How many helium atoms are there in a helium blimp containing 587 kg of helium?

검증된 단계별 안내

Convert the mass of helium from kilograms to grams by multiplying by 1000, since there are 1000 grams in a kilogram.

Determine the number of moles of helium by dividing the mass of helium in grams by the molar mass of helium (4.00 g/mol).

Use Avogadro's number (6.022 x 10^23 atoms/mol) to calculate the number of helium atoms by multiplying the number of moles of helium by Avogadro's number.

Ensure all units are consistent and cancel appropriately during calculations to maintain dimensional accuracy.

Review the steps to ensure each conversion and calculation aligns with the principles of stoichiometry and dimensional analysis.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For helium, the molar mass is approximately 4.00 g/mol. This concept is essential for converting between the mass of helium and the number of moles, which is necessary to determine the number of atoms.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms, ions, or molecules in one mole of a substance. This constant allows us to relate the amount of substance in moles to the actual number of particles, making it crucial for calculating the total number of helium atoms in the blimp.

Conversion from Mass to Moles

To find the number of atoms in a given mass of a substance, one must first convert the mass to moles using the formula: moles = mass (g) / molar mass (g/mol). This step is vital in the problem, as it establishes the foundation for using Avogadro's number to find the total number of atoms present in the helium blimp.