The final concentration after 172 seconds is 1.15 M. To obtain this answer, use the the integrated rate law for the order of reaction. Based on the problem, this is a second order reaction. The units of the rate constant also support that it is a second order reaction.
Further Explanation:
The solution to this problem is straightforward.
STEP 1: Since the reaction is a second order reaction, the integrated rate law will be:
[tex]\frac{1}{C_{f}} = \ kt \ + \frac{1}{C_{i}}[/tex]
where:
C(f) is the final concentration
k is the rate constant
t is the time
C(i) is the initial concentration
STEP 2: Plugging in the values given in the problem into the equation, the following equation should be obtained:
[tex]\frac{1}{C_{f}} \ = (1.30 \ x \ 10^{-3} \frac{ \ 1 }{ \ M-s})(172 \ s) \ + \ \frac{1}{1.54 \ M} \\[/tex]
STEP 3: Using algebra to solve for C(f):
[tex]\frac{1}{C_{f}} = \ 0.87295\\ \\C_{f} = \ 1.14554 \ M[/tex]
Since the given values only have 3 significant figures, the final answer must be expressed with 3 significant figures as well.
Therefore,
[tex]\boxed {C_{f}\ = \ 1.15 \ M}[/tex]
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Keywords: rate law, second order, integrated rate law
