Which of the following statements are correct?
(Given: At. wt. of Ca = 40 u, Mg = 24 u, N = 14 u, H = 1u, Na = 23 u, Cl = 35.5 u)
I. 240g of calcium and 240 g of magnesium elements have a molar ratio of 3 : 5.
II. 100 g of `N_(2)` contains more atoms than 100 g of `NH_(3)`.
III. Total number of ions in 5.85 g of sodium chloride is `1.2 xx 10^(22)`.
IV. 1 gram molecule of hydrogen gas contains `12.046 xx 10^(23)` atoms of hydrogen.
V. 5.6 g of nitrogen gas occupies 3.2 L of volume at STP.

Options

A. II and III only
B. I, II and III only
C. I and IV only
D. IV and V only

Answer

To determine which of the statements are correct, we will analyze each statement one by one.

### Step 1: Analyze Statement I
**Statement I:** 240g of calcium and 240g of magnesium elements have a molar ratio of 3:5.

1. **Calculate moles of Calcium (Ca):**
- Molar mass of Ca = 40 g/mol
- Moles of Ca = Mass / Molar Mass = 240 g / 40 g/mol = 6 moles

2. **Calculate moles of Magnesium (Mg):**
- Molar mass of Mg = 24 g/mol
- Moles of Mg = Mass / Molar Mass = 240 g / 24 g/mol = 10 moles

3. **Molar ratio of Ca to Mg:**
- Molar ratio = Moles of Ca : Moles of Mg = 6 : 10 = 3 : 5

**Conclusion for Statement I:** Correct.

### Step 2: Analyze Statement II
**Statement II:** 100 g of N₂ contains more atoms than 100 g of NH₃.

1. **Calculate moles of N₂:**
- Molar mass of N₂ = 28 g/mol (2 x 14 g/mol)
- Moles of N₂ = 100 g / 28 g/mol = 3.57 moles

2. **Calculate total atoms in N₂:**
- Total atoms = Moles x 2 (since each N₂ has 2 nitrogen atoms) = 3.57 moles x 2 = 7.14 moles of atoms

3. **Calculate moles of NH₃:**
- Molar mass of NH₃ = 17 g/mol (14 g/mol + 3 x 1 g/mol)
- Moles of NH₃ = 100 g / 17 g/mol = 5.88 moles

4. **Calculate total atoms in NH₃:**
- Total atoms = Moles x 4 (since each NH₃ has 4 atoms: 1 nitrogen + 3 hydrogen) = 5.88 moles x 4 = 23.52 moles of atoms

**Conclusion for Statement II:** 100 g of NH₃ contains more atoms than 100 g of N₂. Therefore, Statement II is incorrect.

### Step 3: Analyze Statement III
**Statement III:** Total number of ions in 5.85 g of sodium chloride is 1.2 x 10²².

1. **Calculate moles of NaCl:**
- Molar mass of NaCl = 58.5 g/mol (23 g/mol + 35.5 g/mol)
- Moles of NaCl = 5.85 g / 58.5 g/mol = 0.1 moles

2. **Calculate total ions in NaCl:**
- Each NaCl unit dissociates into 2 ions (Na⁺ and Cl⁻).
- Total ions = Moles x 2 = 0.1 moles x 2 = 0.2 moles of ions

3. **Convert moles of ions to number of ions:**
- Number of ions = 0.2 moles x Avogadro's number (6.02 x 10²³) = 1.204 x 10²³ ions.

**Conclusion for Statement III:** Correct.

### Step 4: Analyze Statement IV
**Statement IV:** 1 gram molecule of hydrogen gas contains 12.046 x 10²³ atoms of hydrogen.

1. **1 gram molecule of hydrogen gas (H₂) contains:**
- 1 mole of H₂ = 6.02 x 10²³ molecules.
- Each molecule of H₂ contains 2 atoms of H.
- Total atoms = 6.02 x 10²³ x 2 = 1.204 x 10²⁴ atoms.

**Conclusion for Statement IV:** Incorrect.

### Step 5: Analyze Statement V
**Statement V:** 5.6 g of nitrogen gas occupies 3.2 L of volume at STP.

1. **Calculate moles of N₂:**
- Molar mass of N₂ = 28 g/mol.
- Moles of N₂ = 5.6 g / 28 g/mol = 0.2 moles.

2. **Volume of gas at STP:**
- 1 mole of gas occupies 22.4 L at STP.
- Volume = Moles x 22.4 L = 0.2 moles x 22.4 L = 4.48 L.

**Conclusion for Statement V:** Incorrect.

### Final Conclusion
- **Correct Statements:** I and III.
- **Incorrect Statements:** II, IV, and V.