4.0g of an unknown potassium halide (KX, where X is the halide) is dissolved in 100g of water. The solution freezes at -1.28 degrees Celsius. What is the identity of the halide?
To determine the identity of the halide (X), we can use the concept of freezing point depression. Freezing point depression occurs when a solute is dissolved in a solvent, causing the freezing point of the solution to be lower than that of the pure solvent.
The freezing point depression can be calculated using the formula:
ΔTf = Kf * m
Where:
ΔTf is the change in freezing point (in degrees Celsius)
Kf is the cryoscopic constant (in degrees Celsius per molal)
m is the molality of the solution (in mol solute per kg solvent)
First, we need to calculate the molality of the solution by determining the moles of the solute (KX) and the mass of the solvent (water).
Given:
Mass of KX = 4.0g
Mass of water = 100g
Freezing point depression = -1.28°C
1. Calculate the molality (m):
Molality (m) = Moles of solute / Mass of solvent (in kg)
To determine the moles of KX, we need to find the molar mass of KX.
The molar mass of K is approximately 39.1 g/mol (from the periodic table).
The molar mass of X is unknown.
2. Assume the molar mass of X is Y g/mol (where Y represents the molar mass of X).
The molar mass of KX = 39.1 g/mol + Y g/mol
Since the mass of KX is 4.0g, we can now calculate the moles of KX:
Moles of KX = Mass of KX / Molar mass of KX = 4.0g / (39.1g/mol + Y g/mol)
To calculate the molality, we need to convert the mass of water to kg:
Mass of water = 100g = 0.1 kg
Now we can substitute the values into the molality formula:
m = Moles of solute / Mass of solvent (in kg)
m = (4.0g / (39.1g/mol + Y g/mol)) / 0.1 kg
3. Calculate the change in freezing point (ΔTf):
Since we are given that the solution freezes at -1.28°C (below the freezing point of pure water, 0°C), we can find the difference in temperatures:
ΔTf = -1.28°C - 0°C = -1.28°C
Now we can rearrange the freezing point depression formula to solve for Kf:
Kf = ΔTf / m
4. Substitute the given values:
Kf = (-1.28°C) / ((4.0g / (39.1g/mol + Y g/mol)) / 0.1 kg)
Now, to determine the identity of the halogen (X), we need to compare the calculated value of Kf to known cryoscopic constants for different solvents.
The cryoscopic constants may vary depending on the solvent, so we need to refer to an appropriate reference source to find the known Kf values for potassium compounds dissolved in water.
To determine the identity of the halide (X) in the potassium halide (KX), we can use the concept of freezing point depression.
Freezing point depression occurs when a solute is added to a solvent. The freezing point of the solvent decreases, and the extent of the depression depends on the concentration of the solute. This phenomenon can be described by the equation:
ΔT = Kf * m
Where:
ΔT = change in freezing point (in Celsius)
Kf = cryoscopic constant (molal freezing point depression constant) that depends on the solvent (water in this case)
m = molality of the solution (moles of solute per kilogram of solvent)
First, we need to calculate the molality (m) of the solution.
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
Given:
Mass of water = 100g
Mass of unknown potassium halide (KX) = 4.0g
To convert the mass of water to kilograms, we divide by 1000:
Mass of water = 100g = 0.1 kg
To calculate the molality (m), we need to determine the number of moles of potassium halide, KX.
The molar mass of KX can vary depending on the halide (X). The molar masses of potassium and the common halogens are:
Potassium (K): 39.10 g/mol
Chlorine (Cl): 35.45 g/mol
Bromine (Br): 79.90 g/mol
Iodine (I): 126.90 g/mol
To find the moles of potassium halide (KX), we divide the given mass by the molar mass of KX (in grams/mol):
Moles of KX = 4.0g / molar mass of KX
Next, we calculate the molality (m):
Molality (m) = Moles of solute / Mass of solvent (in kg)
Now that we have the molality (m), we can use the freezing point depression equation to calculate the change in freezing point (ΔT).
Given:
Change in freezing point (ΔT) = -1.28°C
Finally, to find the identity of the halide, we compare the change in freezing point (ΔT) to the cryoscopic constant (Kf) of water.
The cryoscopic constant of water is 1.86°C * kg/mol.
Now, using the equation ΔT = Kf * m, we can rearrange it to solve for X:
X = ΔT / (Kf * m)
Substituting the given values into the equation will allow us to determine the identity of the halide (X).
freezingpt=-l.86*2*4/molmass*1/.1
molmass=l.86*8*10/1.28=116.3
mass of K is 39
so atomic mass of halide is 77, potassium bromide.
do the math a little more carefully than I did in my head.