The recommended daily dose is 17.6 milligrams of vitamin C (ascorbic acid) having formula `C_(6)H_(8)O_(6)`. Match the following. Given : `N_(A)=6 times 10^(23)`
`{:("Column I", "Column II"), ("(A) O-atoms present", "(P)" 10^(-4)" mole"), ("(B) Moles of vitamin C in 1 gm of vitamin C", "(Q)" 5.68 times 10^(-3)), ("(C) Moles of vitamin C that should be consumed daily","(R)" 3.6 times 10^(20)):}`

Options

A. `A rarr R, B rarr P, C rarr Q`
B. `A rarr P, B rarr Q, C rarr R`
C. `A rarr P, B rarr R, C rarr Q`
D. `A rarr R, B rarr Q, C rarr P`

Answer

To solve the problem, we need to determine the values for each of the items in Column I and match them with the corresponding values in Column II. Let's break it down step by step.

### Step 1: Calculate the Molar Mass of Vitamin C (C₆H₈O₆)

The molar mass of vitamin C can be calculated using the atomic masses of carbon (C), hydrogen (H), and oxygen (O):
- Carbon (C): 12 g/mol
- Hydrogen (H): 1 g/mol
- Oxygen (O): 16 g/mol

The molar mass of vitamin C is calculated as follows:
\[ \text{Molar mass of C}_6\text{H}_8\text{O}_6 = (6 \times 12) + (8 \times 1) + (6 \times 16) = 72 + 8 + 96 = 176 \text{ g/mol} \]

### Step 2: Calculate Moles of Vitamin C in 1 g

Using the molar mass, we can find the number of moles in 1 gram of vitamin C:
\[ \text{Moles of vitamin C in 1 g} = \frac{\text{mass}}{\text{molar mass}} = \frac{1 \text{ g}}{176 \text{ g/mol}} \approx 5.68 \times 10^{-3} \text{ moles} \]

### Step 3: Calculate Moles of Vitamin C that Should Be Consumed Daily

The recommended daily dose is 17.6 mg, which we convert to grams:
\[ 17.6 \text{ mg} = 0.0176 \text{ g} \]
Now, we can calculate the moles of vitamin C that should be consumed daily:
\[ \text{Moles of vitamin C daily} = \frac{0.0176 \text{ g}}{176 \text{ g/mol}} \approx 1 \times 10^{-4} \text{ moles} \]

### Step 4: Calculate the Number of Oxygen Atoms Present

Each molecule of vitamin C contains 6 oxygen atoms. Therefore, the number of moles of oxygen in the daily dose can be calculated as:
\[ \text{Moles of O-atoms} = 6 \times \text{Moles of vitamin C daily} = 6 \times 1 \times 10^{-4} \approx 6 \times 10^{-4} \text{ moles} \]

### Step 5: Calculate the Number of Oxygen Atoms in Molecules

To find the number of oxygen atoms in moles, we can use Avogadro's number:
\[ \text{Number of O-atoms} = \text{Moles of O-atoms} \times N_A = 6 \times 10^{-4} \text{ moles} \times 6.022 \times 10^{23} \approx 3.6 \times 10^{20} \text{ atoms} \]

### Final Matching

Now we can match the results with the options provided:

- (A) O-atoms present: **(P)** \(10^{-4}\) mole
- (B) Moles of vitamin C in 1 gm of vitamin C: **(Q)** \(5.68 \times 10^{-3}\)
- (C) Moles of vitamin C that should be consumed daily: **(R)** \(3.6 \times 10^{20}\)

### Summary of Matches
- (A) → (P)
- (B) → (Q)
- (C) → (R)