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What is a Kaval’s retention index in gas chromatography and how do you calculate it?

Answer
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Hint: Kauats retention index is used to convert retention times into independent constant. The retention index of a chemical compound is retention time interpolated between adjacent alkanes. While retention times vary with the individual chromatographic system. Kovats indexes of the compounds may be conserved if proper method translation is applied.

Complete step by step answer:
Kovati’s retention index is named after the chemist Ervin kovato who outlined this concept during the $1950$ while performing research into the composition of the essential oils.
The retention index of a chemical compound is retention time interpolated between adjacent $n-$ alkanes. While retention times very with the individual chromatographic system, the derived retentions indies are quite independent of these parameters and allow comparing values measured by different analytical laboratories under varying condition and analysis times from second to hours.
It depends on the fact the $\log t\propto n$ where $t$ is the retention time and $n$ is the number of carbon atoms in the alkane for an isothermal chromatogram you see the following equation to calculate the kavati’s index.
$I=100\times \left[ n\times \dfrac{\log {{t}_{x}}-\log {{t}_{n}}}{\log {{t}_{n-1}}-\log {{t}_{n}}} \right]$
Where $n$ is the number of carbon atoms in the $n-$ alkanes and $t$ is the retention time.
Compounds elute in the carrier gas phase only. Compounds solved in the stationary phase stay put. The ratio of gas to and residence time ${{t}_{i}}-$ to. In stationary liquid. Polymer phase is called the capacity factor.
${{K}_{i}}=\dfrac{{{t}_{i}}-{{t}_{o}}}{{{t}_{o}}}=\dfrac{RTSi}{{{P}^{o}}}$
$\beta =\dfrac{{{V}_{i}}}{{{V}_{G}}}=\dfrac{4dt}{dc}$
Where,
$R-$ gas constant
$T-$ temperature
${{S}_{p}}-$ Solubility of compound
${{P}^{i}}-$ vapour pressure.

Additional Information:
Gas chromatography is a common type of chromatography used is analytical chemistry for separating and analyzing compounds that can be vaporized without decomposition. In gas chromatography, the mobile phase is a carrier gas, usually an insert gas such as helium and an unreactive gas such as nitrogen. Gas chromatography is in principle. Similar to column chromatography forms of chromatography, such as high performance liquid chromatography but has several notable differences. Gas chromatography is also sometimes known as vapor phase chromatography is also sometimes known as vapor difference. Gas chromatography is also sometimes known as vapor phase chromatography or gas liquid partition chromatography. A gas chromatography is a chemical instrument for separating chemicals in a complex sample. A gas chromatograph used a flow through a narrow tube known as the “Column” through which different chemicals consistent of a gas stream at different rates depending on their chemical and physical properties and their interaction with a specific column filling the stationary phase.

Note: Gas chromatography is used extensively in forensic science. Factor GC methods have shorter times but Kovats indexes of the compounds may be conserved if proper method translation is applied. Temperature of the temperature program stay the same, but ramps and times change when using a similar column dimensions length $x$ diameter film are divided by $2$ and gas velocity is doubled by using ${{\text{H}}_{\text{2}}}$ is place of $\text{He}$ the hold times must be divided by four and the ramps must be multiplied by four to keep the same index and the same retention temperature for the same compound analyzed. Method translation rules are incorporated in some chromatography data systems.