Question

decide whether 15.0 g of magnesium or 15.0 g of manganese represents the greater number of atoms. (only write the name of the element in your answer.)

Explanation:

Step1: Recall the formula for moles

The number of moles \( n = \frac{m}{M} \), where \( m \) is the mass and \( M \) is the molar mass. The number of atoms is proportional to the number of moles (since \( \text{Number of atoms} = n \times N_A \), where \( N_A \) is Avogadro's number). So, for the same mass, the element with the smaller molar mass will have more moles and thus more atoms.

Step2: Find molar masses

Molar mass of magnesium (Mg) is \( 24.31 \, \text{g/mol} \). Molar mass of manganese (Mn) is \( 54.94 \, \text{g/mol} \).

Step3: Compare moles

For \( m = 15.0 \, \text{g} \), moles of Mg: \( n_{\text{Mg}} = \frac{15.0}{24.31} \approx 0.617 \, \text{mol} \). Moles of Mn: \( n_{\text{Mn}} = \frac{15.0}{54.94} \approx 0.273 \, \text{mol} \). Since \( 0.617 > 0.273 \), Mg has more moles, hence more atoms.

Answer:

Magnesium