Explain the relationship between mass, molecular weight, and numbers of atoms or molecules and perform calculations deriving these quantities from one another
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The relationship between mass, molecular weight, and the number of atoms or molecules can be explained using Avogadro's number. Avogadro's number (symbolized as Nₐ) is defined as the number of atoms or molecules in one mole of a substance. It is approximately equal to 6.022 × 10²³.
Molecular weight (also known as molar mass) is the mass of one mole of a substance, expressed in grams. It is calculated by summing up the atomic weights of each atom in a molecule according to its stoichiometry.
The relationship between mass, molecular weight, and the number of atoms or molecules can be represented using the following equations:
1. Mass = Number of Atoms or Molecules × Atomic or Molecular Weight
Mathematically: m = n × MW
2. Number of Atoms or Molecules = Mass / Atomic or Molecular Weight
Mathematically: n = m / MW
To perform calculations deriving these quantities from one another, we can use the following steps:
Given information:
- Mass of the substance (m) in grams
- Atomic or Molecular Weight (MW) in grams per mole
To calculate the number of atoms or molecules (n), use the equation:
n = m / MW
To calculate the mass (m) of a given number of atoms or molecules (n), use the equation:
m = n × MW
To calculate the molecular weight (MW) when given the number of atoms or molecules (n) and mass (m), rearrange the equation as follows:
MW = m / n
By plugging in the given values into these equations, you can derive the desired quantities.
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