Calculate the number of C , O and Na atoms in 53 gm of `Na_(2)CO_(3)` ?

Explanation

To calculate the number of carbon (C), oxygen (O), and sodium (Na) atoms in 53 grams of sodium carbonate (Na₂CO₃), we will follow these steps:

### Step 1: Calculate the molar mass of Na₂CO₃
The molar mass of Na₂CO₃ can be calculated as follows:
- Sodium (Na): 23 g/mol × 2 = 46 g/mol
- Carbon (C): 12 g/mol × 1 = 12 g/mol
- Oxygen (O): 16 g/mol × 3 = 48 g/mol

Adding these together:
\[ \text{Molar mass of Na}_2\text{CO}_3 = 46 + 12 + 48 = 106 \text{ g/mol} \]

### Step 2: Calculate the number of moles of Na₂CO₃ in 53 grams
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Number of moles of Na}_2\text{CO}_3 = \frac{53 \text{ g}}{106 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Calculate the number of molecules of Na₂CO₃
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol):
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of molecules} = 0.5 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ \text{Number of molecules} \approx 3.011 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the number of carbon atoms
Each molecule of Na₂CO₃ contains 1 carbon atom. Therefore:
\[ \text{Number of carbon atoms} = \text{Number of molecules} \times 1 \]
\[ \text{Number of carbon atoms} = 3.011 \times 10^{23} \text{ atoms} \]

### Step 5: Calculate the number of oxygen atoms
Each molecule of Na₂CO₃ contains 3 oxygen atoms. Therefore:
\[ \text{Number of oxygen atoms} = \text{Number of molecules} \times 3 \]
\[ \text{Number of oxygen atoms} = 3.011 \times 10^{23} \text{ molecules} \times 3 \]
\[ \text{Number of oxygen atoms} = 9.033 \times 10^{23} \text{ atoms} \]

### Step 6: Calculate the number of sodium atoms
Each molecule of Na₂CO₃ contains 2 sodium atoms. Therefore:
\[ \text{Number of sodium atoms} = \text{Number of molecules} \times 2 \]
\[ \text{Number of sodium atoms} = 3.011 \times 10^{23} \text{ molecules} \times 2 \]
\[ \text{Number of sodium atoms} = 6.022 \times 10^{23} \text{ atoms} \]

### Final Results
- Number of Carbon (C) atoms: \(3.011 \times 10^{23}\)
- Number of Oxygen (O) atoms: \(9.033 \times 10^{23}\)
- Number of Sodium (Na) atoms: \(6.022 \times 10^{23}\)