Question

What is the mass, in kilograms, of an Avogadro's number of people, if the average mass of a person is \(160 \mathrm{lb}\) ? How does this compare with the mass of Earth, \(5.98 \times 10^{24} \mathrm{~kg}\) ?

Short answer

The mass of an Avogadro's number of people, with an average mass of 160 lb converted to \(72.574378\ \mathrm{kg}\), is approximately \(4.367 \times 10^{25}\ \mathrm{kg}\). This is about 7.3 times the mass of Earth, which is \(5.98 \times 10^{24}\ \mathrm{kg}\).

Step-by-step solution

Convert 160 lb to kg

To convert pounds (lb) to kilograms (kg), we need to know that 1 lb is equal to approximately 0.453592 kg. Therefore, we can calculate the mass of a person in kilograms by multiplying: \(160\ \mathrm{lb} * 0.453592\ \mathrm{kg/lb} \approx 72.574378\ \mathrm{kg}\)

Find the mass of Avogadro's number of people in kg

Now that we have the average mass of a person in kilograms, we can multiply this by Avogadro's number (6.022 × 10²³) to find the total mass: \(72.574378\ \mathrm{kg} * (6.022 \times 10^{23}) = 4.367 \times 10^{25}\ \mathrm{kg}\)

Compare the mass with the mass of Earth

Now we need to compare this mass with the mass of Earth (5.98 × 10²⁴ kg). To do this, we can divide the mass of Avogadro's number of people by the mass of Earth to see how many times heavier it is: \(\frac{4.367 \times 10^{25}\ \mathrm{kg}}{5.98 \times 10^{24}\ \mathrm{kg}} \approx 7.30\) The mass of an Avogadro's number of people (using the average mass of 160 lb) is approximately 7.3 times the mass of Earth.