How to Find Avogadro's Number

The Avogadro's number (constant) is a number of particles (atoms, molecules) in one mole of a substance. In fact, the Avogadro's constant is a coefficient between atomic and macroscopic scales. The Avogadro's number is a part of several other fundamental values in Physics like Faraday and Boltzmann constants. One way to calculate the Avogadro's number is based on the molar volume of silicon and a dimension obtained from the cubic crystal structure of silicon abbreviated as V(Si) and d(220), respectively. The formula is
Avogadro's Number=V(Si)/(sqrt(8) x d(220)^3). Sqrt(8) is square root of 8.

Things You'll Need

• Calculator

Instructions

1. Obtain molar volume of silicon and the silicon crystal structure dimension from the reference.
   V(Si) = 1.20588254E-5 (cubic meters/mol).
   d(220) =1.920155982E^-10 meters.

2. Calculate Avogadro's number using the formula above.
   Avogadro's number=1.20588254E^-5/[sqrt(8) x (1.920155982E-10)^3] = 6.022E23 mol^-1.
   Note: precision of three digits after the decimal point in the Avogadro's number is sufficient in the majority of calculations.

3. Navigate to the NIST website (see link in resources) to obtain a more precise, currently recommended value for the Avogadro's number.
   The value for the constant given there is 6.02214179E23 mol^-1.

References

• CODATA recommended values of the fundamental physical constants: 2006", P.J. Mohr, B.N. Taylor and D.B. Newell, J. Phys. Chem. Ref. Data , V. 37, pp.1187-1284, 2008.

Resources

• Avogadro constant