At 25 °C, the concentration of H⁺ ions in 1.00 × 10⁻³ M aqueous solution of a weak monobasic acid having acid dissociation constant (K_a) of 4.00 × 10⁻¹¹ is X × 10⁻⁷ M. The value of X is ______.

Use: Ionic product of water (K_w) = 1.00 × 10⁻¹⁴ at 25 °C

Molar volume (V_m) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with V_m as the variable. The ratio (in mol dm⁻³) of the coefficient of V_m² to the coefficient of V_m for a gas having van der Waals constants a = 6.0 dm⁶ atm mol⁻² and b = 0.060 dm³ mol⁻¹ at 300 K and 300 atm is ______.

Use: Universal gas constant (R) = 0.082 dm³ atm mol⁻¹ K⁻¹

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is ______.

Use: Universal gas constant (R) = 8.3 J K⁻¹ mol⁻¹; Atomic mass (in amu): H = 1, O = 16

The monomer (X) involved in the synthesis of Nylon 6,6 gives positive carbylamine test. If 10 moles of X are analyzed using Dumas method, the amount (in grams) of nitrogen gas evolved is ______.

Use: Atomic mass of N (in amu) = 14