<u>Answer:</u> The molality and molarity of zinc in the solution is 4.07 m and 28.11 M respectively.
<u>Explanation:</u>
Solute is the substance which is present in smaller proportion in a mixture and solvent is the substance which is present in larger proportion in a mixture.
We are given:
(m/m) % of Cu = 79 %
This means that 79 g of copper is present in 100 grams of alloy.
(m/m) % of Zn = 21 %
This means that 21 g of zinc is present in 100 grams of alloy.
As, zinc is present in smaller proportion. So, it is solute and copper is the solvent.
- <u>Calculating molality of zinc:</u>
To calculate molality of the zinc, we use the equation:
![Molality=\frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ in grams}}](https://tex.z-dn.net/?f=Molality%3D%5Cfrac%7Bm_%7Bsolute%7D%5Ctimes%201000%7D%7BM_%7Bsolute%7D%5Ctimes%20W_%7Bsolvent%7D%5Ctext%7B%20in%20grams%7D%7D)
where,
= Given mass of solute (Zinc ) = 21 g
= Molar mass of solute (Zinc) = 65.3 g/mol
= Mass of solvent (copper) = 79 g
Putting values in above equation, we get:
![\text{Molality of Zinc}=\frac{21\times 1000}{65.3\times 79}\\\\\text{Molality of zinc}=4.07m](https://tex.z-dn.net/?f=%5Ctext%7BMolality%20of%20Zinc%7D%3D%5Cfrac%7B21%5Ctimes%201000%7D%7B65.3%5Ctimes%2079%7D%5C%5C%5C%5C%5Ctext%7BMolality%20of%20zinc%7D%3D4.07m)
- <u>Calculating molarity of zinc:</u>
To calculate volume of a substance, 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 solution = ![8740kg/m^3=\frac{8740kg\frac{1000g}{1kg}}{1m^3\times \frac{10^6cm^3}{1m^3}}=\frac{8740g}{1000cm^3}=8.740g/cm^3](https://tex.z-dn.net/?f=8740kg%2Fm%5E3%3D%5Cfrac%7B8740kg%5Cfrac%7B1000g%7D%7B1kg%7D%7D%7B1m%5E3%5Ctimes%20%5Cfrac%7B10%5E6cm%5E3%7D%7B1m%5E3%7D%7D%3D%5Cfrac%7B8740g%7D%7B1000cm%5E3%7D%3D8.740g%2Fcm%5E3)
(Conversion factors used are: 1 kg = 1000 g &
)
Mass of solution = 100 g
Putting values in above equation, we get:
![8.740g/cm^3=\frac{100.0g}{\text{Volume of zinc}}\\\\\text{Volume of zinc}=11.44cm^3](https://tex.z-dn.net/?f=8.740g%2Fcm%5E3%3D%5Cfrac%7B100.0g%7D%7B%5Ctext%7BVolume%20of%20zinc%7D%7D%5C%5C%5C%5C%5Ctext%7BVolume%20of%20zinc%7D%3D11.44cm%5E3)
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)
We are given:
Molar mass of zinc = 65.3 g/mol
Volume of solution =
(Conversion factor:
)
Mass of zinc = 21.0 g
Putting values in above equation, we get:
![\text{Molarity of zinc}=\frac{21\times 1000}{65.3\times 11.44}=28.11M](https://tex.z-dn.net/?f=%5Ctext%7BMolarity%20of%20zinc%7D%3D%5Cfrac%7B21%5Ctimes%201000%7D%7B65.3%5Ctimes%2011.44%7D%3D28.11M)
Hence, the molality and molarity of zinc in the solution is 4.07 m and 28.11 M respectively.