Temperature: The higher the temperate, the faster diffusion or osmosis occurs. If the temperature is too high, however (too far past optimum), enzymes begin to de-nature and this may affect the rate of substance movement, especially in terms of active transport. Until that point, the higher the temperature, the faster the movement of particles, as they have more energy, and therefore collide more, making it more likely that they will move into the desired space.
Concentration gradient: If the concentration gradient is high/steep, it means that there is a greater difference in concentration between the substance inside and outside the cell. A steeper concentration gradient means the substance will diffuse faster because molecules have a bigger opportunity of diffusing.
Surface area to volume ratio: If there is a larger surface area to volume ratio, the movement of the substance is likely to be quicker, especially in terms of diffusion, as there is a larger space that particles can get past.
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