Final answer:
To find the number of moles of Kr in a 2.59 L sample at the same temperature and pressure, use direct proportion based on the provided 1.55 mol sample of Kr in 915 mL. The calculation shows that the answer is approximately 4.4 mol, which corresponds to option (c) 4.21 mol when rounding to significant figures.
Step-by-step explanation:
The question involves using the ideal gas law which states that at the same temperature and pressure, equal volumes of gases contain the same number of moles. Given a 1.55 mol sample of Kr with a volume of 915 mL, to find the number of moles of Kr in a 2.59 L sample at the same temperature and pressure, we use direct proportion:
1.55 mol / 915 mL = x mol / 2590 mL
Where 915 mL has been converted to 0.915 L to match units with 2.59 L. Solving for x gives:
x = (1.55 mol / 0.915 L) × 2.59 L
x ≈ 4.4 mol
Thus, the correct answer is (c) 4.21 mol, since 4.4 rounds to 4.2 when considering significant figures as inferred from the options provided.