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Ch.1 - Intro to General Chemistry
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Solution: A 50.0-mL solution is initially 1.54% MgCl2 by mass and has a density of 1.05 g/mL.What is the freezing point of the solution after you add an additional 1.34 g MgCl2? (Use i = 2.5 for MgCl2.)

Problem

A 50.0-mL solution is initially 1.54% MgCl2 by mass and has a density of 1.05 g/mL.

What is the freezing point of the solution after you add an additional 1.34 g MgCl2? (Use i = 2.5 for MgCl2.)

Solution

We’re being asked to find the freezing point of a 50.0- mL 1.54 % MgCl2 by mass solution after adding an additional 1.34 gMgCl2 ( i = 2.5 for MgCl2.)


Recall that the freezing point of a solution is lower than the freezing point of a pure solvent.


When calculating the freezing point of a solution, we’re going to use the equation for Freezing Point Depression:


Tf=i×Kf×m


∆Tf = change in freezing point = Tf pure solvent –Tf solution
Kf = freezing point depression constant
i = van' t Hoff factor of the solute = no. of ions
m = molality


We need to find the molality of the solution after adding additional MgCl2 to solve for its freezing point by doing these steps: 

      

Step 1. Determine the composition of the solution after adding MgCl2.


Since we're given the volume and density of the solution, we can determine its mass using the equation:


density= massvolume


Also, recall that Mass or weight percent (% by mass) is the percentage of a given element or compound within a solution. 


The equation used to calculate for mass percent is shown below:


Mass component mass of solute
• Total mass  mass of solution


mass percent = mass componenttotal mass×100


Step 2. Calculate the moles of the solute


Step 3. Calculate the molality of the solution.


molality = mol solutekg solvent

Solute = MgCl­2 
Solvent = Water (H2O)


Step 4. Calculate the freezing point of the solution.


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