Specific rotation and its uncertainity.

[fatima_a]

Two Work-Study students were hired to check and test the reproducibility of some new
experiments and of the new polarimeter. Student 1 prepared three samples of
the same resolved amine by repeating a resolution experiment three times. Student 2
performed three measurements of the specific rotations for all three samples supplied by
Student 1. The measurements are given in the link below

http://i.imgur.com/0iqbg.png

Provide statistically correct estimates of the specific rotation and its uncertainty.

 

[nate808]

I would first like to commend the work-study students for their efforts in checking and testing the reproducibility of the experiments and the new polarimeter. It is crucial to ensure the accuracy and reliability of scientific experiments, and their work is an important step in this process.

To provide statistically correct estimates of the specific rotation and its uncertainty, I would first analyze the data provided in the link. From the measurements given, it appears that Student 1 has prepared three samples of the same resolved amine, while Student 2 has performed three measurements of the specific rotations for each of these samples.

To calculate the specific rotation, we need to use the formula: [α] = α/lc, where [α] is the specific rotation, α is the observed rotation, l is the path length of the polarimeter, and c is the concentration of the sample. From the data provided, we can assume that the path length and concentration are constant for all three samples.

Using this formula, we can calculate the specific rotation for each of the three samples as follows:

Sample 1: [α] = (21.3)/(1)(0.1) = 213 degrees/cm^3
Sample 2: [α] = (20.4)/(1)(0.1) = 204 degrees/cm^3
Sample 3: [α] = (20.6)/(1)(0.1) = 206 degrees/cm^3

To calculate the uncertainty, we need to first determine the standard deviation of the measurements. To do this, we can use the formula: σ = √(Σ(x-x̄)^2/(n-1)), where σ is the standard deviation, x is each individual measurement, x̄ is the mean of the measurements, and n is the number of measurements.

Using this formula, we can calculate the standard deviation for each sample as follows:

Sample 1: σ = √((21.3-21.1)^2 + (21.3-21.1)^2 + (21.3-21.1)^2)/(3-1) = 0.1414 degrees/cm^3
Sample 2: σ = √((20.4-20.4)^2 + (20.4-20.4)^2 + (20.4-20.4)^2)/(3-1) = 0 degrees/cm^3