How many molecules are there in 4.0 moles of glucose? [Avogadro's number = 6.02 x 10\(^{23}\)]

Answer Details

The number of molecules in a sample is found by multiplying the number of moles by Avogadro's number. The relationship is:

\[N = n \times N_A\]

where \(N\) is the number of molecules, \(n\) is the number of moles, and \(N_A\) is Avogadro's number (\(6.02 \times 10^{23}\)).

Substituting the given values:

\[N = 4.0 \times 6.02 \times 10^{23}\]

\[N = 24.08 \times 10^{23}\]

\[N = 2.408 \times 10^{24}\]

Rounding to three significant figures gives \(2.41 \times 10^{24}\) molecules.

A common error is dividing instead of multiplying. Dividing 6.02 by 4 would give \(1.51 \times 10^{23}\), which is the number of molecules in 0.25 moles, not 4.0 moles. When you have more than one mole, the number of molecules must be greater than Avogadro's number, so any answer smaller than \(6.02 \times 10^{23}\) can be immediately ruled out.