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d. Note which, if any, of the following statements are true, and correct any that are untrue. i. At constant temperature and pressure, a system proceeds spontaneously to a state of minimum enthalpy. ii. The free energy change for an exothermic reaction is positive. iii. Reactions for which ∆H and ∆S are both positive tend to proceed spontaneously at high temperature. At constant temperature and pressure, equilibrium corresponds to the condition of minimum free energy. a. A piece of linen cloth believed to date from Biblical times (about 2000 years old) was subjected to carbon dating. A sample was pyrolyzed to yield carbon dioxide that was trapped and its radioactivity was measured. In units of counts per minute per gram of carbon, the average reading 14.0 compared to a count of 15.3 in carbon from living tissue. Linen is made from flax—a type of flowering plant. Assuming that the flax would have given a reading of 15.3 when alive, determine whether the cloth is likely to have originated in Biblical times. (Assume that t½ for carbon-14 is 5760 years.) b. In a kinetic experiment for a reaction in which A + B C , → the following data were recorded: [A] (M) [B] (M) Rate of C (M/s) 0.020 0.020 2.0 × 10−6 0.040 0.040 8.0 × 10−6 0.040 0.060 1.8 × 10−5 Determine the order of the reaction, the rate equation, and the rate constant. The oxidation of NO by O3 is first order in each of the reactants. Under experimental conditions, the rate constant is 1.5 × 107 mol s–1. Determine the rate of reaction if [NO] and [O3] are each 2.0 × 10−8 M initially.
Calculate the pH of 25 mL of a solution containing 6.00 g of potassium formate, KCO2H. (Ka for formic acid is 1.7 × 10−4.) In concentrated sulphuric acid, nitric acid can act as a base according to the Brønsted definition. Draw the Lewis structure for the conjugate base of HNO3 and write the equation for the acid-base reaction when HNO is dissolved in H2SO4. Determine the pH of a solution in which the equilibrium CO2(g) + H2O(l) HCO3 - (aq) + H+ (aq) occurs and in which [HCO3 − ] = 2.4 × 10−2 M, [CO2] = 1.2 × 10−3 M, and K = 7.9 × 10− [H+] = 4.0 × 10−8 pH = 7. Calculate the free energy change and equilibrium constant for the cell represented by the reaction equation O2(g) + 4H+ (aq) + 4Fe2+ (aq) 4Fe3+ (aq) + 2H2O(l) Standard reduction potentials are: 1.23 V for O2(g) + 4H+ (aq) + 4e– → 2H2O(l) and 0.77 V for Fe3+(aq) + e– → Fe2+(aq) Calculate the half-cell potential for Cu/Cu2+(aq) at 25°C if [Cu2+] = 5.0 M
c. Calculate the time it takes to deposit 0.100 g of copper from a copper sulphate solution if a 3.50 amp current is passed through the solution c. If you have the half-cells Cu/Cu2+, Cr/Cr3+, Mg/Mg2+, Zn/Zn2+, Ag/Ag+ , Fe/Fe2+, in which each solution is 1.0 M, explain the following: i. Which pair would be combined to give the cell with the highest voltage? ii. Which pair would be combined to give the cell with the lowest voltage?