(a) (i) Calculate the number of moles of HCl (g) produced by the absorption of one Joule of radiant energy of wavelength 480 nm in the reaction H₂ (g) + Cl₂ (g) → 2HCl (g) if the quantum yield of the photochemical reaction is 1·0 × 10⁶.
[Given: Nₐ =

Question

(a) (i) Calculate the number of moles of HCl (g) produced by the absorption of one Joule of radiant energy of wavelength 480 nm in the reaction H₂ (g) + Cl₂ (g) → 2HCl (g) if the quantum yield of the photochemical reaction is 1·0 × 10⁶.
[Given: Nₐ = 6·022 × 10²³ mol⁻¹, h = 6·626 × 10⁻³⁴ Js, c = 2·998 × 10⁸ ms⁻¹] (10 marks)

(ii) On passing monochromatic light through a 0·04 molar solution kept in a cell of thickness 2 cm, the intensity of the transmitted light was reduced to 50%. Calculate the molar extinction coefficient. (5 marks)

(b) What is meant by heterogeneously catalyzed reactions? Mention the consecutive steps for a reaction to occur on a surface.

Using Langmuir adsorption theory, account for the experimental observation that the decomposition of PH₃ on tungsten follows first order kinetics at low pressure and zeroth order kinetics at high pressure. (15 marks)

(c) (i) What is 'sodium pump'? Explain the role of sodium pump in biological system. (10 marks)

(ii) What is Bohr effect? Explain the role of Cytochrome P450. (10 marks)

UPSC Answer Check · Accepted Answer

(a)(i) In photochemistry, quantum yield φ is the number of product molecules formed per photon absorbed. Here φ = 1.0×10⁶ molecules of HCl per photon. Energy of one photon by Planck relation E = hc/λ. λ = 480 nm = 480×10⁻⁹ m. E = (6.626×10⁻³⁴ J s × 2.998×10⁸ m s⁻¹)/(480×10⁻⁹ m) = 4.138×10⁻¹⁹ J. Number of photons in 1 J = 1/(4.138×10⁻¹⁹ J) = 2.416×10¹⁸ photons. These photons correspond to (2.416×10¹⁸)/(6.022×10²³ mol⁻¹) = 4.012×10⁻⁶ mol photons. Since each photon produces 1.0×10⁶ HCl molecules, n_HCl = (4.012×10⁻⁶ mol photons) × (1.0×10⁶ mol HCl/mol photons) = 4.01 mol HCl. Direct formula: n_HCl = I λ φ/(h c Nₐ). Answer: 4.01 mol HCl. (a)(ii) Beer-Lambert law: A = log₁₀(I₀/I_t) = ε c l. Transmitted intensity is 50%, so I_t/I₀ = 0.50. A = log₁₀(1/0.50) = log₁₀2 = 0.3010. Given c = 0.04 mol L⁻¹ and l = 2 cm, ε = A/(c l) = 0.3010/(0.04×2) = 3.76 L mol⁻¹ cm⁻¹, assuming no scattering or reflection. Answer: ε ≈ 3.76 L mol⁻¹ cm⁻¹. (b) Heterogeneously catalysed reactions are reactions in which the catalyst and reactants exist in different phases, usually a solid catalyst with gaseous or liquid reactants. The reaction takes place on the catalyst surface, especially at active sites. The consecutive steps are: External diffusion of reactant molecules from the bulk fluid to the catalyst surface. Internal diffusion through pores of the catalyst to active sites. Adsorption of reactants on active sites. Surface reaction between adsorbed species or between an adsorbed species and a bulk molecule to form products. Desorption of products from the surface. Diffusion of products away from active sites and pores into the bulk fluid. Langmuir adsorption theory assumes equivalent surface sites, monolayer adsorption, dynamic adsorption-desorption equilibrium, and negligible interaction between adsorbed molecules. For PH₃ on tungsten, let P be PH₃ pressure and θ the fraction of surface covered. The Langmuir isotherm is θ = K P/(1+K P), where K is the adsorption equilibrium constant. If the decomposition rate is proportional to covered surface, rate = k θ = k K P/(1+K P). At low pressure, K P<<1, so θ≈K P and rate≈k K P; the reaction is first order in PH₃. At high pressure, K P>>1, so θ≈1 and rate≈k; the surface is saturated, and the reaction is zeroth order. At intermediate pressure the order lies between 0 and 1. Thus Langmuir adsorption explains the observed pressure dependence of PH₃ decomposition on tungsten. (c)(i) The sodium pump is the Na⁺/K⁺-ATPase, an integral membrane protein and active transport system. By hydrolysing one ATP, it pumps three Na⁺ ions out of the cell and two K⁺ ions into the cell, both against their concentration gradients. Because one net positive charge is moved out per cycle, the pump is electrogenic. Its roles include maintaining high intracellular K⁺ and high extracellular Na⁺ concentrations; establishing and restoring the resting membrane potential needed for nerve impulse conduction and muscle contraction; maintaining cell volume and osmotic balance; providing the Na⁺ gradient for secondary active transport of glucose, amino acids and other solutes; and regulating intracellular pH and ionic homeostasis. It requires ATP and Mg²⁺, and is inhibited by ouabain/digitalis. (c)(ii) The Bohr effect is the decrease in oxygen affinity of haemoglobin when pH decreases or pCO₂ increases. H⁺ and CO₂ bind to haemoglobin, stabilising the low-affinity T-state and shifting the oxygen dissociation curve to the right, so oxygen is released more readily in actively respiring tissues. In lungs, low CO₂ and higher pH favour oxygen binding. Cytochrome P450 is a superfamily of heme-thiolate monooxygenase enzymes, mainly located in the liver endoplasmic reticulum and in mitochondria of steroidogenic tissues. Using NADPH and molecular oxygen, it inserts one oxygen atom into a substrate: RH + O₂ + NADPH + H⁺ → ROH + H₂O + NADP⁺. It carries out Phase I oxidative metabolism of drugs, xenobiotics and toxins, and also participates in biosynthesis of steroids, bile acids, vitamin D and fatty acids. The name P450 comes from the reduced CO-bound complex absorbing near 450 nm.

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