Two solutions of a substance (non-electrolyte) are mixed in the following manner , 480 mL of 1.5 M [first solution ] + 520 mL of 1.2 M [second solution ] . What is the molarity of the final mixture ?

Options

A. 2.70 M
B. 1.344 M
C. 1.50 M
D. 1.20 M

Explanation

To find the molarity of the final mixture when two solutions are mixed, we can follow these steps:

### Step 1: Identify the given values
- Molarity of the first solution (M1) = 1.5 M
- Volume of the first solution (V1) = 480 mL
- Molarity of the second solution (M2) = 1.2 M
- Volume of the second solution (V2) = 520 mL

### Step 2: Calculate the total volume of the mixture
The total volume (V) of the mixture after mixing the two solutions can be calculated as:
\[ V = V1 + V2 \]
Substituting the values:
\[ V = 480 \, \text{mL} + 520 \, \text{mL} = 1000 \, \text{mL} \]

### Step 3: Calculate the total number of moles of solute in each solution
The number of moles of solute in each solution can be calculated using the formula:
\[ \text{Moles} = \text{Molarity} \times \text{Volume (in liters)} \]
For the first solution:
\[ \text{Moles from first solution} = M1 \times \left( \frac{V1}{1000} \right) = 1.5 \, \text{M} \times \left( \frac{480}{1000} \right) = 0.72 \, \text{moles} \]
For the second solution:
\[ \text{Moles from second solution} = M2 \times \left( \frac{V2}{1000} \right) = 1.2 \, \text{M} \times \left( \frac{520}{1000} \right) = 0.624 \, \text{moles} \]

### Step 4: Calculate the total number of moles of solute in the mixture
Now, we can find the total number of moles of solute in the final mixture:
\[ \text{Total moles} = \text{Moles from first solution} + \text{Moles from second solution} \]
\[ \text{Total moles} = 0.72 + 0.624 = 1.344 \, \text{moles} \]

### Step 5: Calculate the molarity of the final mixture
The molarity of the final mixture (M) can be calculated using the formula:
\[ M = \frac{\text{Total moles}}{\text{Total volume (in liters)}} \]
Converting the total volume from mL to L:
\[ M = \frac{1.344 \, \text{moles}}{1 \, \text{L}} = 1.344 \, \text{M} \]

### Final Answer
The molarity of the final mixture is **1.344 M**.

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