If the molality of a CaCl2 solution is .100 mol/kg, and was made from 500.0 mL of water, how many grams of CaCl2 were needed to make the solution?
Step by step would be appreciated!
DrBob222, do you know how to do this?
The density of H2O=1g/mL, solve for mass.
mass=density*volume=(1g/mL)*(500mL)=500g or 0.500 kg
m=moles of solute/kg of solvent, solve for moles
(0.100 mol/kg)*(0.500 kg)= moles of CaCl2
moles of CaCl2*(111.0g/mole)= mass of CaCl2
****I'm not Dr. Bob222, but I think this is correct.
I'll buy all of that. Something like 5.55 g if I punched in the right numbers
To find the number of grams of CaCl2 needed to make the solution, you can follow these steps:
Step 1: Convert the given volume of water from milliliters (mL) to kilograms (kg).
Given: Volume of water = 500.0 mL
To convert mL to kg, we need to know the density of water. However, for this problem, we can assume the density of water to be exactly 1 g/mL. Therefore, the mass of water is equal to its volume in grams.
So, mass of water = Volume of water = 500.0 g
And mass of water in kg = 500.0 g / 1000 = 0.500 kg
Step 2: Use the molality formula to find the number of moles of CaCl2.
Given: Molality (m) = 0.100 mol/kg
The molality formula is: m = (moles of solute) / (mass of solvent in kg)
Rearrange the formula to solve for moles of solute:
moles of solute = m * mass of solvent in kg
moles of solute = 0.100 mol/kg * 0.500 kg = 0.050 moles of CaCl2
Step 3: Calculate the molar mass of CaCl2.
The molar mass of CaCl2 can be calculated by adding the atomic masses of calcium (Ca) and two chlorine (Cl) atoms.
Calcium (Ca): atomic mass = 40.08 g/mol
Chlorine (Cl): atomic mass = 35.45 g/mol
Molar mass of CaCl2 = (40.08 g/mol) + 2 * (35.45 g/mol) = 110.98 g/mol
Step 4: Use the moles of CaCl2 and the molar mass to calculate the mass of CaCl2.
mass of CaCl2 = moles of CaCl2 * molar mass of CaCl2
mass of CaCl2 = 0.050 moles * 110.98 g/mol = 5.55 grams
Therefore, to make the CaCl2 solution with a molality of 0.100 mol/kg, you would need 5.55 grams of CaCl2.