How much agarose powder would you need to use (include units! ) if you only needed 40 ml of agarose gel and the package recipe states ‘use 6 grams of agarose powder dissolved in 500 ml of water’?

The rule of three is a way to solve problems of proportionality between three known values and one unknown.  This is an operation of finding the fourth term of a proportion knowing the other three.

We can use the rule of three to solve this problem in this way,

500 mL →  6 grams

40 mL  →     x

This is the same as saying: if in 500 mL there should be 6 grams of agarose powder then in 40 mL how many grams should there be?

So,

→ x = 0.48 g = 480 mg

Then, you need to dissolved 480 mg of agarose powder in 40 mL of water to meet the recipe.

answer: the rate of diffusion increases with increase in temperature.

increase in temperature, increases the molecular/particles speed (kinetic energy. diffusion means movement of particles through the material.

generally, the heavier the particle the more it interacts with the environment and more the temperature matters. so higher temperature results in higher diffusion.