Fick's law puts the three factors from the last lesson into one relationship. It says that the rate of diffusion is proportional to the surface area multiplied by the concentration difference, divided by the thickness of the membrane.
rate of diffusion ∝ (surface area × concentration difference) ÷ thickness of membrane
The symbol ∝ means "is proportional to". The concentration difference is the size of the concentration gradient, and the thickness of the membrane is the diffusion distance. Surface area and concentration difference are on the top of the fraction, so a bigger value gives a bigger rate. Thickness is on the bottom, so a bigger value gives a smaller rate.
This lets you predict what happens when one factor changes and the others stay the same. Doubling the surface area doubles the rate. Doubling the concentration difference doubles the rate. Doubling the thickness halves the rate. If you double both the surface area and the thickness, the two changes cancel out and the rate stays the same.
To calculate a rate, multiply the surface area by the concentration difference, then divide by the thickness. Worked example: a membrane has a surface area of 6 cm2, a concentration difference of 4 units and a thickness of 2 units. 6 × 4 = 24, and 24 ÷ 2 = 12, so the rate is 12 arbitrary units. If the membrane were 4 units thick, the rate would be 24 ÷ 4 = 6 arbitrary units, which is half as big. The answer is in arbitrary units because the law shows proportion, not an exact quantity, so use the same units for each quantity when you compare membranes. If a question gives you the rate and two of the other values, rearrange the calculation. For the first membrane, concentration difference = rate × thickness ÷ surface area = 12 × 2 ÷ 6 = 4.