25 mL of 3.0 M HCl are mixed with 75 mL of 4.0 M HCl. If the volumes are additive, the molarity of the final mixture will be :

Options

A. 3.25M
B. 4.0M
C. 3.75M
D. 3.50M

Answer

To find the molarity of the final mixture when 25 mL of 3.0 M HCl is mixed with 75 mL of 4.0 M HCl, we can follow these steps:

### Step 1: Identify the given values
- Molarity of the first solution (HCl1), \( M_1 = 3.0 \, \text{M} \)
- Volume of the first solution (HCl1), \( V_1 = 25 \, \text{mL} \)
- Molarity of the second solution (HCl2), \( M_2 = 4.0 \, \text{M} \)
- Volume of the second solution (HCl2), \( V_2 = 75 \, \text{mL} \)

### Step 2: Calculate the total moles of HCl from each solution
Using the formula for moles:
\[ \text{Moles} = \text{Molarity} \times \text{Volume} \]
- Moles of HCl from the first solution:
\[ \text{Moles}_1 = M_1 \times V_1 = 3.0 \, \text{M} \times 25 \, \text{mL} = 3.0 \, \text{M} \times 0.025 \, \text{L} = 0.075 \, \text{mol} \]
- Moles of HCl from the second solution:
\[ \text{Moles}_2 = M_2 \times V_2 = 4.0 \, \text{M} \times 75 \, \text{mL} = 4.0 \, \text{M} \times 0.075 \, \text{L} = 0.300 \, \text{mol} \]

### Step 3: Calculate the total moles of HCl in the mixture
\[ \text{Total moles} = \text{Moles}_1 + \text{Moles}_2 = 0.075 \, \text{mol} + 0.300 \, \text{mol} = 0.375 \, \text{mol} \]

### Step 4: Calculate the total volume of the mixture
\[ \text{Total volume} = V_1 + V_2 = 25 \, \text{mL} + 75 \, \text{mL} = 100 \, \text{mL} = 0.100 \, \text{L} \]

### Step 5: Calculate the molarity of the final mixture
Using the formula for molarity:
\[ \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume}} \]
\[ \text{Molarity} = \frac{0.375 \, \text{mol}}{0.100 \, \text{L}} = 3.75 \, \text{M} \]

### Final Answer
The molarity of the final mixture is **3.75 M**.

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