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Question: 31.65 g of sodium chloride is added to 220.0 mL of water at 34 °C. How will this affect the freezing point of the water? Assume the sodium chloride completely dissociates in the water. Given: density of water at 35 °C = 0.994 g/mL Kf water = 1.86 °C kg/mol
Solution: To find the temperature change elevation of a solvent by a solute, use the equation: ΔT = iKfm where ΔT = Change in temperature in °C i = van 't Hoff dissociation factor Kf = molal freezing point depression constant or cryoscopic constant in °C kg/mol m = molality of the solute in mol solute/kg solvent.
Step 1: Calculate the molality of the NaCl molality (m) of NaCl = moles of NaCl/kg water From the periodic table atomic mass Na = 22.99 atomic mass Cl = 35.45 moles of NaCl = 31.65 g x 1 mol/(22.99 + 35.45) moles of NaCl = 31.65 g x 1 mol/58.44 g moles of NaCl = 0.542 mol kg water = density x volume kg water = 0.994 g/mL x 220 mL x 1 kg/1000 g kg water = 0.219 kg mNaCl = moles of NaCl/kg water mNaCl = 0.542 mol/0.219 kg mNaCl = 2.477 mol/kg
Step 2: Determine the van 't Hoff factor The van 't Hoff factor, i, is a constant associated with the amount of dissociation of the solute in the solvent. For substances which do not dissociate in water, such as sugar, i = 1. For solutes that completely dissociate into two ions, i = 2. For this example NaCl completely dissociates into the two ions, Na+ and Cl-. Another example could be CaCl2 which dissociates into three ions, Ca2+ and 2Cl-. But, i = 2 for this example.
Step 3: Find ΔT ΔT = iKfm ΔT = 2 x 1.86 °C kg/mol x 2.477 mol/kg ΔT = 9.21 °C
So the final answer is: Adding 31.65 g of NaCl to 220.0 mL of water will lower the freezing point by 9.21 °C.
The normal freezing point of water is 0°C with the addition of NaCl the freezing point for this solution would be -9.21 °C.
nice job tara
one other thing: remember that delta T is the temperature change not the final temperature that the substance was raised or lowered to. so if they ask for the final temperature you'll need to do some rearranging: \[\Delta T = (Tf-Ti) \] to get \[\Delta T + Ti = Tf \]
There should be a way for us to find these tutorials in the future though
There's one of the mods that runs a tutorial site thing on behalf of openstudy or in conjunction with or something along the lines I know that I can't remember which one it is though
after a while you cant bump up the tutorial to the top; i'm guessing you can just paste the link to your profile description?
good job :)