Freezing point depression

[Opejay]

When 10 grams of a certain material are dissolved in 1 kg of water, the freezing point of the solution is -0.46 Celsius. Which of the following could be the substance? ( water has a freezing point depression constant of 1.86K/m)

A. HC2H3O2

B. HNO3

C. NACl

D. CaCl2

thanks

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[gongshow89]

Looks like it's D..

We know water normally has a freezing/melting point of 0. So, if it is now -0.46 then we need to determine which substrate would give this.

The formula to use is deltaT=k*b*i

deltaT is 0.46 in this example as stated above. i is the number of ion particles, and b is the molality.

In this case we have 10 g/1kg of solvent (water). If you use CaCl2 then the molar mass is ~110 g/mole which means we have about 0.09 moles/kg of water. (10/110 = 0.09)

Since there are 3 ion particle in CaCl2 we see that the product of 0.09 * 3 * 1.86 (constant in the formula)= ~0.5 which is close to the 0.46 celsius change. This answer gave me the closest value.

Hope that matches up with the answer in the book.. I take it this is from EK? There may be a non-mathematical way of doing this, but this is the way I worked it out.

 

[Opejay]

Yes it's from EK and D is the answer. I was confused on how they arrived at the answer.

Thanks for your help.

 

[sciencebooks]

Looks like it's D..

We know water normally has a freezing/melting point of 0. So, if it is now -0.46 then we need to determine which substrate would give this.

The formula to use is deltaT=k*b*i

deltaT is 0.46 in this example as stated above. i is the number of ion particles, and b is the molality.

In this case we have 10 g/1kg of solvent (water). If you use CaCl2 then the molar mass is ~110 g/mole which means we have about 0.09 moles/kg of water. (10/110 = 0.09)

Since there are 3 ion particle in CaCl2 we see that the product of 0.09 * 3 * 1.86 (constant in the formula)= ~0.5 which is close to the 0.46 celsius change. This answer gave me the closest value.

Hope that matches up with the answer in the book.. I take it this is from EK? There may be a non-mathematical way of doing this, but this is the way I worked it out.

I also just looked at my options (eliminating A immediately as it wouldn't ionize). I wonder if there was a faster way?