Final answer:
The retention index (I) for the unknown compound in the given gas chromatography experiment is calculated to be 2358 using the Kovats Interpolation Method with the provided retention times for methane, octane, the unknown, and nonane.
Step-by-step explanation:
To determine the retention index (I) for an unknown compound using gas chromatography (GC) data, we apply the formula provided by the Interpolation Method of Kovats: Iunknown = 100 × [ (N – N0) + 100 × fr ].
Where: N = Number of carbon atoms in the longer alkane N0 = Number of carbon atoms in the shorter alkane fr = (tr(unknown) – tr(shorter alkane)) / (tr(longer alkane) – tr(shorter alkane))
Using the retention times given: Methane (1 carbon) = 1.6 minutes Octane (8 carbons) = 13 minutes Unknown = 14.4 minutes Nonane (9 carbons) = 19.2 minutes
Since octane and nonane bracket the unknown's retention time, we use them for N and N0:
N = 9 (nonane) N0 = 8 (octane) fr = (14.4 – 13) / (19.2 – 13) = 1.4 / 6.2 = 0.2258
Now we can calculate the retention index:
Iunknown = 100 × [ (9 – 8) + 100 × 0.2258 ] Iunknown = 100 × [1 + 22.58] Iunknown = 100 × 23.58 Iunknown = 2358