(a)
Interpretation:
It has to be shown that at time
Concept Introduction:
The integrated rate law for first-order reaction is given below.
Where,
The half-life period for first-order reaction is given below.
(b)
Interpretation:
The following relation has to be proved.
(c)
Interpretation:
It has to be shown that for any first-order reaction a plot of
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Chemistry: The Molecular Science
- A drug decomposes in the blood by a first-order process. A pill containing 0.500 g of the active ingredient reaches its maximum concentration of 2.5 mg/ 100 mL of blood. If the half-life of the active ingredient is 75 min, what is its concentration in the blood 2.0 h after the maximum concentration has been reached?arrow_forwardWhen formic acid is heated, it decomposes to hydrogen and carbon dioxide in a first-order decay: HCOOH(g)CO2(g)+H2(g) The rate of reaction is monitored by measuring the total pressure in the reaction container. Time (s) Pressure (torr) 0 220 50 324 100 379 150 408 200 423 250 431 300 435 Calculate the rate constant and half-life in seconds for the reaction. At the start of the reaction (time = 0), only formic acid is present. (HINT: Find the partial pressure of formic acid using Dalton's law of partial pressure and the reaction stoichiometry to find PHCOOH at each time.)arrow_forwardWhen formic acid is heated, it decomposes to hydrogen and carbon dioxide in a first-order decay. HCOOH(g) CO2(g) + H2(g) At 550 C, the half-life of formic acid is 24.5 minutes. (a) What is the rate constant, and what are its units? (b) How many seconds are needed for formic acid, initially 0.15 M, to decrease to 0.015 M?arrow_forward
- The reaction of compound A to give compounds C and D was found to be second-order in A . The rate constant for the reaction was determined to be 2.42 L/mol/s. If the initial concentration is 0.500 mol/L, what is the value of t1/2?arrow_forward11.64 HBr is oxidized in the following reaction: 4 HBr(g) + O2(g) —• 2 H2O(g) + 2 Br,(g) A proposed mechanism is HBr + O2 -* HOOBr (slow) HOOBr + HBr — 2 HOBr (fast) HOBr + HBr — H2O + Bn (fast) Show that this mechanism can account for the correct stoichiometry. Identify all intermediates in this mechanism. What is the molecularity of each elementary’ step? Write the rate expression for each elementary' step. Identify the rate-determining step.arrow_forwardThe hydrolysis of the sugar sucrose to the sugars glucose and fructose, C12H22O11+H2OC6H12O6+C6H12O6 follows a first-order rate equation for the disappearance of sucrose: Rate =k[C12H22O11] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.) (a) In neutral solution, k=2.11011s1 at 27 C and 8.51011s1 at 37 C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature). (b) When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is 1.65107M . How long will it take the solution to reach equilibrium at 27 C in the absence of a catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible. (c) Why does assuming that the reaction is irreversible simplify the calculation in pan (b)?arrow_forward
- The plot below shows the number of collisions with a particular energy for two different temperatures. a. Which is greater, T2 or T1? How can you tell? b. What does this plot tell us about the temperature of the rate of a chemical reaction? Explain your answer.arrow_forwardRegular ?ights of supersonic aircraft in the stratosphere ale of concern because such aircraft produce nitric oxide, NO, as a byproduct in the exhaust of their engines. Nitric oxide reacts with ozone, and it has been suggested that this could contribute to depletion of the ozone layer. The reaction NO+O3NO2+O2 is first order with respect to both NO and O3 with a rate constant of 2.20107 L/mol/s. What is the instantaneous rate of disappearance of NO when [NO]=3.3106 M and [O3]=5.9107M?arrow_forwardExplain why half-lives are not normally used to describe reactions other than first order.arrow_forward
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