GATE CY 2023 Question Paper (05-Feb-2023) (Shift 2)

The intrinsic viscosity of a sample of polystyrene in toluene is 84 cm³ g ⁻¹ at 30 °C. It follows Mark-Houwink equation with empirical constant values of 𝐾 = 1.05 × 10⁻² cm³ g⁻¹ and 𝑎 = 0.75. The molecular weight of the polymer is ________×10³ g mol⁻¹ (rounded off to the nearest integer)

According to Debye-Hückel limiting law, the mean molal activity coefficient for 0.87 g K₂SO₄ (molar mass = 174 g mol⁻¹ ) in 1 kg of water at 25 °C is _________ (rounded off to two decimal places)

A solution is prepared by dissolving 128 g of naphthalene (C₁₀H₈) in 780 g of benzene (C₆H₆). The vapor pressure of pure benzene is 12.6 kPa at 25 °C. Assuming that naphthalene in benzene is an ideal solution, the partial vapor pressure of benzene is _________kPa (rounded off to two decimal places)

For the galvanic cell: H₂ (g) | HCl (aq) | Cl₂ (g)

the standard electromotive force (𝐸⁰) value is given by

𝐸⁰ = 1.73 − (1.25 × 10⁻³)𝑇 + (1.00 × 10⁻⁶ )𝑇²

where 𝐸⁰ is in Volts and 𝑇 is in Kelvin. For the cell reaction, the standard enthalpy change (∆${}_{\text{r}}$ 𝐻⁰) at 300 K is _________ kJ mol⁻¹ (rounded off to the nearest integer)

(Given: Faraday constant, 𝐹 = 96500 C mol⁻¹ )

A solution of three non-interacting compounds P, Q, and R is taken in a cuvette of 1 cm path length. Their concentrations are [P] = 1 ×10⁻⁶ M, [Q] = 2 × 10⁻⁶ M, [R] = 3 × 10⁻⁶ M and the molar extinction coefficients at 300 nm are ε${}_P$ = 1 × 10⁵ M⁻¹ cm⁻¹ , ε${}_Q$ = 2 × 10⁵ M⁻¹ cm⁻¹ and ε${}_R$ = 3 × 10⁵ M⁻¹ cm⁻¹ . The % transmittance at 300 nm is ____________ (rounded off to two decimal places)