Silver oxide `(Ag_2O)` decomposes at temperature `300^@C` yielding matellic silver and oxygen gas. A `1.60g` sample of impure silver oxide yields `0.104g` of oxygen gas. What is the per cent by mass of the silver oxide in the sample ?

Options

A. `5.9`
B. `47.125`
C. `94.25`
D. `88.2`

Answer

To solve the problem of determining the percent by mass of silver oxide `(Ag_2O)` in a sample, we can follow these steps:

### Step 1: Write the decomposition reaction
The decomposition of silver oxide can be represented by the following balanced chemical equation:
\[ 2 \, Ag_2O \, \rightarrow \, 4 \, Ag \, + \, O_2 \]

### Step 2: Calculate the moles of oxygen produced
Given that the sample yields `0.104 g` of oxygen gas, we can calculate the moles of oxygen produced using the molar mass of oxygen (O₂), which is `32 g/mol`.
\[ \text{Moles of } O_2 = \frac{0.104 \, g}{32 \, g/mol} = 0.00325 \, mol \]

### Step 3: Relate moles of oxygen to moles of silver oxide
From the balanced equation, we see that `2 moles of Ag₂O` produce `1 mole of O₂`. Therefore, the moles of silver oxide that decomposed can be calculated as follows:
\[ \text{Moles of } Ag_2O = 2 \times \text{Moles of } O_2 = 2 \times 0.00325 \, mol = 0.0065 \, mol \]

### Step 4: Calculate the mass of silver oxide
Next, we need to find the mass of silver oxide that corresponds to the calculated moles. The molar mass of silver oxide `(Ag₂O)` is calculated as follows:
- Molar mass of Ag = 108 g/mol
- Molar mass of O = 16 g/mol
\[ \text{Molar mass of } Ag_2O = (2 \times 108) + 16 = 216 + 16 = 232 \, g/mol \]

Now, we can calculate the mass of silver oxide:
\[ \text{Mass of } Ag_2O = \text{Moles of } Ag_2O \times \text{Molar mass of } Ag_2O = 0.0065 \, mol \times 232 \, g/mol = 1.508 \, g \]

### Step 5: Calculate the percent by mass of silver oxide in the sample
Finally, we can calculate the percent by mass of silver oxide in the original sample:
\[ \text{Percent by mass of } Ag_2O = \left( \frac{\text{Mass of } Ag_2O}{\text{Mass of sample}} \right) \times 100 = \left( \frac{1.508 \, g}{1.60 \, g} \right) \times 100 = 94.25\% \]

### Final Answer
The percent by mass of silver oxide in the sample is **94.25%**.

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