In the aqueous solution of H2SO4 its mole fraction is 0.2 then closest value of molality of
solution is
(1) 13.9 (2) 9.8
(3) 10.2 (4) 11.2
XH2SO4 = 0.2 so
XH2O = 0.8
Take 1 mol of the solution. That will contain 0.8 mols H2O. How many grams is that?
0.8 mol x 18 gH2O/mol = 14.4 g or 0.0144 kg.
molality = mols H2SO4/kg solvent
0.2/0.0144 = ?m
13.9
To solve this problem, we need to convert the mole fraction into molality.
The mole fraction (χ) of a component in a solution is defined as the ratio of the moles of that component to the total moles of all components in the solution. In equation form:
χ = moles of component / total moles
The molality (m) of a solution is defined as the moles of solute per kilogram of solvent. In equation form:
m = moles of solute / mass of solvent (in kg)
Given that the mole fraction (χ) of H2SO4 is 0.2, we can calculate the moles of H2SO4 using the mole fraction and the total moles of all components in the solution. Since H2SO4 is the only component mentioned, the total moles can be considered as the moles of H2SO4.
Let's assume the total moles of H2SO4 in the solution is x. Then, according to the mole fraction formula:
0.2 = x / x
Simplifying the equation:
0.2 = 1
This is a contradiction, which means there is an error in the problem statement. The mole fraction cannot be equal to 1 for a component in a solution. Therefore, it is not possible to determine the molality of the solution based on the given information.
Thus, none of the options provided (1) 13.9, (2) 9.8, (3) 10.2, or (4) 11.2 can be the correct answer.
To find the molality of a solution, we need to know the amount of solute (in moles) and the mass of the solvent (in kilograms).
In this case, we are given the mole fraction of H2SO4 in the aqueous solution, which is 0.2. The mole fraction is the ratio of moles of solute to the total moles of solute and solvent.
Let's assume we have 1 mole of the solution. Since the mole fraction of H2SO4 is 0.2, the moles of H2SO4 will be 0.2 moles.
Now we need to calculate the mass of the solvent. The mass of the solvent can be calculated using the formula:
mass of solvent = moles of solvent × molar mass of solvent.
Since water (H2O) is the solvent in this case, the molar mass of water is 18 g/mol.
From the mole fraction, we know that the moles of H2O will be 1 - 0.2 = 0.8 moles.
Therefore, the mass of the solvent will be:
mass of solvent = 0.8 moles × 18 g/mol = 14.4 g.
Finally, we can calculate the molality of the solution using the formula:
molality = moles of solute / mass of solvent (in kg).
molality = 0.2 moles / 14.4 g = 0.0139 mol/kg.
To choose the closest value from the given options, we need to convert molality to the required decimal places.
The closest value to 0.0139 in the given options is 0.014, therefore, the closest value of molality of the solution is (1) 13.9.
So, the answer is (1) 13.9.