Atoms of elements A, B and C combine to form a compound in the atomic ratio of `1 : 6 : 2`. Atomic masses of A, B and C are 64, 4 and 16 respectively. What will be the maximum mass of a compound formed from 1.28 g of A, `3xx10^(23)` atoms of B and 0.04 moles of C ?

Options

A. 12 g
B. 24 g
C. 2.4 g
D. 0.12 g

Explanation

To solve the problem step by step, we will determine the moles of each element (A, B, and C), check the limiting reactant based on the given atomic ratio, and then calculate the maximum mass of the compound formed.

### Step 1: Calculate the moles of each element

1. **Moles of A**:
- Given mass of A = 1.28 g
- Atomic mass of A = 64 g/mol
- Moles of A = mass / atomic mass = 1.28 g / 64 g/mol = 0.02 moles

2. **Moles of B**:
- Given number of atoms of B = \(3 \times 10^{23}\) atoms
- Avogadro's number (NA) = \(6.022 \times 10^{23}\) atoms/mol
- Moles of B = number of atoms / Avogadro's number = \(3 \times 10^{23}\) / \(6.022 \times 10^{23}\) = 0.5 moles

3. **Moles of C**:
- Given moles of C = 0.04 moles

### Step 2: Check the atomic ratio

The atomic ratio of A, B, and C is given as 1:6:2.

- From the moles calculated:
- Moles of A = 0.02
- Moles of B = 0.5
- Moles of C = 0.04

### Step 3: Determine the limiting reactant

1. **Required moles based on the ratio**:
- For A: 1 part = 0.02 moles
- For B: 6 parts = 6 * 0.02 = 0.12 moles
- For C: 2 parts = 2 * 0.02 = 0.04 moles

2. **Comparison with available moles**:
- Available moles of B = 0.5 (which is more than 0.12)
- Available moles of C = 0.04 (which matches the required amount)

Since A and C are in the correct ratio, and B has excess, the limiting reactant is A and C.

### Step 4: Calculate the mass of the compound formed

1. **Mass of A in the compound**:
- Mass of A = moles of A * atomic mass of A = 0.02 moles * 64 g/mol = 1.28 g

2. **Mass of B in the compound**:
- Mass of B = moles of B * atomic mass of B = 0.12 moles * 4 g/mol = 0.48 g

3. **Mass of C in the compound**:
- Mass of C = moles of C * atomic mass of C = 0.04 moles * 16 g/mol = 0.64 g

4. **Total mass of the compound**:
- Total mass = Mass of A + Mass of B + Mass of C
- Total mass = 1.28 g + 0.48 g + 0.64 g = 2.4 g

### Conclusion

The maximum mass of the compound formed is **2.4 g**.