Respuesta :
Answer:
For a: The molality and molarity of the given solution is 2.45m and 2.28 M respectively.
For b: The molarity of the solution when more water is added is 0.912 M
Explanation:
- For a:
To calculate the molality of solution, we use the equation:
[tex]Molarity=\frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ in grams}}[/tex]
Where,
[tex]m_{solute}[/tex] = Given mass of solute [tex](C_3H_8O_3)[/tex] = 42.0 g
[tex]M_{solute}[/tex] = Molar mass of solute [tex](C_3H_8O_3)[/tex] = 92.093 g/mol
[tex]W_{solvent}[/tex] = Mass of solvent (water) = 186 g
Putting values in above equation, we get:
[tex]\text{Molality of }C_3H_8O_3=\frac{42\times 1000}{92.093\times 186}\\\\\text{Molality of }C_3H_8O_3=2.45m[/tex]
- To calculate the molarity of solution, we use the equation:
[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}[/tex] .....(1)
We are given:
Molarity of solution = ?
Molar mass of [tex](C_3H_8O_3)[/tex] = 92.093 g/mol
Volume of solution = 200 mL
Mass of [tex](C_3H_8O_3)[/tex] = 42 g
Putting values in above equation, we get:
[tex]\text{Molality of }C_3H_8O_3=\frac{42\times 1000}{92.093\times 200}\\\\\text{Molality of }C_3H_8O_3=2.28M[/tex]
Hence, the molality and molarity of the given solution is 2.45m and 2.28 M respectively.
- For b:
Now, the 300 mL water is added to the solution. So, the total volume of the solution becomes (200 + 300) = 500 mL
Using equation 1 to calculate the molarity of solution, we get:
Molar mass of [tex](C_3H_8O_3)[/tex] = 92.093 g/mol
Volume of solution = 500 mL
Mass of [tex](C_3H_8O_3)[/tex] = 42 g
Putting values in equation 1, we get:
[tex]\text{Molality of }C_3H_8O_3=\frac{42\times 1000}{92.093\times 500}\\\\\text{Molality of }C_3H_8O_3=0.912M[/tex]
Hence, the molarity of the solution when more water is added is 0.912 M
