What mass of cesium bromine must be added to a 0.500 liter of water (d=1.00 g/ml) to produce a 0.981m solution? what are the mole fraction and mass percent of CsBr?

m = mols solute/kg solvent

You know m and kg solvent; solve for mols solute.

Then mols solute = grams/molar mass
You know mols solute and molar mass, solve for grams.

For mole fraction, X CsBr.

mols CsBr = from the problem
mols H2O from the problem = grams/molar mass
Then X CsBr = mols CsBr/total mols.

mass % CsBr is grams CsBr/100 g solution.

To solve this problem, we need to calculate the mass of cesium bromine (CsBr) that must be added to the water.

Step 1: Calculate the moles of CsBr needed in the solution.
We know the molarity (0.981 m) and volume (0.500 L) of the solution. The formula to calculate moles is given by:
Moles = Molarity × Volume
Moles = 0.981 mol/L × 0.500 L

Step 2: Calculate the mass of CsBr needed.
To calculate the mass of CsBr, we need to know the molar mass of CsBr. The molar mass of Cs is 133.0 g/mol, and the molar mass of Br is 79.9 g/mol.
Molar mass of CsBr = (1 × 133.0 g/mol) + (1 × 79.9 g/mol)
Molar mass of CsBr = 212.9 g/mol

Mass = Moles × Molar mass
Mass = (0.981 mol) × (212.9 g/mol)

Step 3: Calculate the mole fraction of CsBr.
The mole fraction of a component in a solution is given by the ratio of the moles of that component to the total number of moles in the solution.

Moles of CsBr in the solution = Moles of CsBr added
Total moles in the solution = Moles of water + Moles of CsBr added

Since water is the solvent and CsBr is the solute, we assume that 0.500 L of water remains as 0.500 L of solution.

Moles of CsBr in the solution = moles of CsBr added = 0.981 mol
Total moles in the solution = Moles of water + Moles of CsBr added = 0.981 mol + 0.000 mol

The mole fraction of CsBr = Moles of CsBr in the solution / Total moles in the solution

Mole fraction of CsBr = 0.981 mol / 0.981 mol

Step 4: Calculate the mass percent of CsBr.
The mass percent of a component in a solution is given by the ratio of the mass of that component to the total mass of the solution.

Mass of CsBr = Mass of solution - Mass of water
Mass of CsBr = (Moles of CsBr added) × (Molar mass of CsBr)

Mass percent of CsBr = (Mass of CsBr / Total mass of solution) × 100

Now, you can substitute the calculated values into the formulas to find the solution.