Calculate the mole fraction of the solute in the following aqueous solution:
a) .112M C6H12O6 (d=1.006g/ml).
b) 3.2% ethanol, by volume (d=.993g/ml);
pure CH3CH2OH, d=.789g/ml
a) Well, we've got some serious chemistry going on here! To calculate the mole fraction of the solute C6H12O6, we first need to determine the number of moles of solute present. Given the molarity of 0.112M, we can say that there are 0.112 moles of C6H12O6 in 1 liter of solution.
To calculate the mass of C6H12O6 present, we can use its density and the given volume. Given that the density is 1.006g/mL, and by multiplying it with the volume, we can determine the mass to be 1.006g/mL * 1L = 1006 g.
So, now we have the number of moles (0.112 moles) and the mass (1006g), we can calculate the mole fraction. The mole fraction (X) is given by the formula X = n/(n + 1), where n is the number of moles.
Therefore, the mole fraction of C6H12O6 is 0.112 moles / (0.112 moles + 1006 g), which is approximately 1.1 x 10^-4. Phew, that's a small fraction! Don't let it get lost in the shuffle!
b) Moving on to ethanol, we have a 3.2% ethanol solution by volume. This means that for every 100 mL of solution, there are 3.2 mL of ethanol.
First, let's calculate the mass of ethanol present. Given that the density is 0.993 g/mL, we multiply it with the volume of ethanol to get the mass: 0.993 g/mL * 3.2 mL = 3.18 g.
Next, let's calculate the number of moles of ethanol. We can use its molar mass, which is approximately 46 g/mol. By dividing the mass of ethanol (3.18 g) by the molar mass (46 g/mol), we get approximately 0.069 moles of ethanol.
Now, we can calculate the mole fraction. The mole fraction (X) is given by the formula X = n/(n + 1), where n is the number of moles.
So, the mole fraction of ethanol is 0.069 moles / (0.069 moles + 3.18 g), which is approximately 0.021. It might be a small fraction, but it's enough to get the party started!
To calculate the mole fraction of the solute in the given aqueous solutions, we need to determine the number of moles of the solute and the number of moles of the solvent.
a) For the solution of 0.112 M C6H12O6 (d = 1.006 g/mL):
To find the mole fraction of the solute, we need to calculate the number of moles of C6H12O6.
Step 1: Calculate the mass of the solute.
Given: Density (d) of C6H12O6 solution = 1.006 g/mL
Let's assume we have 1 L of the solution, so the mass of the solution is 1 L x 1.006 g/mL = 1006 g.
Step 2: Calculate the number of moles of the solute.
First, we need to convert the concentration from Molarity to moles per liter (mol/L).
0.112 M = 0.112 mol/L
The number of moles of C6H12O6 in 1 L of the solution is 0.112 mol/L x 1 L = 0.112 mol.
Step 3: Calculate the mole fraction of the solute.
To find the mole fraction, we need to consider both the solute and the solvent. Since water (H2O) is the solvent, we assume it to be present in 1 L.
The mole fraction (X) of the solute (C6H12O6) is given by:
X(solute) = moles of solute / (moles of solute + moles of solvent)
Since we have 0.112 mol of C6H12O6 and 1 mol of H2O (the solvent), we can calculate:
X(solute) = 0.112 mol / (0.112 mol + 1 mol) = 0.112 mol / 1.112 mol = 0.1007
So, the mole fraction of the solute C6H12O6 in the solution is approximately 0.1007.
b) For the solution of 3.2% ethanol, by volume (d = 0.993 g/mL):
To find the mole fraction of the solute, we need to calculate the number of moles of ethanol (CH3CH2OH).
Step 1: Calculate the mass of the solute.
Given: Density (d) of ethanol solution = 0.993 g/mL
Let's assume we have 100 mL of the solution.
The mass of the solution is 100 mL x 0.993 g/mL = 99.3 g.
Step 2: Calculate the mass of ethanol (CH3CH2OH) in the solution.
The percentage by volume represents grams of ethanol per 100 mL of the solution.
3.2% ethanol by volume = 3.2 g/100 mL = 3.2 g.
Step 3: Calculate the number of moles of ethanol.
To find the number of moles, we need to divide the mass of ethanol by its molar mass.
Molar mass of ethanol (CH3CH2OH) = (12.01 g/mol x 2) + (1.01 g/mol x 6) + 16.00 g/mol + 1.01 g/mol = 46.06 g/mol
Number of moles of ethanol (CH3CH2OH) = 3.2 g / 46.06 g/mol ≈ 0.0695 mol.
Step 4: Calculate the number of moles of water (solvent).
Since water (H2O) is the solvent, we assume it to be present in 100 mL. The molar mass of water is 18.02 g/mol.
Number of moles of water (H2O) = (99.3 g - 3.2 g) / 18.02 g/mol ≈ 5.26 mol.
Step 5: Calculate the mole fraction of the solute.
Using the mole fractions formula from Step 3 for the solution, we have:
X(solute) = moles of solute / (moles of solute + moles of solvent)
X(solute) = 0.0695 mol / (0.0695 mol + 5.26 mol) ≈ 0.013
So, the mole fraction of the solute CH3CH2OH (ethanol) in the solution is approximately 0.013.
To calculate the mole fraction of the solute in a solution, we need to know the number of moles of the solute and the total number of moles in the solution. The mole fraction is calculated by dividing the number of moles of the solute by the total number of moles.
a) For the first solution, we are given the molarity of the solute (0.112M C6H12O6). The molarity represents the number of moles of solute per liter of solution. Therefore, to find the number of moles of the solute, we need to multiply the molarity by the volume of the solution.
To calculate the volume, we need the mass and density of the solution. The formula to calculate volume is:
Volume = mass / density
In this case, we are given the mass of the solution, which is not specified. Therefore, we cannot calculate the volume and subsequently the number of moles of the solute. We would need to know the mass of the solution to proceed with the calculation.
b) For the second solution, we are given the percentage of ethanol by volume (3.2%). To calculate the number of moles of ethanol, we need to know the volume of the solution.
To calculate the volume, we use the density of the solution and the mass of the solution, which is not specified in this case either. So, we cannot calculate the volume or the number of moles of ethanol.
Without knowing the mass or volume of the solution in both cases, we cannot proceed with the calculations to determine the mole fraction of the solute.
0.112M = 0.112 moles/L soln.
0.112 M x molar mass = grams C6H12O6 = ??
1000 mL x 1.006 g/mL = mass soln = ??
mass soln - mass solute = mass solvent
Convert mass solvent to moles.
mole fraction solute = moles solute/total moles.