Question

An aqueous salt solution is formed by adding 11.67 g sodium sulfate (solute) to water (solvent). What mass (in g) of water is used if the freezing point of the solution is -12.9 oF.

Kf H2O = 1.86 oC/m

When Determining The molality Of The Dissolved Particles, Assume Complete Ionization Of Ionic Compounds - 1 Molecule Can Form 1, 2, 3, Or More Dissolved Particles.

Answer 1

I got 64 g and it was wrong. I used the delta T = Kfmolal formula and rearranged it to find that kg solv = (Kf)(Moles solute)/delta T

Answer 2

Then I figured out moles of solute, mol pieces and the change in temperature. The Kf was given. However, I feel my delta T may have been incorrect.

Answer 3

I got 7.1667 C for delta T. I calculated that their was 0.0822 mol of solute and multiplied this by 3 mol pieces to get my moles of solute. Which made that value 0.2466.

Answer 4

dT=iKfm
dT is the change in temperature (Tfinal-Tinitial)
i is the van't Hoff disassociation constant
Kf would be the 1.86
m is moles of solute divided by kg of solvent

Answer 5

It's sodium sulfate not sodium nitrate @Photon336 Na2SO4 -> 2 Na+ + SO4 2-

Answer 6

I understand all that @taramgrant0543664 . I just don't know where I went wrong in my individually calculations or rearranging?

Answer 7

How did you find that temperature?

Answer 8

I converted Fahrenheit to Celsius. I got that -12.9 o F = -24 o C and then I converted 0F to Celsius and that gave me like -17C so i found the delta T of that change in C and it ws like the 7.1667 C value.

Answer 9

Which one is initial and final because you could have possibly put them the wrong way which would change the answer

Answer 10

Should it have been -32 + 12.9 = |-19.1| C because the degree value for both F and C are the same?

Answer 11

Initial had to be -32F cause that's the freezing pt of water, but when the solution was added it went to -12.9

Answer 12

Forget I said that, your math is correct.

\[\Delta T = iK _{b}m \]

\[\frac{ \Delta T }{ iK _{b} } = moles/kg \]

\[\frac{ moles*i*Kb}{ \Delta T } = kg \]


I think here is your formula.
(°F - 32) x 5/9 = °C

Answer 13

So it should be -12.9-(-32) so -12.9+32 as final temperature minus initial temperature

Answer 14

@Photon would it be 24.0 g?

Answer 15

Cause that equals 19.1 @taramgrant0543664 .

Answer 16

And if you put that in to the equation do you get that same number that you already tried?

Answer 17

according to wikipedia the freezing point of water is 32 degrees F

So originally we had Tf as -12.9 F right?

(-12.9-32)*(5/9) = C

-32F = Temperature 1 = 0C

-24 = Temperature 2 tf

i think both have to be in celsius: so T1 = 0 degrees celsius

(T2-T1) = (-24-0) Celcius -24 celcius

Answer 18

but My assumption is that our final answer that the freezing point had to be 0 Degrees C and i converted that -12.9 F right? to Celsius as Temp final

Answer 19

Yes

Answer 20

The change in temperature in celsius would be different in F then it is in C so you would have to convert before hand

Answer 21

With that value I get 19.1 g, but if I use 19.1 as the change in temp I get 24 g solv.

Answer 22

do you guys get 19.1 when you calculate with that value?

Answer 23

Tara what did you get for this?

\[11.67 grams /142 grams/mol = 0.82 moles \]

\[\frac{ 0.82*3*1.86 }{24 } = 0.191 kg \]

Answer 24

one question though that Kf shouldn't that be negative as well?

Answer 25

I got 0.019
Your moles @Photon336 I think you're missing a 0 in there

Answer 26

0.019 you're right

Answer 27

I honestly can't remember the rule when Kf is negative or not it's been a little bit since I've had to do these questions let me see if I can find that rule

Answer 28

It would have been stated if it was negative but water always has a Kf that is 1.86

Answer 29

kg to g would be 19.1 though right?

Answer 30

yep

Answer 31

It says I have a rounding error of less than 10%. Should I try 19.0 or 19.2?

Answer 32

For me it comes out as 19.065 and 10% is +/-0.1 so you could try 19.2 if you want, I'm getting an answer of 19.065 so I would think it would be 19.1 when rounding

Answer 33

Well 12.9 F = -24.9444 and we used 24, so that may be the problem. When I calculate with that value I get 18.4 g

Answer 34

18.4 was correct! Hooray :)

Answer 35

Ya that could be a problem, I never went back and checked the conversion but that could effect it for sure

Answer 36

Yay!!!!

Answer 37

Thank you both !

Answer 38

No problem!