Conductivity of 0.01M NaCl solution is 0.00147 `ohm^(-1) cm ^(-1)`. What happen to this conductivity if extra 100m L of `H_(2)O` will be added to the above solution?

Options

A. Increase
B. Decreases
C. Remains unchanged
D. First increases and then decreases.

Explanation

To solve the problem, we need to understand the relationship between conductivity, concentration, and dilution. Here's a step-by-step solution:

### Step 1: Understand the initial conditions
We have a 0.01 M NaCl solution with a conductivity of 0.00147 `ohm^(-1) cm^(-1)`. This means that in its current state, the solution has a certain concentration of ions (Na⁺ and Cl⁻) that contribute to its conductivity.

**Hint:** Remember that conductivity is directly related to the concentration of ions in the solution.

### Step 2: Analyze the effect of dilution
When we add 100 mL of water to the 0.01 M NaCl solution, we are effectively diluting the solution. Dilution means that the total volume of the solution increases, which decreases the concentration of the ions present.

**Hint:** Think about how adding more solvent (water) affects the number of ions per unit volume.

### Step 3: Calculate the new concentration after dilution
The initial volume of the NaCl solution is not specified, but we can denote it as V mL. After adding 100 mL of water, the new total volume becomes (V + 100) mL.

The new concentration (C') after dilution can be calculated using the formula:
\[ C' = \frac{C \times V}{V + 100} \]
where C is the initial concentration (0.01 M).

**Hint:** Use the dilution formula \( C_1V_1 = C_2V_2 \) to find the new concentration.

### Step 4: Determine the effect on conductivity
As the concentration of ions decreases due to dilution, the conductivity of the solution will also decrease. This is because conductivity is dependent on the number of charge carriers (ions) in the solution. Fewer ions mean less conductivity.

**Hint:** Recall that conductivity is proportional to the concentration of ions in the solution.

### Step 5: Conclusion
Thus, after adding 100 mL of water to the 0.01 M NaCl solution, the conductivity will decrease.

**Final Answer:** The conductivity of the solution will decrease.