A compound (\( x \)) with molar mass \( 108 \, \text{g mol}^{-1} \) undergoes acetylation to give a product with molar mass \( 192 \, \text{g mol}^{-1} \). The number of amino groups in the compound (\( x \)) is ______.
Correct Answer: 2
Approach Solution - 1
To find the number of amino groups in the compound (\( x \)), we need to understand the change in molar mass due to acetylation. Acetylation involves replacing an amino hydrogen atom with an acetyl group (\( \text{CH}_3\text{CO} \)), which adds \( 42 \, \text{g mol}^{-1} \) to the molar mass per amino group modified.
1. Compute the difference in molar mass between the acetylated product and the original compound: \( 192 \, \text{g mol}^{-1} - 108 \, \text{g mol}^{-1} = 84 \, \text{g mol}^{-1} \).
2. Since each acetyl group increases the molar mass by \( 42 \, \text{g mol}^{-1} \), determine the number of acetyl groups added: \( \frac{84 \, \text{g mol}^{-1}}{42 \, \text{g mol}^{-1}} = 2 \) amino groups.
This computed value of 2 fits within the expected range of 2,2, confirming the solution is correct.
Approach Solution -2
Each \(\text{NH}_2\) group increases molecular weight by 42 upon acetylation:
\[ 192 - 108 = 84 \] \[ \frac{84}{42} = 2 \]Thus, the compound \(x\) has:
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