Questions: We have 100 ml of 0.5 M NaCl solution in a container and 100 ml of 0.1 M NaCl solution in another container, we want to prepare 50 ml of 0.3 M NaCl solution by mixing appropriate volume of each solution. Calculate volume of each solution.

We have 100 ml of 0.5 M NaCl solution in a container and 100 ml of 0.1 M NaCl solution in another container, we want to prepare 50 ml of 0.3 M NaCl solution by mixing appropriate volume of each solution.

Calculate volume of each solution.

Transcript text: We have 100 ml of 0.5 M NaCl solution in a container and 100 ml of 0.1 M NaCl solution in another container, we want to prepare 50 ml of 0.3 M NaCl solution by mixing appropriate volume of each solution. Calculate volume of each solution.

Solution

Solution Steps

Step 1: Define the Variables

Let \( V_1 \) be the volume of the 0.5 M NaCl solution needed, and \( V_2 \) be the volume of the 0.1 M NaCl solution needed. The total volume of the final solution is 50 ml.

Step 2: Set Up the Equations

The total volume equation is: \[ V_1 + V_2 = 50 \]

The equation for the concentration of NaCl is: \[ 0.5V_1 + 0.1V_2 = 0.3 \times 50 \]

Step 3: Solve the Equations

Substitute the total volume equation into the concentration equation: \[ 0.5V_1 + 0.1(50 - V_1) = 15 \]

Simplify and solve for \( V_1 \): \[ 0.5V_1 + 5 - 0.1V_1 = 15 \] \[ 0.4V_1 = 10 \] \[ V_1 = 25 \]

Substitute \( V_1 = 25 \) into the total volume equation to find \( V_2 \): \[ V_2 = 50 - 25 = 25 \]

Final Answer

The volume of the 0.5 M NaCl solution needed is \( \boxed{25 \, \text{ml}} \) and the volume of the 0.1 M NaCl solution needed is \( \boxed{25 \, \text{ml}} \).

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