A solution is 0.0480 *m* LiF. What is the molarity of the solution if the density is 1.10 g/mL?


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.

Learn how to calculate the molarity of a solution given molality and density. Step-by-step solution using chemistry concepts including molarity, density, and solution concentrations. Suitable for high school students.

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