<u>Answer:</u> The molarity of solution is 0.799 M , molality of solution is 1.02 m, mole fraction of camphor is 0.045 and mass percent of camphor in solution is 13.43 %
<u>Explanation:</u>
- <u>Calculating the molarity of solution:</u>
To calculate the molarity of solution, we use the equation:
![\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}](https://tex.z-dn.net/?f=%5Ctext%7BMolarity%20of%20the%20solution%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20solute%7D%5Ctimes%201000%7D%7B%5Ctext%7BMolar%20mass%20of%20solute%7D%5Ctimes%20%5Ctext%7BVolume%20of%20solution%20%28in%20mL%29%7D%7D)
Given mass of camphor = 70.0 g
Molar mass of camphor = 152.2 g/mol
Volume of solution = 575 mL
Putting values in above equation, we get:
![\text{Molarity of camphor}=\frac{70\times 1000}{152.2\times 575}\\\\\text{Molarity of camphor}=0.799M](https://tex.z-dn.net/?f=%5Ctext%7BMolarity%20of%20camphor%7D%3D%5Cfrac%7B70%5Ctimes%201000%7D%7B152.2%5Ctimes%20575%7D%5C%5C%5C%5C%5Ctext%7BMolarity%20of%20camphor%7D%3D0.799M)
- <u>Calculating the molarity of solution:</u>
To calculate the mass of ethanol, we use the equation:
![\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}](https://tex.z-dn.net/?f=%5Ctext%7BDensity%20of%20substance%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20substance%7D%7D%7B%5Ctext%7BVolume%20of%20substance%7D%7D)
Density of ethanol = 0.785 g/mL
Volume of ethanol = 575 mL
Putting values in above equation, we get:
![0.785g/mL=\frac{\text{Mass of ethanol}}{575mL}\\\\\text{Mass of ethanol}=(0.785g/mL\times 575mL)=451.38g](https://tex.z-dn.net/?f=0.785g%2FmL%3D%5Cfrac%7B%5Ctext%7BMass%20of%20ethanol%7D%7D%7B575mL%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20ethanol%7D%3D%280.785g%2FmL%5Ctimes%20575mL%29%3D451.38g)
To calculate the molality of solution, we use the equation:
![\text{Molality of solution}=\frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ (in grams)}}](https://tex.z-dn.net/?f=%5Ctext%7BMolality%20of%20solution%7D%3D%5Cfrac%7Bm_%7Bsolute%7D%5Ctimes%201000%7D%7BM_%7Bsolute%7D%5Ctimes%20W_%7Bsolvent%7D%5Ctext%7B%20%28in%20grams%29%7D%7D)
where,
= Given mass of solute (camphor) = 70 g
= Molar mass of solute (camphor) = 152.2 g/mol
= Mass of solvent (ethanol) = 451.38 g
Putting values in above equation, we get:
![\text{Molality of camphor}=\frac{70\times 1000}{152.2\times 451.38}\\\\\text{Molality of camphor}=1.02m](https://tex.z-dn.net/?f=%5Ctext%7BMolality%20of%20camphor%7D%3D%5Cfrac%7B70%5Ctimes%201000%7D%7B152.2%5Ctimes%20451.38%7D%5C%5C%5C%5C%5Ctext%7BMolality%20of%20camphor%7D%3D1.02m)
- <u>Calculating the mole fraction of camphor:</u>
To calculate the number of moles, we use the equation:
.....(1)
<u>For camphor:</u>
Given mass of camphor = 70 g
Molar mass of camphor = 152.2 g/mol
Putting values in equation 1, we get:
![\text{Moles of camphor}=\frac{70g}{152.2g/mol}=0.459mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20camphor%7D%3D%5Cfrac%7B70g%7D%7B152.2g%2Fmol%7D%3D0.459mol)
<u>For ethanol:</u>
Given mass of ethanol = 451.38 g
Molar mass of ethanol = 46 g/mol
Putting values in equation 1, we get:
![\text{Moles of ethanol}=\frac{451.38g}{46g/mol}=9.813mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20ethanol%7D%3D%5Cfrac%7B451.38g%7D%7B46g%2Fmol%7D%3D9.813mol)
Mole fraction of a substance is given by:
![\chi_A=\frac{n_A}{n_A+n_B}](https://tex.z-dn.net/?f=%5Cchi_A%3D%5Cfrac%7Bn_A%7D%7Bn_A%2Bn_B%7D)
Moles of camphor = 0.459 moles
Total moles = [0.459 + 9.813] = 10.272 moles
Putting values in above equation, we get:
\
- <u>Calculating the mass percent of camphor:</u>
To calculate the mass percentage of camphor in solution, we use the equation:
![\text{Mass percent of camphor}=\frac{\text{Mass of camphor}}{\text{Mass of solution}}\times 100](https://tex.z-dn.net/?f=%5Ctext%7BMass%20percent%20of%20camphor%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20camphor%7D%7D%7B%5Ctext%7BMass%20of%20solution%7D%7D%5Ctimes%20100)
Mass of camphor = 70 g
Mass of solution = [70 + 451.38] = 521.38 g
Putting values in above equation, we get:
![\text{Mass percent of camphor}=\frac{70g}{521.38g}\times 100=13.43\%](https://tex.z-dn.net/?f=%5Ctext%7BMass%20percent%20of%20camphor%7D%3D%5Cfrac%7B70g%7D%7B521.38g%7D%5Ctimes%20100%3D13.43%5C%25)
Hence, the molarity of solution is 0.799 M , molality of solution is 1.02 m, mole fraction of camphor is 0.045 and mass percent of camphor in solution is 13.43 %