We have an aqueous solution that contains

22% (by mass) of a hypothetical solute Z. The
formula weight of the solute Z is 173 g/mol.
The density of the solution is observed to be
1.4 g/mL. What is the molarity of Z in this
solution?
Answer in units of mol/L.

To find the molarity of solute Z in the solution, we need to use the following equation:

Molarity (M) = moles of solute / volume of solution in liters

First, we need to calculate the moles of solute Z in the solution.

Step 1: Calculate the mass of solute Z in the solution.
Given that the solution is 22% by mass, we can calculate the mass of solute Z in the solution:

Mass of solute Z = Mass of solution × Percent composition of solute Z
= Mass of solution × (22% / 100%)
= Mass of solution × 0.22

Step 2: Calculate the volume of the solution.
Given the density of the solution is 1.4 g/mL, we can use the density formula to calculate the volume of the solution:

Volume of solution = Mass of solution / Density of solution

Step 3: Convert the volume of the solution to liters.
Since the molarity needs to be in mol/L, we need to convert the volume from milliliters to liters:

Volume of solution (in liters) = Volume of solution (in mL) / 1000

Step 4: Calculate the moles of solute Z.
Now we can calculate the moles of solute Z in the solution by using its formula weight:

Moles of solute Z = Mass of solute Z / Formula weight of solute Z

Finally, we can use the equation for molarity to find the molarity of solute Z in the solution:

Molarity (M) = Moles of solute Z / Volume of solution (in liters)

By following these steps and plugging in the given values, we can find the molarity of solute Z in the solution.

1.78