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 calculate the number of moles of each element (A, B, and C) based on the given data, and then determine the maximum mass of the compound formed.

### Step 1: Calculate the number of moles of element A
Given:
- Mass of A = 1.28 g
- Atomic mass of A = 64 g/mol

Using the formula for number of moles:
\[ \text{Number of moles of A} = \frac{\text{Mass of A}}{\text{Atomic mass of A}} = \frac{1.28 \, \text{g}}{64 \, \text{g/mol}} = 0.02 \, \text{moles} \]

### Step 2: Calculate the number of moles of element B
Given:
- Number of atoms of B = \(3 \times 10^{23}\)
- 1 mole contains \(6.02 \times 10^{23}\) atoms (Avogadro's number)

Using the formula for number of moles:
\[ \text{Number of moles of B} = \frac{\text{Number of atoms of B}}{6.02 \times 10^{23}} = \frac{3 \times 10^{23}}{6.02 \times 10^{23}} \approx 0.5 \, \text{moles} \]

### Step 3: Calculate the number of moles of element C
Given:
- Moles of C = 0.04 moles

### Step 4: Verify the atomic ratio
The atomic ratio of A : B : C is given as 1 : 6 : 2. We need to check if the calculated moles fit this ratio.

- Ratio of A to C:
\[ \text{Ratio of A to C} = \frac{0.02}{0.04} = 0.5 \quad \text{(which is } 1 : 2\text{)} \]

- Ratio of A to B:
To maintain the ratio of 1 : 6, we need to find the required moles of B:
\[ \text{Required moles of B} = 0.02 \times 6 = 0.12 \, \text{moles} \]

### Step 5: Determine the limiting reactant
We have:
- Moles of A = 0.02
- Moles of B = 0.5 (available)
- Moles of C = 0.04

Since we need 0.12 moles of B to react with 0.02 moles of A, and we have 0.5 moles of B available, A is the limiting reactant.

### Step 6: Calculate the maximum mass of the compound formed
Using the formula for mass:
\[ \text{Mass} = \text{Number of moles} \times \text{Atomic mass} \]
The total mass of the compound formed will be the sum of the masses of A, B, and C used in the reaction.

- Mass of A:
\[ \text{Mass of A} = 0.02 \, \text{moles} \times 64 \, \text{g/mol} = 1.28 \, \text{g} \]

- Mass of B:
\[ \text{Mass of B} = 0.12 \, \text{moles} \times 4 \, \text{g/mol} = 0.48 \, \text{g} \]

- Mass of C:
\[ \text{Mass of C} = 0.02 \, \text{moles} \times 16 \, \text{g/mol} = 0.32 \, \text{g} \]

### Step 7: Total mass of the compound
Now, we add the masses:
\[ \text{Total mass} = \text{Mass of A} + \text{Mass of B} + \text{Mass of C} = 1.28 \, \text{g} + 0.48 \, \text{g} + 0.32 \, \text{g} = 2.08 \, \text{g} \]

### Final Answer
The maximum mass of the compound formed is **2.08 grams**.

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