A solution is prepared by dissolving 15.0 g of NH3 in 250.g of water. The density of the resulting solution is 0.974 g/ml. The mole fraction of NH3 in the solution is?
To find the mole fraction of NH3 in the solution, we need to calculate the moles of NH3 and water separately, and then use those values to determine the mole fraction.
Step 1: Calculate the moles of NH3.
The molar mass of NH3 (ammonia) is 17.03 g/mol.
moles of NH3 = mass of NH3 / molar mass of NH3
moles of NH3 = 15.0 g / 17.03 g/mol
moles of NH3 = 0.881 mol
Step 2: Calculate the moles of water.
The molar mass of H2O (water) is 18.02 g/mol.
moles of water = mass of water / molar mass of water
moles of water = 250.0 g / 18.02 g/mol
moles of water = 13.87 mol
Step 3: Calculate the total number of moles in the solution.
total moles = moles of NH3 + moles of water
total moles = 0.881 mol + 13.87 mol
total moles = 14.75 mol (rounded to two decimal places)
Step 4: Calculate the mole fraction of NH3.
mole fraction of NH3 = moles of NH3 / total moles
mole fraction of NH3 = 0.881 mol / 14.75 mol
mole fraction of NH3 ≈ 0.060 (rounded to three decimal places)
Therefore, the mole fraction of NH3 in the solution is approximately 0.060.
To find the mole fraction of NH3 in the solution, we first need to find the total mass of the solution.
The total mass of the solution is calculated by adding the mass of the solute (NH3) and the mass of the solvent (water).
Mass of NH3: 15.0 g
Mass of water: 250 g
Total mass of the solution = Mass of NH3 + Mass of water
Total mass of the solution = 15.0 g + 250 g
Total mass of the solution = 265 g
Next, we need to find the volume of the solution. To do this, we will divide the total mass of the solution by its density.
Density of the solution: 0.974 g/ml
Total mass of the solution: 265 g
Volume of the solution = Total mass of the solution / Density of the solution
Volume of the solution = 265 g / 0.974 g/ml
Volume of the solution ≈ 272.13 ml
Now, we can calculate the mole fraction of NH3 in the solution. The mole fraction of a component in a solution is the ratio of moles of that component to the total moles in the solution.
To find the moles of NH3, we need to convert the mass of NH3 to moles using its molar mass.
Molar mass of NH3: 17.03 g/mol
Moles of NH3 = Mass of NH3 / Molar mass of NH3
Moles of NH3 = 15.0 g / 17.03 g/mol
Moles of NH3 ≈ 0.8807 mol
Similarly, to find the moles of water, we need to convert the mass of water to moles.
Molar mass of water (H2O): 18.015 g/mol
Moles of water = Mass of water / Molar mass of water
Moles of water = 250 g / 18.015 g/mol
Moles of water ≈ 13.8747 mol
Total moles in the solution = Moles of NH3 + Moles of water
Total moles in the solution ≈ 0.8807 mol + 13.8747 mol
Total moles in the solution ≈ 14.7554 mol
Finally, we can calculate the mole fraction of NH3:
Mole fraction of NH3 = Moles of NH3 / Total moles in the solution
Mole fraction of NH3 = 0.8807 mol / 14.7554 mol
Mole fraction of NH3 ≈ 0.05968
moles NH3 = 15.0/molar mass NH3.
If you didn't make a typo, you don't need density of water since you are given grams.
moles H2O = grams/molar mass.
XNH3 = moles NH3/total moles.