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?
i know it would be
-0.735= -1.86 * m
m= 3g/ X g/mol/kg solvent
however the answer I get from that doesn't work, please help
Your mistake is you didn't take into account the van't Hoff factor, i.
The equation is delta T = i*Kf*m
is for CsX is 2.
To determine the chemical formula of the salt, we can use the concept of freezing point depression. The freezing point depression (∆Tf) is calculated by the formula:
∆Tf = -Kf * m
Where:
- ∆Tf is the change in freezing point
- Kf is the molal freezing point depression constant for the solvent (water), which is equal to 1.86 °C/molal
- m is the molality of the solution, given by the formula:
m = moles of solute / mass of solvent (kg)
Now, let's apply these concepts to the given information. We are told that when 3.00 grams of the salt is dissolved in 100.0 grams of water, the solution freezes at -0.735°C.
Step 1: Calculate the molality (m) of the solution.
m = (3.00 g) / (X g/mol/kg solvent) --> Assume the molar mass of the salt is X g/mol (to be determined).
Step 2: Calculate the change in freezing point (∆Tf).
∆Tf = -0.735°C
Step 3: Use the equation for ∆Tf to solve for X, the molar mass of the salt:
-0.735 = -1.86 * m
Substitute the value of m calculated in Step 1:
-0.735 = -1.86 * ((3.00 g) / (X g/mol/kg solvent))
Rearrange the equation:
X = (1.86 * 3.00 g) / (0.735 g/mol/kg solvent)
Evaluate the expression:
X = 7.56 g/mol/kg solvent
This gives us the molar mass of the salt per kilogram of the solvent.
Now, in order to determine the chemical formula of the salt, we need to find the ratio of the moles of cesium (Cs) to that of halogen (X). We can use the periodic table to find the atomic masses of cesium and the halogens (fluorine, chlorine, bromine, and iodine) and calculate their molar masses.
By comparing the molar mass of CsX obtained from the equation and rounding it to the nearest whole number, we can determine the chemical formula of the salt. For example, if the molar mass of CsX is 167.5 g/mol, it indicates the formula is CsX2, whereas if it is 111.7 g/mol, it corresponds to CsX3.
Note: This approach assumes that the salt dissociates completely into its ions in the solution.