Two gases `A` and `B` which react according to the equation
`aA_((g)) +bB_((g)) rarr cC_((g)) +dD_((g))`
to give two gases `C` and `D` are taken (amount not known) in an Eudiometer tube (operating at a constant Pressur and temperature) to cause the above.
If one causing the reaction there is no volume change observed then which of the following statement is/are correct.

Options

A. `(a+b)=(c+d)`
B. average molecular mass may increase or decrease if either of `A` or `B` is present in limited amount.
C. Vapour Density of the mixture will remain same throughout the course of reaction.
D. Total moles of all the component of mixture will change.

Answer

To solve the problem, we need to analyze the reaction of gases A and B producing gases C and D, and the implications of no volume change during the reaction.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction is given as:
\[ aA_{(g)} + bB_{(g)} \rightarrow cC_{(g)} + dD_{(g)} \]
Here, \(a\), \(b\), \(c\), and \(d\) are the stoichiometric coefficients for gases A, B, C, and D respectively.

2. **Volume Change Observation**:
The problem states that there is no volume change observed when the reaction occurs. This means that the total volume of gases before the reaction is equal to the total volume of gases after the reaction.

3. **Applying the Ideal Gas Law**:
According to the ideal gas law, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. Therefore, if there is no volume change, we can equate the total number of moles of reactants to the total number of moles of products:
\[ a + b = c + d \]

4. **Conclusion about the Statements**:
- **Statement 1**: Since \(a + b = c + d\), this statement is correct.
- **Statement 3**: The vapor density of gases is dependent on their volume. Since there is no volume change, the vapor density remains the same. Thus, this statement is also correct.

5. **Final Answer**:
Therefore, both Statement 1 and Statement 3 are correct.