To find the molarity ($M$) of the solution, we'll use the relationship between molality ($m$), density, and molarity. Here’s the step-by-step process:

Given:

• Molality ($m$) = 0.0480 $m$ (mol/kg of solvent)
• Density ($\rho$) = 1.10 g/mL = 1.10 kg/L
• Molar mass of LiF (Lithium Fluoride) ≈ 25.94 g/mol

Step 1: Find the mass of the solution per liter.

The density gives us the mass of the solution per unit volume. Since density is 1.10 g/mL, this converts to:

$\text{Mass of 1 L solution} = 1.10 \, \text{kg}$

Step 2: Calculate the mass of the solvent in 1 liter of solution.

Let's assume we have 1 liter of solution.

$\text{Mass of solvent} = \text{Total mass of solution} - \text{Mass of solute}$

To find the mass of the solute: $\text{Molality} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$ Let's assume the mass of the solvent is $x$ kg. Then:

$\text{Moles of LiF} = 0.0480 \times x$

The mass of the solute (LiF) is:

$\text{Mass of solute} = \text{moles of LiF} \times \text{molar mass of LiF}$

$\text{Mass of solute} = 0.0480 \times x \times 25.94 \, \text{g/mol}$

So the total mass of the solution is:

$\text{Mass of solution} = x \, \text{kg} + 0.0480 \times x \times 25.94 \, \text{g}$

Given that the total mass of the solution for 1 L is 1.10 kg:

$1.10 = x + 0.0480 \times x \times 25.94$

Solving for $x$:

$1.10 = x(1 + 0.0480 \times 25.94)$ $1.10 = x(1 + 1.246)$ $x = \frac{1.10}{2.246} \approx 0.4894 \, \text{kg}$

So the mass of the solvent is approximately 0.4894 kg.

Step 3: Calculate the moles of LiF in the solution.

$\text{Moles of LiF} = 0.0480 \times 0.4894 \approx 0.0235 \, \text{moles}$

Step 4: Find the molarity ($M$) of the solution.

Molarity is the number of moles of solute per liter of solution:

$M = \frac{\text{Moles of LiF}}{\text{Volume of solution in liters}} = \frac{0.0235 \, \text{moles}}{1 \, \text{L}} = 0.0235 \, M$

Thus, the molarity of the solution is approximately 0.0235 M.

Would you like more details or have any other questions?

Here are some related questions:

1. How do you convert between molarity and molality?
2. What is the effect of temperature on the density and molarity of a solution?
3. How would you calculate the volume of solution needed to obtain a certain amount of solute?
4. What role does the density of the solution play in determining concentration?
5. Can you find the molality of a solution if you are given the molarity and density?

Tip: Always remember to check the units during conversion, especially when dealing with molarity and molality.