How many moles of cobalt are in 1.80e22 cobalt atoms?
The correct answer and explanation is:
To find how many moles of cobalt are in 1.80 × 10²² atoms of cobalt, use Avogadro’s number, which is:
6.022 × 10²³ atoms/mol
Step-by-step Solution:
Moles of cobalt=Number of atomsAvogadro’s number=1.80×10226.022×1023\text{Moles of cobalt} = \frac{\text{Number of atoms}}{\text{Avogadro’s number}} = \frac{1.80 \times 10^{22}}{6.022 \times 10^{23}} =0.02989 mol= 0.02989\ \text{mol}
Rounded to three significant figures: 0.0299 mol of cobalt\boxed{0.0299\ \text{mol of cobalt}}
Explanation (300 words):
A mole is a standard unit in chemistry used to express amounts of a chemical substance. One mole of any element contains 6.022 × 10²³ particles (atoms, molecules, ions, etc.). This number is known as Avogadro’s number.
In this case, the goal is to determine how many moles of cobalt are present in 1.80 × 10²² atoms. To do this, the number of atoms must be divided by Avogadro’s number. This gives a ratio that tells how many groups of 6.022 × 10²³ atoms are present in the sample. Because the number of atoms given is smaller than Avogadro’s number, the result is less than one mole.
The formula applied is: Moles=Atoms6.022×1023\text{Moles} = \frac{\text{Atoms}}{6.022 \times 10^{23}}
This method works because the definition of a mole is tied directly to this constant. In practical terms, the result tells that 1.80 × 10²² cobalt atoms make up about 0.0299 moles of cobalt.
Understanding moles is essential in chemistry for converting between the microscopic world (atoms and molecules) and the macroscopic world (grams and liters). It is especially helpful in stoichiometry, where balanced chemical equations are used to calculate the amounts of reactants and products in a reaction.