Chemistry Labs

International Chemistry Olympiad · 2025

Problems

  1. Problem 4Tennis balls are pressurised above atmospheric pressure for a good bounce; old hollow balls simply contained air at atmospheric pressure. Assume a ball inner radius R=3.0R = 3.0 cm constant during pressurisation, air composed of 20 % O2 and 80 % N2 by volume, and that overpressure does not expand the ball. (a) Calculate the mass mm of air inside an old ball at T0=25T_0 = 25 °C. (b) Modern balls are kept at p0=1.80p_0 = 1.80 atm; premium balls contain pure N2. Once the can is opened, gas diffuses out until the inside reaches atmospheric pressure, with no inward diffusion; the process follows first-order kinetics in the overpressure. Premium balls depressurise to p1=1.40p_1 = 1.40 atm after t1=241t_1 = 241 h and to p2=1.19p_2 = 1.19 atm after about t2=21t_2 = 21 days at 25 °C. Demonstrate first-order behaviour and calculate the depressurisation rate constant kN2k_{\mathrm{N_2}} in h−1^{-1}. (c) The initial depressurisation rate of regular (air) balls is 10 % faster than that of premium balls; calculate the rate constant kO2k_{\mathrm{O_2}} assuming the rates of both gases are additive. (d) New premium balls, manufactured and canned at 25 °C, are opened and quickly brought to T=30.0T = 30.0 °C; a match starts t=12.0t = 12.0 h later. With Ea=50.0E_a = 50.0 kJ mol−1^{-1} for premium-ball depressurisation, calculate the ball pressure at the start of the match.Solutions: 1
  2. Problem 5A Dubai desalination plant uses multi-stage flash (MSF) desalination: seawater is heated at high pressure then flashed, releasing pure water vapour. Dubai seawater is at T0=25.00T_0 = 25.00 °C and contains 3.45 % NaCl by mass (assume complete ionisation); the boiling point elevation constant is Kb=0.5120K_b = 0.5120 K kg mol−1^{-1} and the latent heat of vaporisation of water is Evap=2260E_{\text{vap}} = 2260 kJ kg−1^{-1} (40.716 kJ mol−1^{-1}). (a) Calculate the boiling point of Dubai seawater at atmospheric pressure. (b) Calculate its boiling point at p=2.50p = 2.50 atm using the Clausius–Clapeyron equation. (c) A 100 L flash chamber holds 1.00 kg of seawater at 90.0 °C; a second 1.00 kg portion overheated to 110.0 °C is added, pressure is reduced, and the chamber equilibrates at Tf=97.0T_f = 97.0 °C. With cp=3.85c_p = 3.85 kJ kg−1^{-1} K−1^{-1}, calculate the amount nn (mol) of water that vaporised. (d) The plant produces 50 000 m³ of pure water per day, extracting overall 85 % of the water present in the seawater; calculate the mass of Dubai seawater needed per day.Solutions: 1