(Solved) First order: Half life reaction

biostudent123

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10 years ago

Need help answering this.
At 500 ∘C, cyclopropane (C3H6) rearranges to propene (CH3−CH=CH2). The reaction is first order, and the rate constant is 6.7×10−4s−1. If the initial concentration of C3H6 is 5.00×10−2M .

A) What is the half-life (in minutes) of this reaction?
B) How many minutes will it take for the concentration of cyclopropane to drop to 12.5% of its initial value?

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Neji513

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10 years ago Edited: 10 years ago, Neji513

A) if it's first order, then the half life is independent of initial concentration

half life= 0.693 / k

plug in the rate constant for k.. make sure you divide your answer by 60 to convert it from seconds to minutes though

B) ln [final] = ln [initial] - kt.... you can rearrange it to make it ln ( [final]/ [initial] ) / k = t , but make sure to divide the time by 60 to convert from seconds to minutes.... basically to give [ ln ( % you're given ) / .00067 ] / 60 = time

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biostudent123 Author

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10 years ago

I got A) wrong, when i divided 0.693 with K constant, i then divided answer (0.000103433) by 60, I got (0.000001724), i used scientific notation and it turned out "1.7 x 10-6 "

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Neji513

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biostudent123 Author

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10 years ago

For question B) The final would 17.24 minutes right ?, I pluged in the percentage ( 0,12%) and divided it by .00067= and divided the answer by 60, i was given 37.3 minutes.,

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Neji513

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10 years ago

Quote from: biostudent123 (10 years ago)

For question B) The final would 17.24 minutes right ?, I pluged in the percentage ( 0,12%) and divided it by .00067= and divided the answer by 60, i was given 37.3 minutes.,

37.3 is not what i got at all..... did you take the natural log of .125?

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biostudent123 Author

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10 years ago

No i didnt, 125 is 12.5% ? natural log of 125 is 4.83, do i then divide this by .00067 and then divide by 60 ?

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Neji513

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10 years ago Edited: 10 years ago, Neji513

Quote from: biostudent123 (10 years ago)

No i didnt, 125 is 12.5% ? natural log of 125 is 4.83, do i then divide this by .00067 and then divide by 60 ?

when you convert % to decimal, you move the decimal twice to the left..... so 12.5% = .125 in decimal form....take the ln (.125)......%'s are used to report data, you never do calculations with them while they're in % form..

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biostudent123 Author

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10 years ago

is the answer -57.7 ? I loged .125 and used formula

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Neji513

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10 years ago

Quote from: biostudent123 (10 years ago)

is the answer -57.7 ? I loged .125 and used formula

51.73 minutes... the negative cancels out since the ln of .125 is a negative number, and i forgot to add in the - from -kt portion of the equation..... either way, you'll never have a negative answer when it comes to time for problems you do.... time is a scalar quantity

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biostudent123 Author

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#10

10 years ago

Thank you, answer was right without negative sign, where did you get the .00067 ? and the 60 minutes, what happened to the 0.693 of the half life ?

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Neji513

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#11

10 years ago

Quote from: biostudent123 (10 years ago)

Thank you, answer was right without negative sign, where did you get the .00067 ? and the 60 minutes, what happened to the 0.693 of the half life ?

.693/k = half life .... question A asked for half life, so we use this equation to find the half life....you can also use the ln( [final]/[intial] ) = -kt to find the half life as well by doing ln (.5).... .693/k=half life is derived from that equation

part B of the problem isn't asking for the half life, so we don't need the .693/k equation anymore.......

.00067 M/s is the rate constant that you were given just written in decimal form and not scientific notation ( 6.7*10^-4 M/s is the same as .00067 M/s)... again scientific notation is how you report data, decimal form is normally what you use for calculations unless it's a super tiny or large number......

since your rate constant is in Moles per second...this means your time will be in seconds. in order to convert to minutes, you need to divide by 60 since there are 60 seconds in 1 minute

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