V litre decinormal solution of NaCl is prepared. Half of the solution is converted into centionormal and added to the left decinormal solution. Then

Options

A. Number of millimoles of NaCl are reduced by `(1)/(5)`
B. Number of milliequivalents of NaCl do not change
C. Normality of the final solution becomes 0.01 N
D. Molarity of the final solution becomes 0.018 M

Answer

To solve the problem step by step, we need to understand the definitions of decinormal and centinormal solutions and how they relate to the concentrations of the solutions involved.

### Step 1: Understand the Definitions
- A decinormal (dN) solution has a concentration of 0.1 N (normal).
- A centinormal (cN) solution has a concentration of 0.01 N (normal).

### Step 2: Determine the Initial Concentration
Given that we have V liters of a decinormal solution of NaCl:
- Concentration of NaCl = 0.1 N
- Therefore, the number of equivalents in V liters = 0.1 N × V L = 0.1V equivalents.

### Step 3: Convert Half of the Solution
Half of the decinormal solution is taken:
- Volume of half the solution = V/2 liters.
- The concentration of this half remains 0.1 N.

### Step 4: Convert to Centinormal
Now, we convert this half solution into a centinormal solution:
- The number of equivalents in V/2 liters of 0.1 N solution = 0.1 N × (V/2) L = 0.05V equivalents.
- When converted to centinormal, the total volume remains V/2 liters, but the concentration becomes 0.01 N.

### Step 5: Add the Two Solutions
Now, we add the centinormal solution (0.01 N) back to the original decinormal solution (0.1 N):
- The total volume of the combined solution = V/2 + V = (3V/2) liters.
- The total number of equivalents from both solutions:
- From the decinormal solution: 0.1V equivalents.
- From the centinormal solution: 0.05V equivalents.

Total equivalents = 0.1V + 0.05V = 0.15V equivalents.

### Step 6: Calculate the Final Concentration
To find the final concentration of the combined solution:
- Final concentration (N) = Total equivalents / Total volume
- Final concentration (N) = (0.15V) / (3V/2) = 0.15V × (2/3V) = 0.1 N.

### Final Answer
The final concentration of the combined solution is 0.1 N.

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