A soap film is formed on a rectangular frame of 7 cm side dipping into a scop solution. The frame hangs from the arm of a balance. An extra weight of 0.4 gram is to be placed in the opposite pan to balance the pull on the frame. Caluclate the surface tension of the soap solution.

Explanation

To calculate the surface tension of the soap solution using the given information, we can follow these steps:

### Step 1: Understand the setup
A soap film is formed on a rectangular frame with a side length of 7 cm. The frame has two free surfaces because soap films have two sides (front and back).

### Step 2: Calculate the total length of the film
Since the frame has two free surfaces, the total length (L) of the soap film is:
\[ L = 2 \times \text{side length} = 2 \times 7 \text{ cm} = 14 \text{ cm} \]
Convert this length into meters:
\[ L = 14 \text{ cm} = 0.14 \text{ m} \]

### Step 3: Convert the mass of the extra weight to force
The extra weight placed in the opposite pan is 0.4 grams. First, convert this mass into kilograms:
\[ \text{mass} = 0.4 \text{ g} = \frac{0.4}{1000} \text{ kg} = 0.0004 \text{ kg} \]
Now, calculate the force (F) due to this mass using the equation \( F = mg \), where \( g \) is the acceleration due to gravity (approximately \( 9.8 \text{ m/s}^2 \)):
\[ F = 0.0004 \text{ kg} \times 9.8 \text{ m/s}^2 = 0.000392 \text{ N} \]

### Step 4: Use the formula for surface tension
The surface tension (\( \gamma \)) can be calculated using the formula:
\[ \gamma = \frac{F}{2L} \]
Substituting the values we have:
\[ \gamma = \frac{0.000392 \text{ N}}{2 \times 0.14 \text{ m}} \]
\[ \gamma = \frac{0.000392}{0.28} \]
\[ \gamma = 0.0014 \text{ N/m} \]

### Step 5: Final result
Thus, the surface tension of the soap solution is:
\[ \gamma = 0.0014 \text{ N/m} \]