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 is approximately $4.37\times {10}^{25}\mathrm{kg}$, which is about 7.31 times greater than the mass of Earth ($5.98\times {10}^{24}\mathrm{kg}$).

Step-by-step solution

(Step 1: Convert mass from pounds to kilograms)

To convert the mass of an average person from pounds to kilograms, we'll use the following conversion factor: 1 lb = 0.453592 kg. So, we have the mass of a person in kilograms: $160\mathrm{lb}\times \frac{0.453592\mathrm{kg}}{1\mathrm{lb}}\approx 72.57\mathrm{kg}$

(Step 2: Calculate the total mass of Avogadro's number of people)

Now that we know the mass of one person, we can find the mass of Avogadro's number ($N_A=6.022\times {10}^{23}$) of people by multiplying it by the mass of one person: Total mass $=N_A\times$ mass per person $=(6.022\times {10}^{23})\times 72.57\mathrm{kg}$

(Step 3: Calculate the total mass in standard form)

To make it easier to compare the total mass with the mass of Earth, we can express the total mass in standard form: Total mass $=(6.022\times {10}^{23})\times 72.57\mathrm{kg}=4.37\times {10}^{25}\mathrm{kg}$

(Step 4: Compare the total mass with the mass of Earth)

Finally, let's compare the total mass of Avogadro's number of people with the mass of Earth ($5.98\times {10}^{24}\mathrm{kg}$): The mass of an Avogadro's number of people is about $4.37\times {10}^{25}\mathrm{kg}$, and Earth's mass is $5.98\times {10}^{24}\mathrm{kg}$. To find how many times the mass of an Avogadro's number of people is greater than the mass of Earth, we can divide the total mass by the mass of Earth: $\frac{4.37\times {10}^{25}\mathrm{kg}}{5.98\times {10}^{24}\mathrm{kg}}\approx 7.31$ So, the mass of an Avogadro's number of people is about 7.31 times greater than the mass of Earth.