You are watching: What relationships are needed to convert 1.5 grams of carbon to the number of carbon atoms?
When objects are an extremely small, it is regularly inconvenient, inefficient, or even impossible to address the objects one in ~ a time. For these reasons, we often address very small objects in groups, and also have also invented surname for miscellaneous numbers that objects. The most typical of this is "dozen" which describes 12 objects. We typically buy objects in teams of 12, favor doughnuts or pencils. Even smaller objects such as straight pins or staples room usually sold in box of 144, or a dozen dozen. A group of 144 is dubbed a "gross".
This trouble of taking care of things that room too little to operate with as solitary items additionally occurs in jajalger2018.orgistry. Atoms and also molecules room too little to see, let alone to count or measure. Jajalger2018.orgists essential to select a group of atom or molecule that would be practically to operate with.
Avogadro"s Number and also Mole
In jajalger2018.orgistry, it is difficult to address a solitary atom or molecule due to the fact that we can"t view them, count them, or sweet them. Jajalger2018.orgists have selected a number of particles through which to work-related that is convenient. Since molecules are incredibly small, you might suspect this number is going come be an extremely large, and you are right. The variety of particles in this team is \(6.02 \times 10^23\) particles and the name of this team is the mole (the abbreviation for mole is \(\textmol\)). One mole of any type of object is \(6.02 \times 10^23\) of those objects. There is a specific reason that this number to be chosen and also this factor will come to be clear together we proceed.
When jajalger2018.orgists space carrying the end jajalger2018.orgical reactions, it is crucial that the relationship between the numbers of particles of each reactant is known. Any readily measurable fixed of an facet or compound includes an extraordinarily big number of atoms, molecules, or ions, therefore an extremely big numerical unit is required to counting them. The mole is offered for this purpose.
The mole (symbol: mol) is the basic unit of lot of problem ("number that substance") in the global System of units or System international (SI), characterized as specifically 6.02214076×1023 particles, e.g., atoms, molecules, ions or electrons. The current definition was adopted in November 2018, revising its old definition based top top the number of atoms in 12 grams the carbon-12 (12C) (the isotope of carbon with family member atomic massive 12 Daltons, by definition). For many purposes, 6.022 × 1023 offers an adequate number of far-ranging figures. Just as 1 mole that atoms has 6.022 × 1023 atoms, 1 mole the eggs has 6.022 × 1023 eggs. This number is called Avogadro’s number, ~ the 19th-century Italian scientist who an initial proposed a relationship in between the volumes of gases and also the number of corpuscle they contain.
It is not obvious why egg come in dozens fairly than 10s or 14s, or why a ream of paper contains 500 sheets rather than 400 or 600. The meaning of a mole—that is, the decision to basic it ~ above 12 g of carbon-12—is additionally arbitrary. The important suggest is the 1 mole of carbon—or of anything else, even if it is atoms, compact discs, or houses—always has the same variety of objects: 6.022 × 1023.
Converting Between number of Atoms to Moles and also Vice Versa
We have the right to use Avogadro"s number together a counter factor, or ratio, in dimensional analysis problems. If we are offered the variety of atoms that an facet X, we can transform it right into moles by making use of the relationship
\<\text1 mol X = 6.022 \times 10^23 \text X atoms.\>
Example \(\PageIndex1\): mole of Carbon
The element carbon exist in two major forms: graphite and also diamond. How many moles of carbon atom is \(4.72 \times 10^24\) atom of carbon?
|Identify the "given" information and also what the problem is questioning you to "find."||Given: \(4.72 \times 10^24\) C atom Find: mol C|
|List other well-known quantities.||\(1\, mol = 6.022 \times 10^23\) C atoms|
Prepare a principle map and also use the proper conversion factor.
Example \(\PageIndex2\): Chromium
Chromium steel is used for decorate electroplating of car bumpers and also other surfaces. Find the massive of 0.560 moles of chromium.