Retention time depends on temperature, T, according to the equation log t’r =(a/T) + b, where a and b are constants for a specific compound on a specific column. A compound is eluted from a gas chromatography column at an adjusted retention time t’r =15.0 min when the column temperature is 373K. At 363 K, t9r 5 20.0 min. Find the parameters a and b and predict t’r at 353K

Short Answer

Expert verified

The relationship between temperature T and retention time(t'r)is shown below:

logtr'=aT+b

where: a and b are constants for a specific compound and specific column

List the given:

-tr'=15.0minatT=373Kt'r=20.0minatT=363K

Step by step solution

01

constant a and b

Find:

- a and b

- t'rat353K

First, to find the parameters a and b, we can set-up two equations from the given t'rand T.

Setting up Equation 1

log(15)=a373+bmultiplyingbothsidesby373:438.6820=a+373b(Equation1)SettingupEquation2:log(20)=a363+bMultiplyingbothsidesby363:472.2739=a+363b(Equation2)

Solve for parameters a and b using Equations 1 and 2:

a=1691.658b=-3.3592

02

Step 2:b) t'r at 353 K 

log(tr')=aT+blog(t'r)=1691.658353+(-3.3592)log(tr')=1.4330t'r=27.10min

03

final answer

t'r=27.10min

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