If `"20.0 cm''^(3)` of `"1.0 M CaCl"_(2)` and `"60.0 cm"^(3)` of `"0.20 M CaCl"_(2)` are mixed, what will be the molarity of the final solution?

Explanation

To find the molarity of the final solution when mixing two solutions of calcium chloride (CaCl₂), we can follow these steps:

### Step 1: Determine the volumes of the solutions
We have:
- Volume of the first solution (V₁) = 20.0 cm³
- Volume of the second solution (V₂) = 60.0 cm³

### Step 2: Calculate the total volume of the final solution
The total volume (V) of the final solution is the sum of the two volumes:
\[ V = V₁ + V₂ = 20.0 \, \text{cm}³ + 60.0 \, \text{cm}³ = 80.0 \, \text{cm}³ \]

### Step 3: Calculate the number of moles of solute in each solution
Using the formula for moles:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (in liters)} \]

For the first solution:
- Molarity (M₁) = 1.0 M
- Volume (V₁) = 20.0 cm³ = 0.020 L
\[ \text{Moles of CaCl₂ in first solution} = M₁ \times V₁ = 1.0 \, \text{mol/L} \times 0.020 \, \text{L} = 0.020 \, \text{mol} \]

For the second solution:
- Molarity (M₂) = 0.20 M
- Volume (V₂) = 60.0 cm³ = 0.060 L
\[ \text{Moles of CaCl₂ in second solution} = M₂ \times V₂ = 0.20 \, \text{mol/L} \times 0.060 \, \text{L} = 0.012 \, \text{mol} \]

### Step 4: Calculate the total number of moles in the final solution
\[ \text{Total moles} = \text{Moles from first solution} + \text{Moles from second solution} = 0.020 \, \text{mol} + 0.012 \, \text{mol} = 0.032 \, \text{mol} \]

### Step 5: Calculate the molarity of the final solution
Using the formula for molarity:
\[ \text{Molarity} (M) = \frac{\text{Total moles}}{\text{Total volume (in liters)}} \]
Convert the total volume to liters:
\[ V = 80.0 \, \text{cm}³ = 0.080 \, \text{L} \]
Now, calculate the molarity:
\[ M = \frac{0.032 \, \text{mol}}{0.080 \, \text{L}} = 0.40 \, \text{M} \]

### Final Answer
The molarity of the final solution is **0.40 M**.

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