Answer : The the concentration of
in mass percent is, 41.18 %
Solution : Given,
Molar mass of water = 18 g/mole
Molar mass of
= 110.98 g/mole
First we have to calculate the mole fraction of solute.
According to the relative lowering of vapor pressure, the vapor pressure of a component at a given temperature is equal to the mole fraction of that component of the solution multiplied by the vapor pressure of that component in the pure state.
![\fac{p^o-p_s}{p^o}=X_B](https://tex.z-dn.net/?f=%5Cfac%7Bp%5Eo-p_s%7D%7Bp%5Eo%7D%3DX_B)
where,
= vapor pressure of the pure component (water) = 92.6 mmHg
= vapor pressure of the solution = 83.1 mmHg
= mole fraction of solute, ![(CaCl_2)](https://tex.z-dn.net/?f=%28CaCl_2%29)
Now put all the given values in this formula, we get the mole fraction of solute.
![\fac{92.6-83.1}{92.6}=X_B](https://tex.z-dn.net/?f=%5Cfac%7B92.6-83.1%7D%7B92.6%7D%3DX_B)
![X_B=0.102](https://tex.z-dn.net/?f=X_B%3D0.102)
Now we have to calculate the mole fraction of solvent (water).
As we know that,
![X_A+X_B=1\\\\X_A=1-X_B\\\\X_A=1-0.102\\\\X_A=0.898](https://tex.z-dn.net/?f=X_A%2BX_B%3D1%5C%5C%5C%5CX_A%3D1-X_B%5C%5C%5C%5CX_A%3D1-0.102%5C%5C%5C%5CX_A%3D0.898)
The number of moles of solute and solvent will be, 0.102 and 0.898 moles respectively.
Now we have to calculate the mass of solute,
and solvent,
.
![\text{Mass of }CaCl_2=(0.102mole)\times (110.98g/mole)=11.32g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20%7DCaCl_2%3D%280.102mole%29%5Ctimes%20%28110.98g%2Fmole%29%3D11.32g)
![\text{Mass of }H_2O=(0.898mole)\times (18g/mole)=16.164g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20%7DH_2O%3D%280.898mole%29%5Ctimes%20%2818g%2Fmole%29%3D16.164g)
Mass of solution = Mass of solute + Mass of solvent
Mass of solution = 11.32 + 16.164 = 27.484 g
Now we have to calculate the mass percent of ![CaCl_2](https://tex.z-dn.net/?f=CaCl_2)
![Mass\%=\frac{\text{Mass of}CaCl_2}{\text{Mass of solution}}\times 100=\frac{11.32g}{27.484g}\times 100=41.18\%](https://tex.z-dn.net/?f=Mass%5C%25%3D%5Cfrac%7B%5Ctext%7BMass%20of%7DCaCl_2%7D%7B%5Ctext%7BMass%20of%20solution%7D%7D%5Ctimes%20100%3D%5Cfrac%7B11.32g%7D%7B27.484g%7D%5Ctimes%20100%3D41.18%5C%25)
Therefore, the the concentration of
in mass percent is, 41.18 %