Quantitative Analysis & Statistics - Analytical Chemistry IV

This flashcard set covers the vocabulary and foundational concepts of quantitative analysis and statistics from the 2nd Year Analytical Chemistry IV lecture, including sample processing types, error classifications, analyte levels, and key statistical measures.

Heterogeneous materials

Materials that are not uniform and whose constituent parts can be distinguished visually or with the aid of a microscope, such as coal, animal tissues, and soil.

Homogeneous materials

Materials that are uniform throughout, meaning every part is in the same state and has the same composition, such as water, air, and gases.

Replicate samples

Samples of the same masses or volumes measured carefully by an analytical balance or precise volumetric device to improve result quality and provide a measure of precision.

Interferent

Any chemical species that causes an error in an analysis by enhancing or reducing the quantity of the analyte being measured.

Calibration

An important analytical step where a constant ($K$) is determined by using standards for which the concentration ($C_A$) is known.

Correlation coefficients ($r$)

A statistical measure used to determine the strength of the relationship between a concentration ($x$) and an instrument signal ($y$).

Precision

The closeness of results that have been obtained in exactly the same way, expressed through repeatability or reproducibility.

Repeatability

The precision obtained when all measurements are made by the same analyst during a single period of laboratory work, using the same solutions and equipment.

Reproducibility

The precision obtained under varied conditions, including different analysts or different laboratory sessions for a single analyst.

Accuracy

The closeness of measurements to the true or accepted value, characterized by absolute error or percent relative error.

Absolute Error ($E$)

The difference between a measured value ($x_i$) and the true or accepted value ($x_t$), expressed as $E = x_i - x_t$.

Percent Relative Error ($E_r$)

An expression of accuracy calculated as $E_r = \frac{x_i - x_t}{x_t} \times 100\%$.

Random (Indeterminate) Error

An error type that causes data to be scattered symmetrically around the mean value due to uncontrollable variables, affecting the precision of measurements.

Systematic (Determinate) Error

An error type that causes the mean of a data set to differ from the accepted value, resulting in bias where results are consistently too high or too low.

Gross Error

An error that usually occurs occasionally, is often large, and leads to outlier results that differ markedly from other data in a set.

Blunder

An outright mistake, such as recording a wrong value or misreading a scale, which should be excluded from data analysis.

Macro analysis

Analytical procedures performed on samples with a mass of more than $0.1\,g$.

Semi micro analysis

Analytical procedures performed on samples in the mass range of $0.01\,g$ to $0.1\,g$.

Micro analysis

Analytical procedures performed on samples in the mass range of $10^{-4}\,g$ to $10^{-2}\,g$.

Ultra micro analysis

Analytical procedures performed on samples whose mass is lower than $10^{-4}\,g$.

Major analytes

Constituents present in a sample in the relative weight range of $1\%$ to $100\%$.

Trace analytes

Constituents present in a sample in amounts between $100\,ppm$ ($0.01\%$) and $1\,ppb$.

Mean ($\bar{x}$)

The numerical average obtained by dividing the sum of individual measurements by the total number of measurements, defined as $\bar{x} = \frac{\sum x_i}{n}$.

Median

The middle value or most central item in a data set that has been arranged in numerical order.

Mode

The most frequently occurring number in a distribution of a data set.

The Q-test (Dixon Q-Test)

A statistical test used to decide if a suspected outlier should be rejected by comparing the experimental quotient ($Q_{exp}$) to a critical value ($Q_{table}$).

Standard Deviation ($S$)

A measure of how spread out data is relative to the mean, calculated using the formula $S = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$.

Degrees of Freedom

The value represented by $(n - 1)$ in the denominator of the standard deviation formula.

Variance ($S^2$)

A measure of variation equal to the square of the absolute standard deviation.

Coefficient of Variation ($CV$)

The percent relative standard deviation, calculated as $CV = \frac{S}{\bar{x}} \times 100\%$.