Problem 31 - Chemistry: The Central Science

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

Step-by-Step Solution

Answer

The mass of an Avogadro's number of people, with an average mass of \(72.57472 kg\), is approximately \(4.3673 \times 10^{25} kg\). This mass is about 7.3 times the mass of Earth, which is \(5.98 \times 10^{24} kg\).

Step 1: Convert mass unit from lbs to kg

To convert the average mass of a person from lbs to kg, we will use the following conversion factor: 1lb = 0.453592 kg So, the average mass of a person in kg is: \(160 lb \times 0.453592 \frac{kg}{lb} = 72.57472 kg\)

Step 2: Compute the mass of an Avogadro's number of people

Now we will multiply the average mass of one person in kg by Avogadro's number to find the mass of Avogadro's number of people. Avogadro's number, N_A, is approximately \(6.022 \times 10^{23}\). Total mass of an Avogadro's number of people (M_p) is: \(M_p = 72.57472 kg \times (6.022 \times 10^{23})\)

Step 3: Calculate the mass of Avogadro's number of people

Now, calculate the mass, \(M_p\): \(M_p = 72.57472 kg \times (6.022 \times 10^{23}) = 4.3673 \times 10^{25} kg\)

Step 4: Compare with Earth's mass

The mass of Earth (M_e) is given as \(5.98 \times 10^{24} kg\). To compare the mass of an Avogadro's number of people with the mass of Earth, we can divide the mass of people by the mass of Earth: \(\frac{M_p}{M_e} = \frac{4.3673 \times 10^{25} kg}{5.98 \times 10^{24} kg} = 7.3\) So, the mass of an Avogadro's number of people is approximately 7.3 times the mass of Earth.