A 15 % (m/m) aqueous solution of glucose is prepared by dissolving 13.5 g of glucose in x g of water. Calculate the value of x.
Answers
Explanation:
Osmotic pressure is proportional to the molarity, C, of the solution at a given temperature T. Thus
π=CRT ...(i)
Where,
π= osmotic pressure
R= gas constant =0.0821dm
3
atm mol
−1
K
−1
T= temperature =298K
C= molarity =
V
n
=
M×V
w
...(ii)
Where,
n= no. of moles
w= Weight of solute glucose =4.5g
M= Molecular weight of solute glucose =180g
V= Volume of solution =100ml=0.1L
Putting the values in the formula (i) and (ii) we get :
π=
MV
wRT
=
180×0.1
4.5×0.0821×298
=
18
110.09
=6.12atm
The osmotic pressure of the solution is 6.12atm.
Given,
The mass by mass percentage of the solution = 15%
Mass of glucose (solute) = 13.5 grams
Mass of water (solvent) = x grams
To find,
The value of x
Solution,
We can simply solve this numerical problem by using the following process.
Now,
Mass by Mass percentage = (Mass of solute / Mass of solution) × 100%
Here,
Mass of solution = Mass of solvent + Mass of solute = (x+13.5) grams
By, putting the given values, we get :
15% = {(13.5)/(x+13.5)} × 100%
0.15 = {(13.5)/(x+13.5)}
0.15x + 2.025 = 13.5
0.15x = 13.5-2.025
0.15x = 11.475
x = 11.475/0.15
x = 76.5
(So, there will be 76.5 grams of water as the solvent, in the given solution.)
Hence, the value of x is 76.5