The molecular formula of the first member of alkyne family is `C_(2)H_(2)`. What is the formula of the fourth member ?

Answer

To find the molecular formula of the fourth member of the alkyne family, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the General Formula for Alkynes**:
The general formula for alkynes is given by:
\[ C_nH_{2n-2} \]
where \( n \) is the number of carbon atoms.

2. **Determine the Value of \( n \) for the First Member**:
The first member of the alkyne family is ethyne (C₂H₂). From this, we can see that:
\[ n = 2 \]

3. **Calculate the Value of \( n \) for the Fourth Member**:
Since we want to find the fourth member, we need to increase \( n \) by 1 for each subsequent member. Therefore, for the fourth member:
\[ n = 2 + 3 = 5 \]

4. **Substitute \( n \) into the General Formula**:
Now that we have \( n = 5 \), we can substitute this value into the general formula:
\[ C_nH_{2n-2} = C_5H_{2(5)-2} \]

5. **Calculate the Hydrogen Count**:
Now, calculate the number of hydrogen atoms:
\[ H = 2(5) - 2 = 10 - 2 = 8 \]

6. **Write the Molecular Formula of the Fourth Member**:
Therefore, the molecular formula for the fourth member of the alkyne family is:
\[ C_5H_8 \]

### Final Answer:
The formula of the fourth member of the alkyne family is \( C_5H_8 \).

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