Exercises — Chromatography — TLC, column, GC, HPLC (principles)

• Stationary phase = plate par silica gel layer. Yeh fixed rehti hai; yeh molecules ko pakadti hai.
• Mobile phase = solvent jo plate par capillary action se chadhta hai. Poori separation in dono ke beech ek tug-of-war hai — mobile phase ke bina kuch bhi move nahi karta.

$K=C_s/C_m$ "kitna atka hua hai" aur "kitna saath chal raha hai" ka ratio hai. $K_Q=8>K_P=2$, isliye Q stationary phase par zyada time spend karta hai. Q zyada se chipkta hai.

$R_f=\frac{\text{distance moved by spot}}{\text{distance moved by solvent front}}$ apply karo. $R_f(X)=\frac{7.5}{10.0}=0.75,R_f(Y)=\frac{3.0}{10.0}=0.30$ Normal-phase (polar silica) par, polar zyada chipakta hai → kam travel karta hai → chhota $R_f$. Y ka $R_f$ chhota hai, isliye Y zyada polar hai. Figure dekho: Y (pink) neeche lag raha hai, X (blue) aage bhaag raha hai. Yeh Polarity and Intermolecular Forces par depend karta hai.

$v_{\text{analyte}}=\frac{v_{\text{mobile}}}{1+k}$ use karo. $v_{\text{analyte}}=\frac{2.0}{1+3}=\frac{2.0}{4}=0.50\text{ mm/s}$ Physically samjho: $k=3$ ke saath molecule har ek unit riding ke liye teen units time atka rehta hai, isliye solvent speed ka ek-chauthai speed se travel karta hai. Hopping picture se match karta hai.

$k=K\frac{V_s}{V_m}$ sirf $K$ ko har phase ki physical amounts se rescale karta hai. $k=12\times \frac{0.5}{2.0}=12\times 0.25=3.0$ Toh chahe $K=12$ ho (stationary phase se pyaar karta hai), aas paas itna kam stationary phase hai ki effective clinginess sirf $k=3$ hai.

Chhota $k$ ⇒ bada $v_{\text{analyte}}=v_{\text{mobile}}/(1+k)$ ⇒ pehle exit karta hai. "Slowdown factor" $1+k$ compute karo: A deta hai $2$, B deta hai $5$, C deta hai $1.5$. Speeds $\propto 1/(1+k)$ hain, isliye fastest→slowest ka order sabse chhote $1+k$ se hai: C ($1.5$) phir A ($2$) phir B ($5$). $\boxed{\text{Elution order: }C,A,B}$

Har molecule randomly stuck aur moving ke beech hop karta hai. Do identical molecules bilkul same instants par hop nahi karte — ek thoda zyada cling kar sakta hai, doosra thoda zyada ride kar sakta hai, purely by chance. Average speed same hoti hai ($v_{\text{mobile}}/(1+k)$), lekin us average ke aas paas spread us distance ke saath badhti hai jo travel ki gayi hai, jaise ek random walk. Toh ek band jo ek tight dot se shuru hoti hai woh ek Gaussian-ish smear mein spread ho jaati hai — jitna lamba path, utni wide aur zyada dilute. Isliye hum ek column ko hamesha ke liye nahi run karte: resolution bands ke centres ke separation ke saath improve hoti hai lekin degrade hoti hai jab har band moti hoti jaati hai.

"Like sticks to like." Ab stationary phase non-polar hai, isliye non-polar molecules (oil) isse chipakti hain aur lag jaati hain; polar molecules (sugar) polar mobile phase prefer karti hain aur baahar nikal jaati hain. ⇒ Polar sugar pehle elute hoti hai, non-polar oil baad mein. Yeh normal-phase TLC rule ko ulta kar deta hai (jahan polar = slow) kyunki humne swap kar diya ki kaunsa phase polar hai. "Polar zyada chipakta hai" ka rule kabhi universal nahi tha — iska matlab hamesha tha "us phase se chipakta hai jo uski polarity se match karta hai." Related: UV-Vis Spectroscopy in bands ko padhne wala usual HPLC detector hai.

Baseline ke paas spots ka matlab hai ki dono compounds polar silica se strongly chipke hue hain — mobile phase itni weak hai ki unhe pull off nahi kar sakti. Solvent ko zyada polar banao. Zyada polar mobile phase silica ke saath analytes ke sticky sites ke liye compete karti hai (woh bhi unse hydrogen-bond / dipole-interact kar sakti hai), isliye molecules zyada time riding mein spend karti hain ⇒ effective $k$ kam ⇒ bada $R_f$. Spots baseline se oopar $0.2$–$0.8$ ke useful window mein aa jaate hain jahan unke chhote $K$ differences unhe alag kar sakte hain. (Rule of thumb: normal phase par $R_f$ badhane ke liye mobile-phase polarity badhao.)

Deciding question hamesha yeh hota hai: kya sample bina decompose hue vaporise ho sakta hai?

• (a) → GC. Light hydrocarbons volatile aur stable hain, isliye woh cleanly evaporate karte hain aur gas ki tarah travel karte hain — fast diffusion sharp peaks aur excellent resolution deta hai.
• (b) → HPLC. Proteins non-volatile aur heat-sensitive hain; heating unhe vaporise hone se pehle char/denature kar deti hai. HPLC unhe room temperature par liquid mein dissolved rakhti hai. Identity baad mein Mass Spectrometry se confirm karo. Yeh ek core purification decision hai.

(a) $k=K{V}_s/V_m$ with $V_s/V_m=1.0/4.0=0.25$: $k_P=8\times 0.25=2.0,k_Q=20\times 0.25=5.0$ (b) $v=v_{\text{mobile}}/(1+k)$: $v_P=\frac{5.0}{1+2.0}=\frac{5.0}{3.0}=1.667\text{ mm/s}$ $v_Q=\frac{5.0}{1+5.0}=\frac{5.0}{6.0}=0.833\text{ mm/s}$ (c) time $=L/v$ with $L=100\text{ mm}$: $t_P=\frac{100}{1.667}=60.0\text{ s},t_Q=\frac{100}{0.833}=120.0\text{ s}$ (d) Time gap $=t_Q-t_P=120.0-60.0=\boxed{60.0\text{ s}}$. P (chhota $K$, chhota $k$) pehle $60$ s par elute hota hai; Q do baar utna chipakta hai aur poora ek minute baad aata hai — cleanly separated.

Equal $K$ ke saath: $k=12\times 0.25=3.0$ dono ke liye. $v=\frac{5.0}{1+3.0}=1.25\text{ mm/s}(\text{same for both})$ $t=\frac{100}{1.25}=80.0\text{ s}(\text{same for both})$ Dono peaks $80$ s par aati hain — woh ek hi peak mein overlap ho jaati hain; koi separation nahi hoti. Lesson: chromatography tab sirf separate karta hai jab compounds ke alag $K$ (hence alag $k$) hon. Poora method "differential affinity se rigged ek race" hai — difference hatao aur race tie ho jaati hai. Saara fancy hardware sirf $K$ mein ek difference ko arrival time mein ek difference mein amplify karne ka ek tarika hai.

$K\to k\to v\to t$. Alag $K$ alag $t$ banata hai; equal $K$ ek peak banata hai. Baki sab — TLC, GC, HPLC — phases chunna hai taaki jinki tumhe parwah hai unke $K$ values jitna ho sake utna alag hon.