calculate the necessary amounts of solutes and solvent to make a 4l bottle of antifreeze that will have a 35 degree change in the freezing point of water. soultes are: Al2(SO4), KBr) and Mg(NO3)2.
Are you assuming 4L H2O has a mass of 4,000 g (a density of 1.0 g/mL)? AND that the addition of the Al2(SO4)3, KBr, and Mg(NO3)2 will not change the volume? You can't solve this problem without knowing the density of each of the solutions unless those assumptions are made.
delta T = i*Kf*molality
Solve for molality. See i at bottom of this response.
molality = moles/kg solvent
Solve for moles.
grams = moles x molar mass
Solve for grams.
i = 5 for Al2(SO4)3
i = 2 for KBr
i = 3 for Mg(NO3)2
thanks
To calculate the necessary amounts of solutes and solvent to make a 4L bottle of antifreeze with a 35-degree change in the freezing point of water, we need to determine the quantities of each solute required.
First, let's understand the concept behind lowering the freezing point of water using solutes. When a solute is added to a solvent, the freezing point of the resulting solution decreases compared to the pure solvent. This phenomenon is known as freezing point depression. The extent of the depression depends on the concentration and type of solute.
In this case, we have three solutes: Al2(SO4)3, KBr, and Mg(NO3)2. To determine the necessary amounts of each solute, we'll utilize the concept of molality (moles of solute per kilogram of solvent) and their respective cryoscopic constants.
The cryoscopic constant for water (Kf) is 1.86°C/m. This means that for every mole of solute dissolved in one kilogram of solvent, the freezing point of the solvent will decrease by 1.86°C.
Step 1: Calculate the molality (m) required for a 35°C decrease in freezing point.
- The freezing point depression (∆Tf) is given as 35°C.
- Convert the temperature change to Kelvin: 35°C + 273.15 = 308.15K.
- Determine molality using the formula: m = (∆Tf) / Kf.
m = 308.15K / 1.86°C/m = 165.75 molal.
Step 2: Calculate the amount of solute needed for each compound.
- For Al2(SO4)3:
The formula weight of Al2(SO4)3 is approximately 342.15 g/mol.
So, the amount of Al2(SO4)3 can be calculated by: (165.75 molal) * (342.15 g/mol) = 56718.26 grams or 56.7 kg.
- For KBr:
The formula weight of KBr is approximately 119 g/mol.
Thus, the amount of KBr needed is: (165.75 molal) * (119 g/mol) = 19708.25 grams or 19.71 kg.
- For Mg(NO3)2:
The formula weight of Mg(NO3)2 is approximately 148.32 g/mol.
Therefore, the amount of Mg(NO3)2 required is: (165.75 molal) * (148.32 g/mol) = 24601.56 grams or 24.60 kg.
Step 3: Calculate the amount of solvent needed.
Since the total volume of the antifreeze solution is 4 liters, the amount of solvent (water) required will be 4 kg.
To summarize, to make a 4L bottle of antifreeze with a 35-degree change in the freezing point of water, you would need approximately 56.7 kg of Al2(SO4)3, 19.71 kg of KBr, and 24.60 kg of Mg(NO3)2, along with 4 kg of solvent (water).