The molarity of a solution obtained by mixing 750 mL of 0.5 M HCl with 250 mL of 2 M HCl will be

Options

A. (a)0.875 M
B. (b)1.00 M
C. (c )1.75 M
D. (d)0.0975 M

Explanation

To find the molarity of the resulting solution after mixing two solutions of hydrochloric acid (HCl), we can follow these steps:

### Step 1: Identify the given data
- Volume of the first solution (V1) = 750 mL
- Molarity of the first solution (M1) = 0.5 M
- Volume of the second solution (V2) = 250 mL
- Molarity of the second solution (M2) = 2 M

### Step 2: Convert volumes to liters
Since molarity is expressed in moles per liter, we need to convert the volumes from milliliters to liters:
- V1 = 750 mL = 750/1000 = 0.75 L
- V2 = 250 mL = 250/1000 = 0.25 L

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

For the first solution:
\[ \text{Moles of HCl from solution 1} = M1 \times V1 = 0.5 \, \text{M} \times 0.75 \, \text{L} = 0.375 \, \text{moles} \]

For the second solution:
\[ \text{Moles of HCl from solution 2} = M2 \times V2 = 2 \, \text{M} \times 0.25 \, \text{L} = 0.5 \, \text{moles} \]

### Step 4: Calculate the total number of moles of HCl
Now, add the moles from both solutions:
\[ \text{Total moles of HCl} = 0.375 \, \text{moles} + 0.5 \, \text{moles} = 0.875 \, \text{moles} \]

### Step 5: Calculate the total volume of the mixed solution
The total volume of the mixed solution is:
\[ \text{Total volume} = V1 + V2 = 0.75 \, \text{L} + 0.25 \, \text{L} = 1.0 \, \text{L} \]

### Step 6: Calculate the molarity of the resulting solution
Using the formula for molarity:
\[ \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume (L)}} \]
\[ \text{Molarity} = \frac{0.875 \, \text{moles}}{1.0 \, \text{L}} = 0.875 \, \text{M} \]

### Final Answer
The molarity of the resulting solution is **0.875 M**.

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