Final answer:
Sugarwater, as a solution, has the smallest particles and is followed by egg white, a colloid, with larger protein molecules. Muddy water, being a suspension, has the largest particles that can settle over time.
Step-by-step explanation:
To arrange the mixtures of muddy water, sugarwater, and egg white in order of increasing particle size, we need to understand the classifications of mixtures based on the size of their particles. A solution has the smallest particles, usually ions or small molecules that do not settle out or filter out, like sugar dissolved in water. Colloids have larger particles that do not settle but can scatter light, such as the proteins in egg white. Suspensions have the largest particles that will settle over time, which is characteristic of muddy water.
Therefore, in order of increasing particle size, the mixtures are: sugarwater (solution), egg white (colloid), and muddy water (suspension). This is because sugarwater has very small dissolved particles which makes it a true solution. Egg white consists of larger protein molecules that are dispersed to form a colloid, and muddy water contains even larger particles that can settle down if left undisturbed, classifying it as a suspension.