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, \(5.98 \times 10^{24} \mathrm{~kg}\) ?

To convert the mass of one person from pounds to kilograms, we will use the conversion factor that 1 pound is equivalent to 0.453592 kg. So, \(1 \mathrm{lb} = 0.453592 \mathrm{kg}\) Now, we will convert the given average mass of a person (160 lb) into kilograms by multiplying it by the conversion factor: \(160 \mathrm{lb} * 0.453592 \frac{\mathrm{kg}}{\mathrm{lb}}\)

To calculate the mass of Avogadro's number of people, we need to multiply the mass of one person (in kilograms) by Avogadro's number (6.022 x 10^23). The mass of one person (in kg) is: \(160 \mathrm{lb} * 0.453592 \frac{\mathrm{kg}}{\mathrm{lb}} = 72.57472 \mathrm{kg}\) Now, multiply this mass by Avogadro's number: \(72.57472 \mathrm{kg}\ * 6.022\times10^{23}\)

Now we will compare the mass of Avogadro's number of people obtained in Step 2 with the mass of Earth (5.98 x 10^24 kg). First, calculate the mass of Avogadro's number of people: \(72.57472 \mathrm{kg}\ * 6.022\times10^{23} = 4.367 \times 10^{25} \mathrm{kg}\) Now, compare this mass to the mass of Earth: \(\frac{4.367 \times 10^{25} \mathrm{kg}}{5.98 \times 10^{24} \mathrm{kg}}\) Finally, we have the mass of Avogadro's number of people and how it compares to the mass of Earth. To complete the solution, let's perform these calculations: Mass of one person in kg: \(160 \mathrm{lb} * 0.453592 \frac{\mathrm{kg}}{\mathrm{lb}} = 72.57472 \mathrm{kg}\) Mass of Avogadro's number of people: \(72.57472 \mathrm{kg}\ * 6.022\times10^{23} = 4.367 \times 10^{25} \mathrm{kg}\) Comparison of the masses: \(\frac{4.367 \times 10^{25} \mathrm{kg}}{5.98 \times 10^{24} \mathrm{kg}} = 7.3\) So, the mass of Avogadro's number of people is \(4.367 \times 10^{25}\) kilograms, which is approximately 7.3 times the mass of Earth.