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 __________.
A) 16.8 B) 0.940 C) 0.0597 D) 0.922 E) 0.0640
To find the mole fraction of NH3 in the solution, we need to calculate the moles of NH3 and the moles of water in the solution.
Step 1: Calculate the moles of NH3.
To do this, we need to use the given mass and molar mass of NH3.
Given mass of NH3 = 15.0 g
Molar mass of NH3 = 17.03 g/mol
Moles of NH3 = (Given mass of NH3) / (Molar mass of NH3)
Moles of NH3 = 15.0 g / 17.03 g/mol
Moles of NH3 ≈ 0.881 mol (approx.)
Step 2: Calculate the moles of water.
To do this, we need to use the given mass and density of water.
Given mass of water = 250 g
Density of water = 0.974 g/mL
Volume of water = (Given mass of water) / (Density of water)
Volume of water = 250 g / 0.974 g/mL
Volume of water ≈ 256.70 mL (approx.)
However, the above volume is in mL, and we need it in liters to calculate moles. So, we convert it to liters.
Volume of water = (256.70 mL) * (1 L / 1000 mL)
Volume of water ≈ 0.2567 L (approx.)
Since the density of water is very close to 1 g/mL, we can assume that the volume of water is approximately equal to its mass in grams. Therefore, the moles of water are approximately equal to its mass in grams divided by its molar mass.
Moles of water ≈ 250 g / 18.015 g/mol
Moles of water ≈ 13.87 mol (approx.)
Step 3: Calculate the mole fraction of NH3.
The mole fraction of NH3 can be calculated using the formula:
Mole fraction of NH3 = (Moles of NH3) / (Moles of NH3 + Moles of water)
Mole fraction of NH3 = 0.881 mol / (0.881 mol + 13.87 mol)
Mole fraction of NH3 = 0.881 mol / 14.751 mol
Mole fraction of NH3 ≈ 0.0597
Therefore, the mole fraction of NH3 in the solution is approximately 0.0597.
The correct option is C) 0.0597.
To calculate the mole fraction of NH3 in the solution, we need to determine the number of moles of NH3 and the number of moles of water in the solution.
First, let's find the number of moles of NH3.
Given the mass of NH3 is 15.0 g, we can use the molar mass of NH3 to calculate the number of moles.
The molar mass of NH3 is 17.03 g/mol.
Number of moles of NH3 = Mass of NH3 / Molar mass of NH3
= 15.0 g / 17.03 g/mol
≈ 0.88 mol
Next, let's find the number of moles of water.
Given the mass of water is 250 g, we can use the molar mass of water to calculate the number of moles.
The molar mass of water is 18.015 g/mol.
Number of moles of water = Mass of water / Molar mass of water
= 250 g / 18.015 g/mol
≈ 13.88 mol
Now, let's calculate the mole fraction of NH3.
Mole fraction of NH3 = Moles of NH3 / (Moles of NH3 + Moles of water)
= 0.88 mol / (0.88 mol + 13.88 mol)
= 0.0597
The mole fraction of NH3 in the solution is 0.0597.
Therefore, the answer is C) 0.0597.
Mole fraction=molesNH3/total moles
where total moles=moleNH3 + moleswater
I will be happy to critque your work, if you need it.