20 mL of 0.5 M HCl is mixed with 30 mL of 0.3 M HCl, the molarity of the resulting solution is :

Options

A. 0.8 M
B. 0.53 M
C. 0.38 M
D. 0.83 M

Explanation

To find the molarity of the resulting solution when 20 mL of 0.5 M HCl is mixed with 30 mL of 0.3 M HCl, we can follow these steps:

### Step 1: Calculate the total volume of the mixed solution.
- The total volume (V) is the sum of the volumes of the two solutions.
- \( V = V_1 + V_2 = 20 \, \text{mL} + 30 \, \text{mL} = 50 \, \text{mL} \)

### Step 2: Calculate the number of moles of HCl in each solution.
- For the first solution (0.5 M HCl):
- Moles of HCl = Molarity × Volume (in liters)
- \( \text{Moles}_1 = 0.5 \, \text{M} \times \frac{20 \, \text{mL}}{1000 \, \text{mL/L}} = 0.5 \times 0.020 = 0.01 \, \text{moles} \)

- For the second solution (0.3 M HCl):
- \( \text{Moles}_2 = 0.3 \, \text{M} \times \frac{30 \, \text{mL}}{1000 \, \text{mL/L}} = 0.3 \times 0.030 = 0.009 \, \text{moles} \)

### Step 3: Calculate the total number of moles of HCl in the mixed solution.
- Total moles of HCl = \( \text{Moles}_1 + \text{Moles}_2 = 0.01 \, \text{moles} + 0.009 \, \text{moles} = 0.019 \, \text{moles} \)

### Step 4: Calculate the molarity of the resulting solution.
- Molarity (M) is defined as the number of moles of solute divided by the volume of solution in liters.
- \( M = \frac{\text{Total moles}}{\text{Total volume in liters}} \)
- \( M = \frac{0.019 \, \text{moles}}{0.050 \, \text{L}} = 0.38 \, \text{M} \)

### Final Answer:
The molarity of the resulting solution is **0.38 M**.

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