In chemistry, 'mole' is an essential tool for the chemical calculations. It is a basic SI unit adopted by the `14^(th)` general conference on weights and measurements in 1971. A mole contains as many elementary particles as the number of atoms present in 12 g of `""^(12)C` . 1 mole of a gas at STP occupies 22.4 litre volume. Molar volume of solids and liquids is not definite. Molar mass of a substance is also called gram-atomic mass or gram molecular mass. The virtual meaning of mole is plenty, heap or the collection of large numbers. 1 mole of a substance contains `6.022 xx 10^(23)` elementary particles like atom or molecule. Atomic mass unit (amu) is the unit of atomic mass, e.g., atomic mass of single carbon is 12 amu.
How many atoms are present in 49 g of `H_(2)SO_(4)?`

Options

A. `7xx6.022x10^(23)`
B. `5xx6.022xx10^(23)`
C. `6xx6.022xx^(23)`
D. `7xx3.01xx10^(23)`

Explanation

To find out how many atoms are present in 49 g of \( H_2SO_4 \), we can follow these steps:

### Step 1: Calculate the Molar Mass of \( H_2SO_4 \)
First, we need to determine the molar mass of sulfuric acid (\( H_2SO_4 \)). The molar mass is calculated by adding the atomic masses of all the atoms in the formula:

- Hydrogen (H): 1 g/mol (2 atoms) = \( 2 \times 1 = 2 \) g/mol
- Sulfur (S): 32 g/mol (1 atom) = \( 1 \times 32 = 32 \) g/mol
- Oxygen (O): 16 g/mol (4 atoms) = \( 4 \times 16 = 64 \) g/mol

Now, add them together:
\[ \text{Molar mass of } H_2SO_4 = 2 + 32 + 64 = 98 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of \( H_2SO_4 \)
Next, we calculate the number of moles in 49 g of \( H_2SO_4 \) using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{49 \text{ g}}{98 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Calculate the Total Number of Atoms in \( H_2SO_4 \)
Now, we need to find out how many atoms are in 0.5 moles of \( H_2SO_4 \). First, we determine how many atoms are present in one molecule of \( H_2SO_4 \):
- 2 Hydrogen atoms
- 1 Sulfur atom
- 4 Oxygen atoms

Total atoms in one molecule of \( H_2SO_4 \):
\[ 2 + 1 + 4 = 7 \text{ atoms} \]

### Step 4: Calculate the Total Number of Atoms in 0.5 Moles
Since 1 mole of any substance contains \( 6.022 \times 10^{23} \) molecules (Avogadro's number), we can find the total number of atoms in 0.5 moles:
\[ \text{Total atoms} = \text{Number of moles} \times \text{Avogadro's number} \times \text{Number of atoms per molecule} \]
Substituting the values:
\[ \text{Total atoms} = 0.5 \times 6.022 \times 10^{23} \times 7 \]
Calculating this gives:
\[ \text{Total atoms} = 0.5 \times 6.022 \times 10^{23} \times 7 = 21.067 \times 10^{23} \text{ atoms} \]

### Final Answer
Thus, the total number of atoms present in 49 g of \( H_2SO_4 \) is approximately:
\[ \text{Total atoms} \approx 2.11 \times 10^{24} \text{ atoms} \]

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