calculate the necessary amounts of solutes and solvent to make a 4 liter bottle of antifreeze that will have a 35 degree change in freezing point of water. solutes are Al2(SO4)3, KBr, Mg(NO3)2
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To calculate the necessary amounts of solutes and solvent to make a 4 liter bottle of antifreeze with a 35-degree change in freezing point of water, we need to determine the appropriate concentration of solutes.
To begin, it's important to note the colligative properties of freezing point depression. In this case, the change in freezing point is directly proportional to the concentration of solute particles in the solution.
Next, we need to identify the number of solute particles each compound will contribute to the solution. The constituent elements and their respective valences in each compound are:
- Al2(SO4)3: Al3+ and (SO4)2- (3 x 2 = 6 solute particles)
- KBr: K+ and Br- (2 solute particles)
- Mg(NO3)2: Mg2+ and (NO3)- (3 solute particles)
Now, we can calculate the required amounts of each compound as follows:
1. Determine the molality (moles of solute per kilograms of solvent) needed to achieve the desired freezing point depression using the formula:
∆T = Kf * m
Where:
∆T = Change in freezing point
Kf = Freezing point depression constant (depends on the solvent)
m = Molality of the solution
Assuming the freezing point depression constant (Kf) of water is 1.86 °C/m, and we want a 35 °C change (∆T) in freezing point, we can rearrange the formula to find the molality (m):
m = ∆T / Kf
m = 35 °C / 1.86 °C/m
m ≈ 18.82 mol/kg
2. Calculate the total number of moles of solute particles required using the molality and the mass of the solvent:
moles = m x kg of solvent
Given that the volume of the solution is 4 liters and assuming the density of the solution is close to that of water (1 g/mL), the mass of the solvent can be estimated as:
mass of water = volume x density
mass of water = 4 L x 1000 g/L
mass of water = 4000 g ≈ 4 kg
Therefore, the number of moles of solute particles for each compound would be:
- Al2(SO4)3: 18.82 mol/kg x 4 kg x 6 solute particles = 452.16 moles
- KBr: 18.82 mol/kg x 4 kg x 2 solute particles = 150.56 moles
- Mg(NO3)2: 18.82 mol/kg x 4 kg x 3 solute particles = 339.36 moles
These calculations give us the number of moles required for each compound. To convert moles into grams, we need to know the molar mass of each compound. The molar masses are as follows:
- Al2(SO4)3: 342.15 g/mol
- KBr: 119.00 g/mol
- Mg(NO3)2: 148.32 g/mol
3. Convert moles to grams using the formula:
grams = moles x molar mass
The final results will give you the necessary amounts of solutes and solvent to make a 4 liter bottle of antifreeze with a 35-degree change in freezing point of water.