Question

Among $ 10^{-10} $ g (each) of the following elements, which one will have the highest number of atoms? 
Element : Pb, Po, Pr and Pt

• A. Po
• B. Pr
• C. Pb
• D. Pt

Hint:

The number of atoms in a given mass is inversely proportional to the molar mass of the element.

Answer 1

The Correct Option is B

To identify the element with the highest atom count for a mass of \(10^{-10}\) grams, we utilize the concept of moles and Avogadro's number. The number of atoms is directly proportional to the number of moles, so we will calculate the moles for each element.

The molar quantity is calculated using the formula:

\(n = \frac{m}{M}\)

Where:

• \(n\) represents the molar quantity in moles
• \(m\) is the mass of the element in grams (\(10^{-10}\) g in this case)
• \(M\) is the molar mass of the element in grams per mole

The molar quantities for each element are calculated as follows:

1. Lead (Pb): Molar mass = 207 g/mol
2. Polonium (Po): Molar mass = 209 g/mol
3. Praseodymium (Pr): Molar mass = 140 g/mol
4. Platinum (Pt): Molar mass = 195 g/mol

The calculated moles for each element are:

• \(n_{\text{Pb}} = \frac{10^{-10}}{207}\) moles
• \(n_{\text{Po}} = \frac{10^{-10}}{209}\) moles
• \(n_{\text{Pr}} = \frac{10^{-10}}{140}\) moles
• \(n_{\text{Pt}} = \frac{10^{-10}}{195}\) moles

To determine the greatest number of moles, we observe the denominators:

• For a constant mass, the element with the smallest molar mass (denominator) will yield the largest number of moles.
• Pr (Praseodymium) has the lowest molar mass. Therefore, it possesses the highest number of moles and consequently the highest number of atoms.

Conclusion: For a mass of \(10^{-10}\) grams, Praseodymium (Pr) has the greatest number of atoms.