Label each process as a physical or chemical change and state how you know. fogging a mirror with your breath

breaking a bone

mending a broken bone

burning paper

slicing potatoes for fries

mixing sugar with coffee

frying chicken

a nail rusting

paper ripping

wood burning

mixing water and food coloring

food molding (rotting)

writing on paper

dyeing fabric

Fogging a mirror with your breath is a physical change because it involves a phase change of water vapor condensing and adsorbing to the mirror surface. Phase changes are physical changes.

Breaking a bone is a physical change insofar as we're focusing on the  "breaking" part.

Mending a broken bone, however, is a different story. Bones are living things: They consist of tissues that in turn consist of cells. The actual mending process involves some very complicated biochemistry. Suffice it to say that mending a broken bone would be a chemical change.

Burning paper is a chemical change. Burning anything implies combustion, which is a chemical reaction where some fuel is oxidized (usually by oxygen gas, producing carbon dioxide gas and water vapor).

Slicing potatoes for fries is a physical change. You can slice, dice, smash, mash, stretch, bend, compress, or grind a potato: What you will have is still a potato (okay, there are some chemical changes going on as you're rupturing cells in the process, causing them to release their contents which may participate in chemical reactions). But the key, again, is that cutting up some material doesn't fundamentally change the chemical identity of that material.

Mixing sugar with coffee actually involves two physical processes: the mixing and the (presumed) solvation of the solid sugar particles as they dissolve into the coffee. In either case, either mixing or dissolving would be a physical change. The sugar molecules are still in the coffee and are chemically unchanged.

Frying chicken is a chemical change. In fact, frying chicken likely entails several different types of chemical changes. The common thread among them is that frying involves breaking chemical bonds in and on the chicken by the addition of thermal energy, and new chemical bonds end up being formed. That's the hallmark of a chemical change.

A nail rusting is a chemical change. Rusting is an electrochemical process; the familiar corrosion of iron into rust is, at bottom, a chemical reaction where iron reacts with oxygen to form iron oxides (often catalyzed by the presence of water and salts).

A paper ripping is analogous to slicing potatoes: it's a physical change. If you ripped one sheet of paper into two halves, each half would retain all the chemical properties of the original sheet.

Likewise, wood burning is analogous to burning paper, and as such is a chemical change. Again, combustion is a chemical process.

As we said earlier with sugar in coffee, mixing in itself is a physical process. While it may seem like you've permanently changed the nature of the water by dyeing it with food coloring, the molecules comprising the food coloring are simply dispersed within the vast sea of water molecules. There are no intramolecular bonds that are broken or formed; the chemical identities of all the substances here are preserved. So, this is a physical change.

Food molding (rotting) is a chemical change. Rotting is biochemical decomposition: the chemical bonds that make up the food are broken down by enzymes released by the mold.

Writing on paper, whether it be with a pen, pencil, crayon, or marker, is a physical change. The molecules from the writing instrument are physically stuck to the paper. But unless you're writing on paper by, say, burning letters onto it, there are no chemical changes occurring when the writing instrument meets the paper.

As with writing on paper, dyeing fabric can be a physical change. The dye consists of molecules that interact with light in a way that we perceive a certain color. When dyeing fabric, these molecules are transferred and fixed into the fabric by adsorption, absorption, and other intermolecular phenomena. But the molecules of the dye (and the molecules in the fabric) don't experience any breaking and forming of bonds. All of the substances involved retain their chemical identities.

However, it's possible that, depending on the dye, there may be chemical changes involved. Some dyes, appropriate named "reactive dyes," undergo chemical reactions with their substrate (which, in this case, would be the fabric), or dyes may be used that undergo chemical reactions with one another, both of which would constitute chemical changes. And it can depend on what you mean by "dyeing": Bleaching a colored shirt can technically be conceived of as "dyeing" the shirt white, and this process involves cleavage of bonds within the color-producing molecules in the fabric by reacting with the molecules in the bleach.

So, for dyeing fabric, it can be a physical or chemical change depending on the dye.