How many kilograms of H2O must be added to 76.0 g of Ca(NO3)2 to form a 0.509 m solution?
m stands for molality; I'm assuming that's what you mean.
mols Ca(NO3)2 = 76g/molar mass = ?
Then m = mols solute/kg solvent
m = 0.509 = ?mol/x kg
?mols from above.
Solve for x kg.
To determine the amount of water (H2O) needed to form a 0.509 m (molality) solution, we need to calculate the moles of solute (Ca(NO3)2) and then use the relationship between moles, mass, and moles per kilogram of solvent (water).
1. Calculate the moles of Ca(NO3)2:
- Convert the given mass of Ca(NO3)2 from grams to moles using its molar mass.
- The molar mass of Ca(NO3)2 is:
M(Ca(NO3)2) = M(Ca) + 2 × [M(N) + 3 × M(O)]
M(Ca(NO3)2) = 40.08 g/mol + 2 × [14.01 g/mol + 3 × 16.00 g/mol]
= 40.08 g/mol + 2 × (14.01 g/mol + 48.00 g/mol)
= 40.08 g/mol + 2 × (14.01 g/mol + 48.00 g/mol)
= 40.08 g/mol + 2 × (62.01 g/mol)
= 40.08 g/mol + 124.02 g/mol
= 164.10 g/mol
- Now, calculate the moles of Ca(NO3)2:
Moles of Ca(NO3)2 = Mass of Ca(NO3)2 / Molar mass of Ca(NO3)2
= 76.0 g / 164.10 g/mol
2. Calculate the amount of water (H2O):
- Since we have the moles of Ca(NO3)2, we can use the molality formula to calculate the amount of water required.
Molality (m) = Moles of solute / Mass of solvent (in kg)
- Rearranging the formula, we can solve for the mass of solvent:
Mass of solvent = Moles of solute / Molality
- Since we want to find the mass of water, we substitute the given molality (0.509 m) and solve for the mass of water:
Mass of water = Moles of Ca(NO3)2 / Molality
- Convert the calculated mass of water to kilograms:
Mass of water (in kg) = Mass of water (in g) / 1000
Now, plugging in the values and calculating, we can find the amount of water (H2O) needed in kilograms.