A person has as many notes as number of oxygen atoms in 24.8 g `Na_(2)S_(2)O_(3).5H_(2)O` (mol. Wt. = 248). A note counting machine counts 48 million notes per day. How many days it would take to count these notes?

Options

A. `10^(12)`
B. `10^(14)`
C. `10^(16)`
D. `10^(18)`

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Calculate the number of moles of `Na2S2O3.5H2O`
Given:
- Mass of `Na2S2O3.5H2O` = 24.8 g
- Molar mass of `Na2S2O3.5H2O` = 248 g/mol

Using the formula for moles:
\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{24.8 \, \text{g}}{248 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 2: Determine the number of oxygen atoms in the compound
In one mole of `Na2S2O3.5H2O`, the number of oxygen atoms is calculated as follows:
- From `Na2S2O3`, there are 3 oxygen atoms.
- From `5H2O`, there are \(5 \times 1 = 5\) oxygen atoms.

Total oxygen atoms per mole = \(3 + 5 = 8\) oxygen atoms.

Now, for 0.1 moles:
\[ \text{Total oxygen atoms} = 8 \times 0.1 = 0.8 \, \text{moles of oxygen atoms} \]

### Step 3: Convert moles of oxygen atoms to number of atoms
Using Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol):
\[ \text{Number of oxygen atoms} = 0.8 \times 6.022 \times 10^{23} \approx 4.816 \times 10^{23} \, \text{atoms} \]

### Step 4: Calculate the number of days to count the notes
Given that the note counting machine counts 48 million notes per day:
\[ \text{Notes counted per day} = 48 \times 10^6 \]

To find the number of days required to count \(4.816 \times 10^{23}\) notes:
\[ \text{Days} = \frac{\text{Total notes}}{\text{Notes per day}} = \frac{4.816 \times 10^{23}}{48 \times 10^6} \]

Calculating this gives:
\[ \text{Days} = \frac{4.816 \times 10^{23}}{4.8 \times 10^7} \approx 1.0033 \times 10^{16} \, \text{days} \]

### Final Answer
It would take approximately \(1.0033 \times 10^{16}\) days to count the notes.

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