Calculate the molality of CsCl in a 18% by mass aqueous solution.
Answer in units of m.
To calculate the molality of CsCl in a 18% by mass aqueous solution, we need to determine the number of moles of CsCl dissolved in 1 kilogram of water.
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
Step 1: Calculate the mass of the solution.
Given that the solution is 18% by mass, it means that 18 grams of CsCl is present in 100 grams of the solution.
Therefore, the mass of the solution is equal to the mass of CsCl divided by the mass percent:
Mass of solution = 18 grams CsCl / 0.18 = 100 grams
Step 2: Calculate the number of moles of CsCl using its molar mass.
The molar mass of CsCl can be obtained from the periodic table. The molar mass of Cs is approximately 133.0 g/mol, and the molar mass of Cl is approximately 35.5 g/mol. Therefore, the molar mass of CsCl is:
Molar mass of CsCl = 133.0 g/mol + 35.5 g/mol = 168.5 g/mol
Now, we can calculate the number of moles of CsCl in 18 grams:
Number of moles of CsCl = 18 grams / 168.5 g/mol
Step 3: Calculate the molality.
Molality is defined as the number of moles of solute per kilogram of solvent. In this case, the solute is CsCl, and the solvent is water. The density of water at room temperature is approximately 1.0 g/mL or 1000 g/kg.
Mass of water = Mass of solution - Mass of CsCl = 100 grams - 18 grams = 82 grams
Now, convert the mass of water to kilograms:
Mass of water = 82 grams / 1000 g/kg = 0.082 kg
Finally, we can calculate the molality using the number of moles of CsCl and the mass of water:
Molality = Number of moles of CsCl / Mass of water
Substituting the values:
Molality = (18 grams / 168.5 g/mol) / 0.082 kg
Calculating the above expression will give you the molality of CsCl in the 18% by mass aqueous solution.