**Given information:**
- The work needed to decrease the coverage of the film by 1 cm² is 25 × 10⁻⁷ J.
- The surface tension of pure water is 0.072 N/m.

**Calculating the change in surface area:**
To determine the surface tension of the film, we need to calculate the change in surface area. We know that the work done (W) is equal to the change in surface area (dA) multiplied by the surface tension (γ).

W = dA * γ

Rearranging the equation, we can solve for the change in surface area:

dA = W / γ

Given that the work done is 25 × 10⁻⁷ J and the surface tension of pure water is 0.072 N/m, we can substitute these values into the equation to find the change in surface area:

dA = (25 × 10⁻⁷ J) / (0.072 N/m)

**Calculating the change in surface area:**

To determine the change in surface area, we need to convert the units of work done from J to N·m. Since 1 J = 1 N·m, the change in surface area can be calculated as:

dA = (25 × 10⁻⁷ N·m) / (0.072 N/m)

Simplifying the equation, we find:

dA = 3.47 × 10⁻⁶ m²

**Calculating the change in coverage:**

The change in coverage can be calculated by converting the change in surface area to square centimeters:

Change in coverage = (3.47 × 10⁻⁶ m²) / (0.0001 m²/cm²)

Simplifying the equation, we find:

Change in coverage = 34.7 cm²

Therefore, the film of stearic acid partially covers an area of 34.7 cm².

**Calculating the surface tension of the film:**

The surface tension of the film can be calculated by dividing the work done by the change in surface area:

Surface tension of the film = (25 × 10⁻⁷ J) / (3.47 × 10⁻⁶ m²)

Simplifying the equation, we find:

Surface tension of the film = 7.20 N/m

Therefore, the surface tension of the film of stearic acid is 7.20 N/m.