The density of a solution containing 40% by mass of HCl is 1.2 g/mL. Calculate the molarity of the solution.

Answer

To calculate the molarity of a solution containing 40% by mass of HCl with a density of 1.2 g/mL, we can follow these steps:

### Step 1: Understand the given data
- Mass percentage of HCl = 40%
- Density of the solution = 1.2 g/mL

### Step 2: Assume a mass of the solution
For simplicity, assume we have 100 g of the solution. This means:
- Mass of HCl = 40% of 100 g = 40 g
- Mass of the solution = 100 g

### Step 3: Calculate the volume of the solution
Using the density formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
We can rearrange this to find the volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
Substituting the values:
\[ \text{Volume} = \frac{100 \text{ g}}{1.2 \text{ g/mL}} = 83.33 \text{ mL} \]

### Step 4: Convert the volume from mL to L
Since molarity is expressed in moles per liter, we need to convert the volume from mL to L:
\[ \text{Volume in L} = \frac{83.33 \text{ mL}}{1000} = 0.08333 \text{ L} \]

### Step 5: Calculate the number of moles of HCl
To find the number of moles of HCl, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]
The molar mass of HCl is approximately 36.5 g/mol. Thus:
\[ \text{Number of moles of HCl} = \frac{40 \text{ g}}{36.5 \text{ g/mol}} \approx 1.0959 \text{ moles} \]

### Step 6: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in L}} \]
Substituting the values:
\[ \text{Molarity} = \frac{1.0959 \text{ moles}}{0.08333 \text{ L}} \approx 13.15 \text{ M} \]

### Final Answer:
The molarity of the solution is approximately **13.15 M**.

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