A pressurized spherical tank is made of 0.5-in.-thick steel. If it is subjected to an internal pressure of p = 200 psi, determine its outer radius if the maximum normal stress is not to exceed 15 ksi.
Chapter 15 Part 2: The Steady State Approximation: o Two limiting cases: Low pressure: When [M] is small, k2>k2[M] and rate is 2ndorder High pressure: When [M] is large, k1[M]>k2 and rate is 1 order Intermediates follow pseudo first-order kinetics Effects of temperature on reaction rates: o Many reactions increase rapidly with T Increase T by 10 degrees, rate doubles o Arrhenius equation states that rate constants depend exponentially on temperature. o k=Ae^-Ea/RT o lnk=lnA-Ea/RT o When plotted with y axis lnk and x axis 1/T, the slope is a negative linear one o Strong temperature dependence of reaction rates can be related to Maxwell-Boltzmann distribution of KE. Fraction of molecules of energies>Ea Potential energy surface (PES): Interaction of reactants described by a potential energy surface Reactants approach on a reaction path. Activation energy for forward reaction: Ea,f Activation energy for reverse reaction: Ea,r Change in internal energy for reaction: DeltaE=Ea,f- Ea,r Elementary reactions always increase with temperature since activation energy for elementary reactions is always positive Kinetics of Catalysis: o Catalysts are substances that are part of a chemical reaction and speed it up, but there’s no permanent chemical change in itself. They modify pathways or provide new pathways for reaction They speed up reactions by increasing the Arrhenius factor A, or lowering the activation energy Ea Have no effect on thermodynaimcs Two types: homogenous and heterogeneous Heterogeneous catalyst: one present in a distinct phase Ex. A solid surface in a solution-phase reaction Homogenous catalyst: Not present in distinct phase Ex. Chlorofluorohydrocarbons and nitrogen oxides in depletion of stratospheric ozone, and catalysis of the oxidation-reduction reaction by silver ions in solution Inhibitors slow reactions by increasing Ea Enzymes are large catalytic protein molecules, and reactions occur by binding of a substrate to the active site of the enzyme. o Most chemical reactions in living systems carried out with enzymes.