Question

part a
which statement is always true for samples of atomic elements, regardless of the type of element present in the samples?
if two samples of different elements have the same mass, they contain the same number of moles.
if two samples of different elements contain the same number of atoms, they contain the same number of moles.
if two samples of different elements have the same mass, they contain the same number of atoms.
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Explanation:

• The formula for the number of moles \(n=\frac{m}{M}\), where \(m\) is mass and \(M\) is molar mass. Different elements have different molar masses. So, if two samples of different elements have the same mass, since \(M\) (molar mass) is different for different elements, \(n\) (number of moles) will be different. So the statement “If two samples of different elements have the same mass, they contain the same number of moles” is false.
• The formula for the number of moles \(n = \frac{N}{N_{A}}\), where \(N\) is the number of atoms and \(N_{A}\) is Avogadro's number (\(N_{A}=6.022\times 10^{23}\text{ mol}^{-1}\)). Since \(N_{A}\) is a constant, if \(N\) (number of atoms) is the same for two samples (regardless of the type of element, because the formula for \(n\) in terms of \(N\) does not depend on the nature of the element, only on the count of atoms), then \(n\) (number of moles) is the same.
• Using \(n=\frac{m}{M}\) and \(N = nN_{A}=\frac{mN_{A}}{M}\). Since \(M\) (molar mass) is different for different elements, if \(m\) (mass) is the same for two different - element samples, \(N\) (number of atoms) will be different.

Answer:

If two samples of different elements contain the same number of atoms, they contain the same number of moles.