The evidence that best supports the student's claim, "Life is possible because of the unique mixture of gases that cycle through the Earth’s spheres," is:
a diagram illustrating how plants use carbon dioxide, water, and sunlight to produce food and oxygen gas.
This evidence directly relates to how essential gases like carbon dioxide and oxygen are involved in processes critical for life, such as photosynthesis, demonstrating the importance of the Earth's gaseous mixture in supporting life.