8. A. A first order chemical reaction has a half-life of 10 minutes, what is the
ID: 713311 • Letter: 8
Question
8. A. A first order chemical reaction has a half-life of 10 minutes, what is the rate constant (k) for this reaction. B. If a first order reaction has a rate constant (k) of.01 min1, and initial concentration o reactant of .01, how long will it take for the reactant concentration to drop to.001M Review A. (2 points) Getting back to that melting ice problem again. Rock salt costs about 30 cents/lbs. How much is that in cents/g? Review B.(2 points) Write the net ionic equation that corresponds to the molecular equation NaCI(aq) + AgNO,(aq)-NaNO,(aq) + AgCI(s)Explanation / Answer
Ans. #A. Half-life of a first order reaction is given by-
t1/2= 0.693 / k ; where, k = rate constant
Or, k = 0.693 / t1/2 = 0.693 / 10 min
Hence, k = 0.0693 min-1
#B. Integrated rate law for first order reaction-
ln [A]t / [A]o ) = - (0.693 / t1/2)t ------------- equation 2
ln [A]t / [A]o ) = - kt ------------- equation 3
where,
[A]t = Concentration of reactant at time t
[A]o = Initial concentration of reactant
t = time of progression of reaction
t1/2 = Half-life
k = rate constant
Putting the values in equation 3-
ln (0.001M / 0.01 M) = - (0.01 min-1) t
Or, 2.303 log 0.1 = - - (0.01 min-1) t
Or, -1 = - (0.01 min-1) t
Or, t = 1 / (0.01 min-1)
Hence, t = 100 min
Therefore, required time, t = 100 min
#C. Given, cost = 30 cents / lbs ; [1 lbs = 453.592 g]
= 30 cents / 453.592 g
= 0.066 cents
#D. Step 1: Write all the chemical species, EXCEPT those in SOLID form, in their respective ions as follow-
Na+(aq) + Cl-(aq) + Ag+(aq) + NO3-(aq) ---> Na+(aq) + NO3-(aq) + AgCl(s)
# Step 2: Cancel the terms common on both side of the equation. The resultant equation is the net ionic reaction-
Cl-(aq) + Ag+(aq) ---> AgCl(s)
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