How many helium atoms are there in a helium blimp containing 536 kg of helium?

검증된 단계별 안내

Step 1: Convert the mass of helium from kilograms to grams. Remember that 1 kg is equal to 1000 g. So, multiply 536 kg by 1000 to get the mass in grams.

Step 2: Use the molar mass of helium to convert the mass in grams to moles. The molar mass of helium is approximately 4 g/mol. To do this, divide the mass in grams by the molar mass of helium.

Step 3: Use Avogadro's number to convert the number of moles to the number of atoms. Avogadro's number is approximately \(6.022 \times 10^{23}\) atoms/mol. Multiply the number of moles by Avogadro's number to get the number of atoms.

Step 4: The result from step 3 is the number of helium atoms in the blimp. Remember that this is a very large number because atoms are extremely small.

Step 5: Always remember to check your units at each step to ensure they cancel out appropriately, leaving you with the desired unit (in this case, atoms).

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주요 개념

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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 value is crucial for converting between the mass of helium and the number of moles, which is necessary for determining 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 essential 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). Once the number of moles is determined, it can be multiplied by Avogadro's number to find the total number of atoms present in the sample.