Question

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

Explanation:

Step1: Recall the mole - atom relationship

The formula \(n=\frac{N}{N_A}\), where \(n\) is the number of moles, \(N\) is the number of atoms, and \(N_A\) (Avogadro's number, \(N_A = 6.022\times10^{23}\text{ mol}^{-1}\)) is a constant. If \(N_1 = N_2\) (same number of atoms for two different elements), then \(n_1=\frac{N_1}{N_A}\) and \(n_2=\frac{N_2}{N_A}\), so \(n_1 = n_2\).

Step2: Analyze option b

The formula \(n=\frac{m}{M}\), where \(m\) is the mass and \(M\) is the molar mass. Different elements have different molar masses (\(M\)). If \(m_1 = m_2\) (same mass), but \(M_1
eq M_2\), then \(n_1=\frac{m_1}{M_1}\) and \(n_2=\frac{m_2}{M_2}\), and \(n_1
eq n_2\).

Step3: Analyze option c

From \(n=\frac{m}{M}\) and \(N = nN_A=\frac{mN_A}{M}\). If \(m_1 = m_2\), but \(M_1
eq M_2\), then \(N_1=\frac{m_1N_A}{M_1}\) and \(N_2=\frac{m_2N_A}{M_2}\), and \(N_1
eq N_2\).

Answer:

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