The percentage of nitrogen by mass in ammonium sulphate is closest to (atomic masses H=1 , N= 14, O=16,S = 32 )

Options

A. 0.21
B. 0.24
C. 0.36
D. 0.16

Explanation

To find the percentage of nitrogen by mass in ammonium sulfate \((NH_4)_2SO_4\), we can follow these steps:

### Step 1: Determine the molecular formula of ammonium sulfate
The molecular formula of ammonium sulfate is \((NH_4)_2SO_4\).

### Step 2: Calculate the total mass of nitrogen in ammonium sulfate
In the formula \((NH_4)_2SO_4\), there are 2 nitrogen atoms. The atomic mass of nitrogen (N) is given as 14 g/mol. Therefore, the total mass of nitrogen in ammonium sulfate is:
\[ \text{Mass of Nitrogen} = 2 \times 14 = 28 \text{ g/mol} \]

### Step 3: Calculate the total mass of ammonium sulfate
Next, we need to calculate the total molar mass of ammonium sulfate. The components are:
- 2 Nitrogen (N): \(2 \times 14 = 28 \text{ g/mol}\)
- 8 Hydrogen (H) (from \(NH_4\)): \(8 \times 1 = 8 \text{ g/mol}\)
- 1 Sulfur (S): \(1 \times 32 = 32 \text{ g/mol}\)
- 4 Oxygen (O): \(4 \times 16 = 64 \text{ g/mol}\)

Now, adding these together gives:
\[ \text{Total mass of } (NH_4)_2SO_4 = 28 + 8 + 32 + 64 = 132 \text{ g/mol} \]

### Step 4: Calculate the percentage of nitrogen by mass
Now, we can find the percentage of nitrogen by mass in ammonium sulfate using the formula:
\[ \text{Percentage of Nitrogen} = \left(\frac{\text{Mass of Nitrogen}}{\text{Total Mass of } (NH_4)_2SO_4}\right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage of Nitrogen} = \left(\frac{28}{132}\right) \times 100 \approx 21.21\% \]

### Final Answer
The percentage of nitrogen by mass in ammonium sulfate is approximately **21.21%**.

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