salt and a hydrate. It contains a magnesium sulfate. It is a naturally occurring mineral used to control low blood levels of magnesium. Magnesium sulfate injection is also used for pediatric acute nephritis and to prevent seizures in severe pre-eclampsia.

Complete step by step answer:
First, we find the molar mass,
The molar mass of solvent $= 120 + 18x$
Mass of water which is present in the salt $= \dfrac{{18x}}{{120 + 18x}} \times 32g$
Now, we will find the molality of solution
$= \dfrac{{32}}{{120 + 18x}} \times \left[ {\dfrac{{1000}}{{84 + \dfrac{{18 \times 32x}}{{120 + 18x}}}}} \right] = \dfrac{{4000}}{{1260 + 261x}}$
$\Delta {T_f} = 4.836 = 2 \times 1.86 \times \dfrac{{4000}}{{1260 + 261x}}$
$\Rightarrow x = 6.9 \approx 7$

Hence, option (A) is the correct answer.

Note: A final way to express the concentration of a solution is by its molality. The molality of a solution is the moles of solute divided by the kilograms of solvent. The symbol for molality is a lower case m written in italics.
Molality = Moles of solute/kilograms of solvent $= \dfrac{{mol}}{{kg}}$
Molality differs from molarity only in the denominator. While molarity is based on the liters of solution, molality is based on the kilograms of solvent. Concentration expressed in molality is used when studying properties of solutions related to vapor pressure and temperature changes. The volume of a solution, on the other hand, is slightly dependent on temperature.