Explanation:
Molarity of solution = 1.00 M = 1.00 mol/L
In 1 L of solution 1.00 moles of calcium chloride is present.
Mass of solute or calcium chloride = m
![m = 1 mol\times 111 g/mol = 111 g](https://tex.z-dn.net/?f=m%20%3D%201%20mol%5Ctimes%20111%20g%2Fmol%20%3D%20111%20g)
Mass of solution = M
Volume of solution = V = 1L = 1000 mL
Density of solution , d= 1.07 g/mL
![M=d\times V=1.07 g/mL\times 1000 mL=1,070 g](https://tex.z-dn.net/?f=M%3Dd%5Ctimes%20V%3D1.07%20g%2FmL%5Ctimes%201000%20mL%3D1%2C070%20g)
1) The value of %(m/M):
![\frac{m}{M}\times 100=\frac{111 g}{1,070 g}\times 100=10.37\%](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7BM%7D%5Ctimes%20100%3D%5Cfrac%7B111%20g%7D%7B1%2C070%20g%7D%5Ctimes%20100%3D10.37%5C%25)
2) The value of %(m/V):
![\frac{m}{V}\times 100=\frac{111 g}{1000 L}\times 100=11.1\%](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7BV%7D%5Ctimes%20100%3D%5Cfrac%7B111%20g%7D%7B1000%20L%7D%5Ctimes%20100%3D11.1%5C%25)
![Molality = \frac{\text{Moles of compound }}{\text{mass of solvent in kg}}](https://tex.z-dn.net/?f=Molality%20%3D%20%5Cfrac%7B%5Ctext%7BMoles%20of%20compound%20%7D%7D%7B%5Ctext%7Bmass%20of%20solvent%20in%20kg%7D%7D)
![Normality=\frac{\text{Moles of compound }}{n\times \text{volume of solution in L}}](https://tex.z-dn.net/?f=Normality%3D%5Cfrac%7B%5Ctext%7BMoles%20of%20compound%20%7D%7D%7Bn%5Ctimes%20%5Ctext%7Bvolume%20of%20solution%20in%20L%7D%7D)
n = Equivalent mass
n = ![\frac{\text{molar mass of ion}}{\text{charge on an ion}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7Bmolar%20mass%20of%20ion%7D%7D%7B%5Ctext%7Bcharge%20on%20an%20ion%7D%7D)
3) Normality of calcium ions:
Moles of calcium ion = 1 mol (1
mole has 1 mole of calcium ion)
![n=\frac{40 g/mol}{2}=20](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B40%20g%2Fmol%7D%7B2%7D%3D20%20)
![=\frac{1 mol}{20 g/mol\times 1L}=0.050 N](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%20mol%7D%7B20%20g%2Fmol%5Ctimes%201L%7D%3D0.050%20N)
4) Normality of chlorine ions:
Moles of chlorine ion = 2 mol (1
mole has 2 mole of chlorine ion)
![n=\frac{35.5 g/mol}{1}=35.5](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B35.5%20g%2Fmol%7D%7B1%7D%3D35.5)
![=\frac{2 mol}{35.5 g/mol\times 1L}=0.056 N](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%20mol%7D%7B35.5%20g%2Fmol%5Ctimes%201L%7D%3D0.056%20N)
Moles of calcium chloride = 1.00 mol
Mass of solvent = Mass of solution - mass of solute
= 1,070 g - 111 g = 959 g = 0.959 kg ( 1 g =0.001 kg)
5) Molality of the solution :
![\frac{1 mol}{0.959 kg}=1.043 mol/kg](https://tex.z-dn.net/?f=%5Cfrac%7B1%20mol%7D%7B0.959%20kg%7D%3D1.043%20mol%2Fkg)
Moles of calcium chloride = ![n_1=1mol](https://tex.z-dn.net/?f=n_1%3D1mol)
Mass of solvent = 959 g
Moles of water = ![n_2=\frac{959 g}{18 g/mol}=53.28 mol](https://tex.z-dn.net/?f=n_2%3D%5Cfrac%7B959%20g%7D%7B18%20g%2Fmol%7D%3D53.28%20mol)
Mass of solvent = 959 g
6) Mole fraction of calcium chloride =
![\chi_1=\frac{n_1}{n_1+n_2}=\frac{1mol}{1 mol+53.28 mol}=0.01842](https://tex.z-dn.net/?f=%5Cchi_1%3D%5Cfrac%7Bn_1%7D%7Bn_1%2Bn_2%7D%3D%5Cfrac%7B1mol%7D%7B1%20mol%2B53.28%20mol%7D%3D0.01842)
7) Mole fraction of water =
![\chi_2=\frac{n_2}{n_1+n_2}=\frac{53.28 mol}{1mol+53.28 mol}=0.9816](https://tex.z-dn.net/?f=%5Cchi_2%3D%5Cfrac%7Bn_2%7D%7Bn_1%2Bn_2%7D%3D%5Cfrac%7B53.28%20mol%7D%7B1mol%2B53.28%20mol%7D%3D0.9816)
8) Mass of solution = m'
Volume of the solution= v = 100 mL
Density of solution = d = 1.07 g/mL
![m'=d\times v=1.07 g/ml\times 100 g= 107 g](https://tex.z-dn.net/?f=m%27%3Dd%5Ctimes%20v%3D1.07%20g%2Fml%5Ctimes%20100%20g%3D%20107%20g)
Mass of 100 mL of this solution 107 grams of solution.
9) Volume of solution = V = 100 mL
Mass of solution = M'' = 107 g
Mass of solute = m
The value of %(m/V) of solution = 11.1%
![11.1\%=\frac{m}{100 mL}\times 100](https://tex.z-dn.net/?f=11.1%5C%25%3D%5Cfrac%7Bm%7D%7B100%20mL%7D%5Ctimes%20100)
m = 11.1 g
Mass of solvent = M''- m = 107 g -11.1 g = 95.9 g
95.9 grams of water was present in 100 mL of given solution.