We have an aqueous solution that contains
47% (by mass) of a hypothetical solute Z. The
formula weight of the solute Z is 209 g/mol.
The density of the solution is observed to be
1.3 g/mL. What is the molarity of Z in this
solution?
Answer in units of mol/L
1.3 g/mL x 1000 = ? g = mass of 1L soln.
?g x 0.47 = ? g Z in the L.
mols Z = ?g Z/209 = ? mols in that L; therefore that is the M in moles/L.
Thank you for your help.
To find the molarity of solute Z in the solution, we need to use the formula:
Molarity (M) = (mass of solute Z in grams) / (volume of solution in liters)
First, let's calculate the mass of solute Z in the solution:
Mass of solute Z = (percentage by mass) x (mass of solution)
= (47%) x (mass of solution)
Since the density of the solution is observed to be 1.3 g/mL and the volume of the solution is not given, we need to calculate the volume of the solution first.
Volume of solution = (mass of solution) / (density of solution)
= (mass of solution) / (1.3 g/mL)
Now, substituting the value of the mass of solute Z into the molarity formula:
Molarity (in mol/L) = (mass of solute Z in grams) / (volume of solution in liters)
= (47%) x (mass of solution) / (volume of solution in liters)
= (47%) x (mass of solution) / [(mass of solution) / (1.3 g/mL)]
= 0.47 x 1.3 g/mL
= 0.611 g/mL
= 0.611 mol/L
Therefore, the molarity of solute Z in this solution is 0.611 mol/L.
To find the molarity of solute Z in the solution, we need to know the amount of solute in moles and the volume of the solution in liters.
First, let's calculate the mass of solute Z in the solution. Since the solution is 47% by mass, we can find the mass of solute Z in grams by multiplying the total mass of the solution by 0.47:
Mass of Z = 0.47 * Mass of solution
Next, we need to calculate the moles of solute Z. We can do this by dividing the mass of solute Z by its molar mass (formula weight):
Moles of Z = Mass of Z / Molar mass of Z
Now, let's determine the volume of the solution in liters. We know that the density of the solution is 1.3 g/mL, so we can convert the mass of the solution to volume in milliliters and then divide by 1000 to get the volume in liters:
Volume of solution = Mass of solution / Density of solution
Finally, we can calculate the molarity of solute Z by dividing the moles of Z by the volume of the solution in liters:
Molarity of Z = Moles of Z / Volume of solution
Let's substitute the given values and calculate the molarity:
Given:
Percent mass of Z = 47%
Molar mass of Z = 209 g/mol
Density of solution = 1.3 g/mL
Step 1: Calculate the mass of solute Z
Mass of Z = 0.47 * Mass of solution
Step 2: Calculate the moles of solute Z
Moles of Z = Mass of Z / Molar mass of Z
Step 3: Calculate the volume of the solution in liters
Volume of solution = Mass of solution / Density of solution
Step 4: Calculate the molarity of solute Z
Molarity of Z = Moles of Z / Volume of solution
Plugging in the given values:
Mass of Z = 0.47 * Mass of solution
Moles of Z = Mass of Z / Molar mass of Z
Volume of solution = Mass of solution / Density of solution
Molarity of Z = Moles of Z / Volume of solution
By performing the calculations using the given values, we can determine the molarity of solute Z in the solution.