An aqueous solution of nacl has a mole fraction of 0.21. What is the mass of NaCl dissolved in 100.0 mL of solution?
Don't I need the density of the solution. We can work out the numbers for 100.0 mL of SOLVENT without the density but not 100.0 mL SOLUTION.
. 21*58.4=12.3
1 molH2O-. 21=.79
.79*18=14.2gH2o
12.3:14.2=x:100
x=86.4
To find the mass of NaCl dissolved in 100.0 mL of solution, we need to use the mole fraction and the molar mass of NaCl.
First, let's understand what mole fraction is. Mole fraction (X) is a measure of the concentration of a component in a mixture. It is the ratio of the number of moles of the component to the total number of moles of all components in the mixture.
In this case, the mole fraction of NaCl is given as 0.21. This means that out of every 100 parts of the solution, 21 parts are NaCl.
To calculate the mass of NaCl, we need to know the total mass of the solution. However, since we are only provided with the volume (100.0 mL), we need to make an assumption about the density of the solution in order to convert it to mass.
Let's assume the density of the solution is 1.00 g/mL. This means that the mass of the solution is 100.0 g (since density = mass/volume).
Now, we can calculate the mass of NaCl. To do this, we'll use the mole fraction and molar mass of NaCl.
The molar mass of NaCl is 58.44 g/mol. This means that 1 mole of NaCl weighs 58.44 grams.
Since the mole fraction (X) is the ratio of moles of NaCl to the total moles of all components in the solution, we can write:
X(NaCl) = moles of NaCl / (moles of NaCl + moles of water)
Given that the mole fraction of NaCl is 0.21, we can rearrange the equation to solve for moles of NaCl:
moles of NaCl = X(NaCl) * (moles of NaCl + moles of water)
Since we are assuming the density is 1.00 g/mL, the mass of water is equal to the volume of solution (100.0 mL) multiplied by the density (1.00 g/mL), which gives us 100.0 g.
From the equation, we can now calculate the moles of NaCl:
moles of NaCl = 0.21 * (moles of NaCl + 100.0 g / molar mass of water)
To solve for moles of NaCl, we can rearrange the equation:
0.21 * (moles of NaCl + 100.0 g / molar mass of water) = moles of NaCl
Now, we substitute the molar mass of water, which is approximately 18.015 g/mol, and solve for moles of NaCl:
0.21 * (moles of NaCl + 100.0 g / 18.015 g/mol) = moles of NaCl
0.21 * (moles of NaCl + 5.548 mol) = moles of NaCl
0.21 * moles of NaCl + 1.165 moles = moles of NaCl
Simplifying the equation, we get:
0.21 * moles of NaCl = 1.165 moles
Dividing both sides by 0.21, we get:
moles of NaCl = 1.165 moles / 0.21
moles of NaCl ≈ 5.548 moles
Finally, we can calculate the mass of NaCl by multiplying the moles of NaCl by the molar mass of NaCl:
mass of NaCl = moles of NaCl * molar mass of NaCl
mass of NaCl = 5.548 moles * 58.44 g/mol
mass of NaCl ≈ 324.249 g
Therefore, the mass of NaCl dissolved in 100.0 mL of solution is approximately 324.249 grams when assuming the density of the solution is 1.00 g/mL.