76 gram of a silver salt of dibasic acid on heating left a residue of 54gram silver. Silver salt contains Ag, C and O only and C and O in mole ratio of `1:2` then find the mass of `CO_(2)` gas liberated during ignition of 76gm silver salt, (Ag = 108)

Options

A. 22.4gm
B. 0.22gm
C. 44gm
D. 22gm

Answer

To solve the problem step-by-step, we need to find the mass of CO₂ gas liberated during the ignition of 76 grams of a silver salt of a dibasic acid. Here’s how we can approach it:

### Step 1: Determine the composition of the silver salt
We know that the silver salt contains silver (Ag), carbon (C), and oxygen (O) only, with the mole ratio of C to O being 1:2.

Let’s assume:
- The formula of the silver salt is Ag₂A, where A is the anion made of carbon and oxygen.

Given the ratio of C to O is 1:2, we can express this as:
- C = x
- O = 2x

### Step 2: Write the molecular formula of the silver salt
From the above, the molecular formula of the silver salt can be expressed as:
- Ag₂C₁O₂ (Ag₂C₁O₂₂ or Ag₂C₂O₄).

### Step 3: Use the conservation of silver
When the silver salt is heated, it decomposes to produce silver and carbon dioxide. The mass of silver produced is given as 54 grams.

Using the molar mass of silver (Ag = 108 g/mol):
- Moles of silver produced = mass of silver / molar mass of silver
- Moles of silver = 54 g / 108 g/mol = 0.5 moles

### Step 4: Calculate the moles of the silver salt
Now, we need to find the moles of the silver salt (Ag₂C₂O₄) in the initial 76 grams.

The molar mass of Ag₂C₂O₄ can be calculated as follows:
- Molar mass = (2 × 108) + (2 × 12) + (4 × 16)
- Molar mass = 216 + 24 + 64 = 304 g/mol

Now, we can find the moles of the silver salt:
- Moles of Ag₂C₂O₄ = mass / molar mass = 76 g / 304 g/mol = 0.25 moles

### Step 5: Relate moles of carbon to moles of CO₂
From the formula Ag₂C₂O₄, we see that each mole of Ag₂C₂O₄ contains 2 moles of carbon (C).

When ignited, each mole of carbon produces one mole of CO₂. Therefore:
- Moles of CO₂ produced = 2 × moles of Ag₂C₂O₄
- Moles of CO₂ = 2 × 0.25 = 0.5 moles

### Step 6: Calculate the mass of CO₂ produced
The molar mass of CO₂ is:
- Molar mass of CO₂ = 12 + (2 × 16) = 12 + 32 = 44 g/mol

Now, we can find the mass of CO₂ produced:
- Mass of CO₂ = moles × molar mass = 0.5 moles × 44 g/mol = 22 grams

### Final Answer
The mass of CO₂ gas liberated during the ignition of 76 grams of silver salt is **22 grams**.

---