The mass of a silver coin is 10.0 g. A person can carry a load of 40 kg. How many persons will be required to carry one Avogadro number of such coins?

Answer

To solve the problem of how many persons are required to carry one Avogadro number of silver coins, we can follow these steps:

### Step 1: Identify the mass of one silver coin and Avogadro's number.
- The mass of one silver coin is given as 10.0 g.
- Avogadro's number is \(6.022 \times 10^{23}\) coins.

### Step 2: Calculate the total mass of one Avogadro number of silver coins.
To find the total mass of \(6.022 \times 10^{23}\) coins, we multiply the mass of one coin by Avogadro's number:
\[ \text{Total mass} = \text{mass of one coin} \times \text{Avogadro's number} \]
\[ \text{Total mass} = 10.0 \, \text{g} \times 6.022 \times 10^{23} = 6.022 \times 10^{24} \, \text{g} \]

### Step 3: Convert the total mass from grams to kilograms.
Since 1 kg = 1000 g, we convert the total mass to kilograms:
\[ \text{Total mass in kg} = \frac{6.022 \times 10^{24} \, \text{g}}{1000} = 6.022 \times 10^{21} \, \text{kg} \]

### Step 4: Determine how many coins one person can carry.
Given that one person can carry a load of 40 kg, we need to find out how many coins this corresponds to:
\[ \text{Number of coins per person} = \frac{\text{Load capacity per person}}{\text{mass of one coin}} = \frac{40 \, \text{kg}}{10.0 \, \text{g}} = \frac{40,000 \, \text{g}}{10.0 \, \text{g}} = 4000 \, \text{coins} \]

### Step 5: Calculate the number of persons required.
To find the number of persons required to carry one Avogadro number of coins, we divide the total number of coins by the number of coins one person can carry:
\[ \text{Number of persons} = \frac{\text{Total number of coins}}{\text{Number of coins per person}} = \frac{6.022 \times 10^{23}}{4000} \]
\[ \text{Number of persons} = 1.5055 \times 10^{20} \]

### Final Answer:
Approximately \(1.506 \times 10^{20}\) persons are required to carry one Avogadro number of silver coins.

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