According to Charles's law, the volume of a gas is directly proportional to its temperature when pressure remains constant. Mathematically, this can be expressed as:

V1 / T1 = V2 / T2

where V1 and T1 represent the initial volume and temperature, and V2 and T2 represent the final volume and temperature, respectively.

Given:

Initial volume (V1) = 0.75 L

Initial temperature (T1) = 25°C = 25 + 273 = 298 K

Final temperature (T2) = –100°C = –100 + 273 = 173 K

We need to find the final volume (V2)

Rearranging the formula, we get:

V2 = (V1 x T2) / T1

Substituting the given values:

V2 = (0.75 L x 173 K) / 298 K

V2 = 0.43 L

Therefore, the new volume of the balloon when cooled to -100°C is 0.43 liters