In the reaction `N_(2)+3H_(2) to 2NH_(3)`, the volume ratio of the gases as 1: 3: 2 was

Options

A. Boyle
B. Gay-Lussac's law
C. Avogadro
D. Charles

Answer

To solve the question regarding the reaction \( N_2 + 3H_2 \rightarrow 2NH_3 \) and the volume ratio of the gases being 1:3:2, we need to analyze the relationship between the volumes of gases involved in this reaction.

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction given is:
\[ N_2 + 3H_2 \rightarrow 2NH_3 \]
This is known as Haber’s process for the synthesis of ammonia.

2. **Understand Volume Ratios**:
According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules. Therefore, the volume ratio of gases in a reaction is directly proportional to the mole ratio of the gases.

3. **Determine the Mole Ratio**:
From the balanced equation:
- 1 mole of \( N_2 \)
- 3 moles of \( H_2 \)
- 2 moles of \( NH_3 \)

This gives us a mole ratio of:
\[ N_2 : H_2 : NH_3 = 1 : 3 : 2 \]

4. **Relate Volume Ratio to Mole Ratio**:
Since the volume ratio of the gases is also given as 1:3:2, we can conclude that:
\[ \text{Volume ratio} = N_2 : H_2 : NH_3 = 1 : 3 : 2 \]
This confirms that the volume ratio matches the mole ratio.

5. **Identify the Relevant Gas Law**:
The relationship that connects the volume of gases to the number of moles is described by Avogadro's law, which states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas.

6. **Conclusion**:
Therefore, the volume ratio of the gases in the reaction \( N_2 + 3H_2 \rightarrow 2NH_3 \) is expressed by Avogadro's law.

### Final Answer:
The volume ratio of the gases \( N_2 : H_2 : NH_3 \) is expressed by **Avogadro's Law**.