Question

How much water has to be evaporated from 250ml of 1M Ca(OH)2 to make it 3M

Answer 1

`(1)/(6)L` or 166.667 ml of water must be evaporated in order to make this solution 3M.

Step-by-step explanation:

1. Analyse the information.

When the problem states "250ml of 1M Ca(OH)₂", it means that you have 250ml of a solution that contains 1 mole of solute (Ca(OH)₂) for each liter of the solution.

In order to make a 1M solution be a 3M solution, we'll have to remove some of the solvent liquid, in order to make it more concentrated.

2. Express the molarity.

The original molarity is: M= Moles of solute (n) / Liters of solution (v).

3. Find the molarity.

Since the problem states that the original molarity is 1M, we have 1 mole of solute per liter of solution in the original solution. Therefore, initial molarity is:
`M=(1mol)/(1liters)=(0.250mol)/(0.250L)`

250ml= 0.250 L.

4. Convert the molarity to 3M.

As you may see, in order to make the molarity fraction equal 3M, we'll have to multiply the numerator by 3 or divide the denominator by the same number:

`M=(0.250mol)/(0.250L/3)=(0.250mol)/((1)/(12) L)`

5. Calculate the amount of solution evaporated.

The amount of solution evaporated is given by the difference between the denominator of the molarity of the original expression and the new expression:

`(0.250-(1)/(12))\\ \\((3)/(12)-(1)/(12))L\\ \\(2)/(12) L\\ \\(1)/(6) L`

6. Conclude.

`(1)/(6)L` or 166.667 ml of water must be evaporated in order to make this solution 3M. The ending product will have the following molarity:

`M=(0.250moles)/((1)/(12) L) =3M`.