2.5 litre of `1M NaOH` solution is mixed with another 3 litre solution of `0.5M NaOH` solution. Then the molarity of the resulting solution is

Options

A. `0.80M`
B. `1.0M`
C. `0.73M`
D. `0.50M`

Explanation

To find the molarity of the resulting solution when mixing two sodium hydroxide (NaOH) solutions, we can follow these steps:

### Step 1: Identify the volumes and molarities of the solutions
- First solution:
- Volume (V1) = 2.5 L
- Molarity (M1) = 1 M
- Second solution:
- Volume (V2) = 3 L
- Molarity (M2) = 0.5 M

### Step 2: Calculate the number of moles of solute in each solution
The number of moles of solute can be calculated using the formula:
\[ \text{Number of moles} = \text{Volume (L)} \times \text{Molarity (mol/L)} \]

- For the first solution:
\[ \text{Number of moles (n1)} = V1 \times M1 = 2.5 \, \text{L} \times 1 \, \text{mol/L} = 2.5 \, \text{mol} \]

- For the second solution:
\[ \text{Number of moles (n2)} = V2 \times M2 = 3 \, \text{L} \times 0.5 \, \text{mol/L} = 1.5 \, \text{mol} \]

### Step 3: Calculate the total number of moles of solute
Now, add the number of moles from both solutions:
\[ \text{Total number of moles (n_total)} = n1 + n2 = 2.5 \, \text{mol} + 1.5 \, \text{mol} = 4 \, \text{mol} \]

### Step 4: Calculate the total volume of the resulting solution
The total volume of the resulting solution is the sum of the volumes of the two solutions:
\[ \text{Total volume (V_total)} = V1 + V2 = 2.5 \, \text{L} + 3 \, \text{L} = 5.5 \, \text{L} \]

### Step 5: Calculate the molarity of the resulting solution
Finally, use the formula for molarity:
\[ \text{Molarity (M)} = \frac{\text{Total number of moles}}{\text{Total volume (L)}} \]
\[ \text{Molarity (M)} = \frac{n_{total}}{V_{total}} = \frac{4 \, \text{mol}}{5.5 \, \text{L}} \approx 0.727 \, \text{M} \]

### Step 6: Round the result
Rounding to two decimal places, we get:
\[ \text{Molarity} \approx 0.73 \, \text{M} \]

Thus, the molarity of the resulting solution is approximately **0.73 M**.

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