An 8% by mass aqueous solution of ammonia has a density of 0.9651g/ml . Calculate the molality molarity and mole fraction of ammonia?

To calculate the molality, molarity, and mole fraction of ammonia in the solution, we first need to determine the molar mass of ammonia (NH3).

The molar mass of NH3 is:
N = 14.01 g/mol
H = 1.01 g/mol (3 hydrogen atoms)
Total molar mass = 14.01 + 3(1.01) = 17.04 g/mol

Now, let's calculate the molality:

Molality (m) = moles of solute / kg of solvent

Since the solution is 8% by mass, we can assume we have 8g of ammonia in 100g of solution. This means we have 8g / 17.04 g/mol = 0.4694 mol of ammonia.

The density of the solution is 0.9651 g/ml, so 100g of solution is equal to 100/0.9651 = 103.59 ml = 0.10359 L.

Now, we can calculate the molality:
m = 0.4694 mol / 0.10359 kg = 4.53 mol/kg

Next, let's calculate the molarity:

Molarity (M) = moles of solute / liters of solution

Since we have 0.4694 mol of ammonia in 0.10359 L of solution, the molarity is:
M = 0.4694 mol / 0.10359 L = 4.53 M

Finally, let's calculate the mole fraction:

Mole fraction = moles of solute / total moles of solution

The total moles of the solution can be calculated by dividing the mass of the solution by the molar mass of ammonia:
Total moles = 100g / 17.04 g/mol = 5.87 mol

Now, we can calculate the mole fraction:
X = 0.4694 mol / 5.87 mol = 0.08

Therefore, the molality of ammonia in the solution is 4.53 mol/kg, the molarity is 4.53 M, and the mole fraction is 0.08.

1. Mass of ammonia

Mass of solution = 100 g
Mass of ammonia = 8 g

2. Volume of solution

Volume of solution = Mass of solution / Density of solution
Volume of solution = 100 g / 0.9651 g/ml
Volume of solution = 103.6 ml

3. Molar mass of ammonia

Molar mass of NH3 = 14.01 g/mol

4. Molality

Molality (m) = Moles of solute / Mass of solvent (in kg)
Mass of solvent = Mass of solution - Mass of ammonia
Mass of solvent = 100 g - 8 g
Mass of solvent = 92 g
Moles of ammonia = Mass of ammonia / Molar mass of ammonia
Moles of ammonia = 8 g / 14.01 g/mol
Moles of ammonia = 0.571 mol
Molality (m) = 0.571 mol / 0.092 kg
Molality (m) = 6.19 m

5. Molarity

Molarity (M) = Moles of solute / Volume of solution (in liters)
Volume of solution = 103.6 ml = 0.1036 L
Molarity (M) = 0.571 mol / 0.1036 L
Molarity (M) = 5.51 M

6. Mole fraction

Mole fraction of ammonia (XNH3) = Moles of ammonia / Total moles in solution
Total moles in solution = Moles of ammonia + Moles of water
Moles of water = Mass of water / Molar mass of water
Mass of water = 92 g
Moles of water = 92 g / 18.02 g/mol
Moles of water = 5.11 mol
Total moles in solution = 0.571 mol + 5.11 mol
Total moles in solution = 5.68 mol
Mole fraction of ammonia (XNH3) = 0.571 mol / 5.68 mol
Mole fraction of ammonia (XNH3) = 0.101