calculate the molality, molarity, and mole fraction of NH3 in an 12.80 mass % aqueous solution (d=0.9651 g/ml)
To calculate the molality, molarity, and mole fraction of NH3 in the aqueous solution, follow these steps:
1. Calculate the mass of NH3 in the solution:
Mass % = (mass of NH3 / total mass of solution) * 100
Mass of NH3 = (Mass % / 100) * Total mass of solution
Given: Mass % = 12.80% and Total mass of solution = density * volume
Density = 0.9651 g/ml
Volume = Assume 1L (since the density is given in g/ml)
Total mass of solution = Density * Volume = 0.9651 g/ml * 1000 ml = 965.1 g
Mass of NH3 = (12.80% / 100) * 965.1 g
2. Calculate the number of moles of NH3:
Moles of NH3 = Mass of NH3 / Molar mass of NH3
Molar mass of NH3 = 17.03 g/mol
Moles of NH3 = Mass of NH3 / 17.03 g/mol
3. Calculate the molality (m):
Molality = Moles of solute / Mass of solvent (in kg)
Mass of solvent = Total mass of solution - Mass of solute (NH3)
Convert the mass of solvent from grams to kilograms.
Molality = Moles of NH3 / (Total mass of solution - Mass of NH3) kg
4. Calculate the molarity (M):
Molarity = Moles of solute / Volume of solution (in liters)
Volume of solution = Assume 1 L
Molarity = Moles of NH3 / Volume of solution (in L)
5. Calculate the mole fraction (X) of NH3:
Mole fraction (X) = Moles of NH3 / Total moles of all components in the solution
Total moles of all components = Moles of NH3
Now we can substitute the values into the equations:
Mass of NH3 = (12.80% / 100) * 965.1 g = 123.41 g
Moles of NH3 = 123.41 g / 17.03 g/mol = 7.252 mol
Mass of solvent = 965.1 g - 123.41 g = 841.69 g = 0.84169 kg
Molality (m) = 7.252 mol / 0.84169 kg = 8.61 mol/kg
Molarity (M) = 7.252 mol / 1 L = 7.252 M
Mole fraction (X) = 7.252 mol / 7.252 mol = 1.0
The molality of NH3 in the solution is 8.61 mol/kg, the molarity is 7.252 M, and the mole fraction is 1.0.
To calculate the molality, molarity, and mole fraction of NH3 in an aqueous solution, we need to first determine the amount of NH3 present in the solution.
Given:
Mass % of NH3 = 12.80%
Density of solution = 0.9651 g/mL
Step 1: Calculate the mass of NH3
We can start by assuming we have 100g of the solution.
Mass of NH3 = Mass % of NH3 * Mass of solution
= 12.80% * 100g
= 12.80g
Step 2: Calculate the moles of NH3
Molar mass of NH3 = 17.03 g/mol
Moles of NH3 = Mass of NH3 / Molar mass of NH3
= 12.80g / 17.03 g/mol
≈ 0.751 mol
Step 3: Calculate the mass of water
Since we assumed we had 100g of the solution, the mass of water can be calculated as:
Mass of water = Mass of solution - Mass of NH3
= 100g - 12.80g
= 87.20g
Step 4: Calculate the volume of solution
Volume of solution = Mass of solution / Density
= 100g / 0.9651 g/mL
= 103.57 mL
Step 5: Calculate molality
Molality (m) = Moles of solute / Mass of solvent (in kg)
= 0.751 mol / 0.0872 kg
≈ 8.62 mol/kg
Step 6: Calculate molarity
Molarity (M) = Moles of solute / Volume of solution (in L)
= 0.751 mol / 0.10357 L
≈ 7.24 M
Step 7: Calculate mole fraction
Mole fraction of NH3 = Moles of NH3 / Total moles of all components
= 0.751 mol / (0.751 mol + 55.52 mol)
≈ 0.0135
So, the molality of NH3 in the solution is approximately 8.62 mol/kg, the molarity is approximately 7.24 M, and the mole fraction is approximately 0.0135.
mass % is grams solute/100 g solution.
12.8% w/w is 12.8g NH3/100 g solution.
mass = density x volume. You know 100 g solution and density of the solution; solve for volume of the solution.
Convert g NH3 to mols NH3. g/molar mass = mols.
Then M = mols/L solution.
m = mols solute (same as for M)/kg solvent.
To do mol fraction, convert g NH3 to mols which you did above.'
Convert g H2O to mols.
Then XNH3 = mols NH3/total mols.