What is the definition of of 'compound', 'mixture', 'element' and 'molecule'?

I am looking for the precise definitions, as I am very confused as to what they are exactly, because although I mostly understand what they mean, I have encountered some conflicting definitions that confused me.

As it stands, this is what I understand them to mean:

• Compound: two or more different atoms bonded together.
• Mixture: two or more different atoms together but not joined.
• Molecule: two particles (same or different) bonded together.
• Element: only 1 type of atom; this definition is applied to things both bonded and not to itself.

I don't know whether these terms apply microscopically, macroscopically, or both. For example: I think 1 $\ce{H2O}$ molecule is a compound, but is a bathtub of them called a mixture (as it contains more than 1 atom type), a compound, or both? That is, to be a compound, do all the atoms in the compound have to be bonded physically together? Generally, to what extent can these four terms overlap?

I would very much like a systematic way of thinking about these terms.

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If one atom, then not molecule and not mixture and not compound. If two atoms and same element, then molecule and not compound and not mixture. If two atoms and not same element, then compound and molecule and not mixture. If two different molecules and evenly mixed, then homogeneous mixture. If two different substances and differentiable on the molecular level, then heterogeneous mixture. The air is a homogeneous mixture. Your oatmeal is a heterogeneous mixture. –  Leonardo Jan 10 '13 at 6:17

I can't really provide a systematic approach, but I can attempt to clarify (as a student myself).

• Elements are classes of atoms. Atoms of the same element are similar (if not identical) in their physical and chemical properties (but be aware of Isotopes which are physical variations among atoms of the same element).
A definite (I suppose, systematic) way to distinguish elements is that their corresponding atoms have different numbers of electrons orbiting the nucleus.
The term is also used to describe a collective of the same atom (element). A bar of gold (Gold being an 'element'; a chemical class) is said to be an element itself.

• Molecules are a group of atoms covalently bonded to each other (which can be considered a 'direct connection', if you will). The molecule can consist of atoms of the same element, or atoms of different elements.
If you joined to molecules via covalent bonding, you'd have created a new molecule (it's nothing special)

• Compounds are (in the chemical sense of the term) made of two or more elements. This means, a lot of molecules (like H2O) are considered compounds (though H2 is not). 'Compound' is often used interchangeably with the word substance, which describes a collective of molecules (water is a substance. It is a large quantity of neighbouring H2O molecules).
A substance (and a compound, when compound is used to describe a quantity of molecules) only consists of the same molecule. In water, all the molecules are H2O. If there were also some H2 molecules among them, it would no longer be considered a compound/substance (but instead; a mixture).
These molecules are not directly bonded to each other (or they'd be one big molecule), they are just in close* proximity to one another and are attracted to one another, keeping them in proximity. Even when the substance is a solid, like ice, they are not directly connected, the molecules are just slower (less energetic) and closer together (and in some special cases, like ice, stronger, such as Hydrogen Bonding. Don't be confused, though it is referred to as 'bonding', there is no direct covalent bond, just an attraction).

• Mixtures are collectives of different molecules or atoms. The molecules and atoms are like that in a substance; they're not bonded to each other, but are attracted, and in a mixture specifically, the molecules/atoms are not all the same. Juice, for instance, is a mixture. It contains some Vitamin C molecules, some water molecules, some sugar molecules, et c.

Here is a horribly drawn diagram to help clarify the distinctions.

Reflecting on this, here is what in your understanding needs specific attention.

Compound: two or more different atoms bonded together A molecule or a group of identical molecules.
Mixture: two or more different atoms or molecules together but not joined (they're not covalently bonded).
Molecule: two or more particles atoms (same or different) bonded together.

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What about ionic substances? Is NaCl a compound? I always thought it was but if we take your definition there is no such thing as an ionic compound. –  surelyourejoking Oct 14 '14 at 13:53
@AntiEarth we can still have monoatomic molecules, e.g. neon atoms. I think the definition of a molecule is that its the smallest possible particle capable of independent existence or something. –  Sherlock Holmes Oct 15 '14 at 1:10
@SherlockHolmes It is my understanding that single atoms are not molecules; the wikipedia definition reads "A molecule /ˈmɒlɪkjuːl/ is an electrically neutral group of two or more atoms held together by chemical bonds" –  Anti Earth Oct 15 '14 at 2:12

In a sample of water, you'll find the compound $H_2O$. In a sample of hydrogen gas, you'll find the element hydrogen, though it'll take the form of the molecule $H_2$. In a mixture, you may find different molecules, compounds, and elements.

At this point, you may find it helpful to look at the following classification of matter.
The left side of the tree denotes chemical bonds/changes. The right is physical. (i.e., you can get a hetergeneous mixture to convert to a homogeneous mixture by changing physical things about the mixture like adding in another element. You can't do the same to elements and compounds.)

Does this genearlly clean up your understandings of compounds, molecules, elements, and mixtures?

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I was also confused when I learned this all stuff first time. When you get any element, molecule, compound or mixture don't think about complex stuff but think on basic level.

I have given most basic definition(properties) of element, molecule, compound or mixture(As simple as i could).

Element:

• The substance which cannot be broken down chemically is called elements.

• All substance listed in Periodic Table are element.

Molecule

• To or more atom or element combine together is called molecule.

Compound:

• Two or more element combine together and form compound.

• Smallest particle of compound is molecule.

• compound posses different characteristic compared to constituent element.

• Example: $\ce{H2O}$.

• $\ce{H}$ is Highly combustible

• $\ce{O}$ helps in combustion

• $\ce{H2O}$. is fire extinguisher(different characteristic than $\ce{H}$ and $\ce{O}$ )

Mixture:

• When two or more matter mix without changing their original property is called mixture.

• Mixture can be separated by simple process like Filtration.

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Compound: a pure substance formed from the bonding of two or more different elements together. It can be decomposed into its constituent elements by chemical means.

Element: a pure substance consisting of one type of atom only.

Mixture: two or more different substances are mixed but they are not chemically bonded together and may be separated by a physical process such as filtration, distillation and so on.

Molecule: I'm actually not sure about this - I always read that it's a group of atoms (same or different) bonded together and is the smallest particle of an element/compound capable of independent existence; however, we treat monoatomic gases as a molecule, e.g. Neon.

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