How many grams of potassium chloride should be added to 1.5kg of water to lower it's freezing point to -7.5°c kf for water =1.86°ckg mol-1
To solve this problem, we need to use the concept of freezing point depression and the formula:
ΔT = Kf * m
where:
ΔT is the change in freezing point,
Kf is the freezing point depression constant for water (given as 1.86 °C kg mol^(-1)),
m is the molality of the solute.
Firstly, we need to calculate the molality of the solute (potassium chloride) using the formula:
molality (m) = moles of solute / mass of solvent (in kg)
Given that the mass of water is 1.5 kg, we can calculate the moles of solute (potassium chloride) using the formula:
moles = mass / molar mass
The molar mass of potassium chloride (KCl) is the sum of the atomic masses of potassium (39.1 g mol^(-1)) and chlorine (35.5 g mol^(-1)). Therefore, the molar mass of KCl is 74.6 g mol^(-1).
Now, let's calculate the moles of potassium chloride:
moles = (mass of potassium chloride) / (molar mass of KCl)
Next, we can calculate the molality:
molality (m) = (moles of potassium chloride) / (mass of water in kg)
Substitute the values:
molality (m) = (moles of KCl) / (1.5 kg)
Now that we have the molality (m), we can use the freezing point depression formula to determine the change in freezing point (ΔT):
ΔT = Kf * m
Substituting the values:
ΔT = 1.86 °C kg mol^(-1) * molality
Finally, we want to find the grams of potassium chloride required to achieve a ΔT of -7.5 °C. To calculate this, we need to know the molar mass of KCl and use the equation:
grams of KCl = moles of KCl * molar mass of KCl
Substitute the values:
grams of KCl = (moles of KCl) * (molar mass of KCl)
By following these steps, you will be able to calculate the number of grams of potassium chloride needed to lower the freezing point of 1.5 kg of water to -7.5 °C.