Select the correct statement(s) for `(NH_(4))_(3)PO_(4)`

Options

A. Ratio of number of oxygen atoms to number of hydrogen atoms is 1:3
B. Ratio of number of cations to number of anions is 3:1
C. Ratio of number of gm-atoms of nitrogen to gm-atoms of oxygen is 3:2
D. Total number of atoms in one mole of `(MH_(4))_(3)PO_(4)` is 20.

Answer

To solve the question regarding the compound ammonium phosphate, \((NH_4)_3PO_4\), we will analyze each statement provided.

### Step-by-Step Solution:

1. **Identify the number of atoms in ammonium phosphate**:
- The formula \((NH_4)_3PO_4\) indicates that there are:
- 3 ammonium ions, each containing 4 hydrogen atoms (total: \(3 \times 4 = 12\) hydrogen atoms).
- 1 phosphate ion, which contains 4 oxygen atoms.
- Therefore, in one molecule of ammonium phosphate, we have:
- Hydrogen (H): 12
- Oxygen (O): 4

2. **Calculate the ratio of oxygen to hydrogen**:
- The ratio of the number of oxygen atoms to the number of hydrogen atoms is:
\[ \text{Ratio} = \frac{\text{Number of O atoms}}{\text{Number of H atoms}} = \frac{4}{12} = \frac{1}{3} \]
- **Conclusion**: The first statement is correct.

3. **Determine the ratio of cations to anions**:
- In ammonium phosphate, the cation is ammonium \((NH_4^+)\) and the anion is phosphate \((PO_4^{3-})\).
- There are 3 ammonium cations for every 1 phosphate anion.
- Therefore, the ratio of cations to anions is:
\[ \text{Ratio} = \frac{3 \text{ (cations)}}{1 \text{ (anion)}} = 3:1 \]
- **Conclusion**: The second statement is also correct.

4. **Calculate the ratio of gram atoms of nitrogen to gram atoms of oxygen**:
- In \((NH_4)_3PO_4\):
- There are 3 nitrogen atoms (from 3 ammonium ions).
- There are 4 oxygen atoms (from the phosphate ion).
- The ratio of the number of gram atoms of nitrogen to the number of gram atoms of oxygen is:
\[ \text{Ratio} = \frac{3 \text{ (N atoms)}}{4 \text{ (O atoms)}} = \frac{3}{4} \]
- **Conclusion**: The third statement is incorrect (it claims a ratio of \(3:2\)).

5. **Calculate the total number of atoms in one mole of ammonium phosphate**:
- Each molecule of ammonium phosphate contains:
- 3 nitrogen (N) + 12 hydrogen (H) + 1 phosphorus (P) + 4 oxygen (O) = 20 atoms in total.
- Therefore, in one mole (which is \(6.022 \times 10^{23}\) molecules), the total number of atoms is:
\[ 20 \text{ (atoms per molecule)} \times 6.022 \times 10^{23} \text{ (molecules)} = 20N_a \]
- **Conclusion**: The fourth statement is incorrect (it claims a total of 20 atoms instead of \(20N_a\)).

### Final Answer:
The correct statements are:
- Statement A: Correct (Ratio of O to H is \(1:3\))
- Statement B: Correct (Ratio of cations to anions is \(3:1\))
- Statement C: Incorrect (Ratio of N to O is \(3:4\))
- Statement D: Incorrect (Total number of atoms is \(20N_a\))