Which of the following elements has the lowest density at 298 K and 101.3 kPa?

• A. Oxygen (O)
• B. Hydrogen (H)
• C. Nitrogen (N)
• D. Helium (He)

Answer: (B)

Verified step by step guidance

1. Recall that the density of a gas under given conditions can be found using the ideal gas law rearranged to density form: \(\rho = \frac{PM}{RT}\), where \(\rho\) is density, \(P\) is pressure, \(M\) is molar mass, \(R\) is the ideal gas constant, and \(T\) is temperature.
2. Note that the problem gives standard conditions: temperature \(T = 298\ \text{K}\) and pressure \(P = 101.3\ \text{kPa}\), so these values are constant for all gases considered.
3. Identify the molar masses (\(M\)) of each element in grams per mole: Hydrogen (H) approximately 2 g/mol for \(H_2\), Helium (He) about 4 g/mol, Nitrogen (N) about 28 g/mol for \(N_2\), and Oxygen (O) about 32 g/mol for \(O_2\).
4. Since \(P\), \(R\), and \(T\) are constant, the density \(\rho\) is directly proportional to the molar mass \(M\). Therefore, the gas with the lowest molar mass will have the lowest density under the same conditions.
5. Compare the molar masses and conclude that Hydrogen (\(H_2\)) has the lowest molar mass and thus the lowest density at 298 K and 101.3 kPa.