A compound is known to be a cesium halide, CsX. If 3.00 grams of the salt is dissolved in exactly 100.0 grams of water, the solution freezes at -0.735°C. What is the chemical formula for the salt?
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To determine the chemical formula for the salt, we need to analyze the freezing point depression caused by the presence of the salt in the water.
Freezing point depression is a colligative property, which depends only on the number of particles in a solution, not their identity. In this case, since the salt dissociates into ions in water, we should consider the Van't Hoff factor (i) to determine the number of particles produced by each formula unit of the salt.
Cesium halides typically have an empirical formula of CsX, where X represents a halogen (chlorine, bromine, or iodine). The dissociation of CsX would result in the formation of Cs+ cations and X− anions.
Now we can use the formula for freezing point depression:
ΔT = i * K_f * m
Where:
ΔT is the freezing point depression (given as -0.735°C),
i is the Van't Hoff factor,
K_f is the freezing point depression constant for water (equal to 1.86 °C/m),
and m is the molality of the solution (moles of solute per kilogram of solvent).
First, let's calculate the molality of the solution:
molality (m) = moles of solute / mass of solvent (in kg)
Given that 3.00 grams of the salt is dissolved in 100.0 grams of water, the mass of the solvent is:
mass of solvent = 100.0 g = 0.100 kg
To calculate the moles of solute, we need to know the molar mass of CsX.
Since we don't have the actual molar mass, let's assume X represents iodine (I) and calculate the molar mass based on that assumption.
The molar mass of CsI is approximately 259.81 g/mol.
Now let's calculate the moles of solute:
moles of solute = mass of solute / molar mass
mass of solute = 3.00 g
molar mass of CsI = 259.81 g/mol
moles of solute = 3.00 g / 259.81 g/mol
Next, let's calculate the molality:
molality (m) = moles of solute / mass of solvent
moles of solute = 3.00 g / 259.81 g/mol
mass of solvent = 0.100 kg
Now we can substitute the values into the formula for freezing point depression:
-0.735 °C = i * 1.86 °C/m * (moles of solute / 0.100 kg)
Rearranging the equation to solve for i:
i = (-0.735 °C) / (1.86 °C/m * (moles of solute / 0.100 kg))
i = (-0.735 °C * 0.100 kg) / (1.86 °C/m * moles of solute)
By plugging in the calculated values and solving the equation, we can find the Van't Hoff factor (i).
Substituting the Van't Hoff factor and using the commonly observed formulas for cesium halides, the chemical formula for the salt is CsI (cesium iodide).
However, note that the value of i could yield a different result if the actual molar mass or composition of the salt is different from the assumed values.