Measurement Errors and Uncertainty

Flashcards covering key concepts related to measurement errors, uncertainty, and definitions relevant to the topic.

1 ppm

1 part per million, equivalent to 1 mg per liter.

Gross Error

An error caused by human mistakes, often preventable by double checking measurements.

Systematic Error

A consistent error that can be identified and corrected, often caused by a miscalibrated instrument.

Random Errors

Errors that fluctuate and occur without a predictable pattern, affecting measurements in both directions.

Absolute Uncertainty

The uncertainty of a measurement expressed as a fixed value, e.g., ± 0.00 mL.

Relative Uncertainty

The absolute uncertainty divided by the measured value, often expressed as a percentage.

Density (D)

Defined as mass divided by volume (D = mass/volume).

Standard Deviation (SD)

A measure of the amount of variation or dispersion in a set of values.

Confidence Interval

A range of values that is likely to contain the true value of a measurement, influenced by the degree of freedom.

Bell Curve

A graphical representation of a normal distribution of data, often used to describe random errors.

What is an outlier in a data set?

A data point that is significantly different from other observations in a set.

What is the formula for the Grubbs test (G-test) to identify an outlier?

G = \frac{|x{outlier} - \bar{x}|}{SD}, where x{outlier} is the suspected outlier, \bar{x} is the mean of the data, and SD is the standard deviation.

What is an analyte?

The substance or chemical component that is being measured or analyzed in a sample.

What is the matrix in analytical chemistry?

Everything else in a solution besides the analyte that may affect the analytical signal.

What is a calibration curve and how is it used?

A graph plotting an instrument's response (e.g., absorbance, current) against the known concentrations of a series of standard solutions. It is used to determine the concentration of an unknown sample by interpolating its instrument response.

When is the standard addition method used?

It is used when the sample matrix is complex and affects the analytical signal, making it difficult to prepare accurate standards without the matrix.

Describe the principle of the standard addition method.

Known quantities of the analyte (the 'standard') are added directly to aliquots of the unknown sample. The increase in signal upon addition of the standard is used to determine the initial concentration of the analyte in the unknown.

What is the purpose of using an internal standard method?

To compensate for random and systematic errors such as instrument fluctuations, matrix effects, or sample loss during preparation and analysis.

What is an internal standard?

A known amount of a different compound (not the analyte) that is added to all samples (blanks, standards, and unknowns) during an analysis.

What is the formula for calculating the response factor (F) in the internal standard method?

F = \frac{Ax}{[X]} \times \frac{[S]}{As}, where Ax and As are the signals from the analyte and internal standard, respectively, and [X] and [S] are their concentrations.

What is a titration?

A quantitative chemical analysis method used to determine the concentration of an identified analyte by reacting it with a precisely known concentration of a reagent (titrant).

List some common types of titrations.

Acid-base titrations, precipitation titrations, EDTA titrations, and potentiometric titrations.

What is a primary standard?

A readily available, highly pure (e.g., \ge 99.9\%), stable, and accurately weighed substance used to prepare a standard solution or to standardize another solution.

What is standardization in analytical chemistry?

The process of accurately determining the concentration of a solution (e.g., a titrant) by reacting it with a primary standard or a previously standardized solution.

When is back titration used?

It is used when the reaction between the analyte and the first reagent is too slow, incomplete, or when the analyte is volatile, or when a direct titration is difficult to observe.

Describe the general process of back titration.

An accurately known excess of a first reagent is added to the analyte. After the reaction, the unreacted excess of the first reagent is then titrated with a second standard reagent.

What is the acid ionization constant (K_a) and its significance?

It is an equilibrium constant for the dissociation of a weak acid in water, indicating the strength of the acid. A smaller Ka value indicates a weaker acid (Ka << 1 for weak acids, K_a >> 1 for strong acids).

Provide the formula for the acid ionization constant (K_a) for a weak acid, HA.

For the reaction HA(aq) + H2O(l) \rightleftharpoons H3O^+(aq) + A^-(aq), the formula is Ka = \frac{[H3O^+][A^-]}{[HA]}.

What is an amphiprotic (or amphoteric) substance?

A substance that can act as both a proton donor (acid) and a proton acceptor (base), depending on the chemical environment. Water is a common example.

What is the definition of pH?

A measure of the acidity or alkalinity of an aqueous solution, defined as the negative base-10 logarithm of the hydrogen ion activity (or concentration): pH = -\log[H_3O^+].

What is the definition of pOH?

A measure of the hydroxide ion concentration in an aqueous solution, defined as the negative base-10 logarithm of the hydroxide ion activity (or concentration): pOH = -\log[OH^-].

What is the relationship between pH and pOH at $25^
Tiers $?

At $25^
Tiers $, the sum of pH and pOH is 14: pH + pOH = 14.00.

What is the autoionization constant of water (K_w) and its relationship to pH and pOH?

For the reaction 2H2O(l) \rightleftharpoons H3O^+(aq) + OH^-(aq), Kw = [H3O^+][OH^-]. At $25^
Tiers $, Kw is 1.0 \times 10^{-14}, which leads to pH + pOH = pKw = 14.00.

What is the purpose of an ICE (Initial, Change, Equilibrium) table?

It is a tool used to calculate the equilibrium concentrations of reactants and products in a reversible reaction, especially useful for weak acid-base problems.

What is a buffer region in a titration curve?

The region in a titration curve (typically of a weak acid/base with a strong base/acid) where the pH changes relatively slowly upon addition of the titrant. This occurs when significant amounts of both the weak acid/base and its conjugate are present.

What is the Henderson-Hasselbalch equation and when is it typically used?

The equation is pH = pK_a + \log\frac{[A^-]}{[HA]}. It is used to calculate the pH of a buffer solution or at any point in the buffer region of a weak acid titration.

What is the equivalence point (or stoichiometric point) in a titration?

The point in a titration where the amount (moles) of titrant added is exactly chemically equivalent to the amount (moles) of analyte initially present in the sample.