Question

question one
a) clearly distinguish between the following terms as applied in analytical chemistry
i)end point and equivalence point. (2 marks)
ii)random and systematic errors. (2 marks)
iii)contamination and interference. (2 marks)
b) explain the following terms as used in analytical chemistry;
i)precision. (2 marks)
ii)standard solution. (2 marks)
iii)accuracy. (2 marks)
iv)outlier. (2 marks)
c) the following results were obtained in the replicate determination of the iron content of animal supplement: 0.442, 0.446, 0.442, 0.441 and 0.440 ppm.
calculate the following:
i)mean

Answer:

Part (a)

i) End point and equivalence point

• End point: The point in a titration where a visible change (like color change of an indicator) occurs, signifying that the titration is stopped. It is an experimental observation.
• Equivalence point: The theoretical point where the amount of titrant added is stoichiometrically equivalent to the amount of analyte in the sample. It is based on chemical reaction stoichiometry.

ii) Random and systematic errors

• Random errors: Errors that occur randomly, causing measured values to fluctuate around the true value. They are unpredictable in sign and magnitude, and can be reduced by increasing the number of measurements (e.g., fluctuations in instrument readings due to environmental noise).
• Systematic errors: Errors that occur consistently in the same direction (either always positive or always negative) and are repeatable. They arise from flaws in the measurement system (e.g., a poorly calibrated instrument, or a biased sampling method) and cannot be reduced by increasing the number of measurements, but can be corrected by identifying and eliminating the source.

iii) Contamination and interference

• Contamination: The introduction of an unwanted substance (impurity) into the sample or analytical system, which can affect the measurement (e.g., dust falling into a sample, or a reagent containing impurities).
• Interference: A situation where a substance other than the analyte reacts with the reagent or affects the measurement process, leading to an incorrect result. Interfering substances can mimic the analyte’s behavior or inhibit the analyte’s reaction (e.g., a metal ion that reacts with a ligand intended for the analyte, causing a false signal).

Part (b)

i) Precision

Precision in analytical chemistry refers to the degree of agreement (closeness) between multiple replicate measurements of the same quantity. It reflects the reproducibility of the measurement and is often expressed using statistics like standard deviation or relative standard deviation. A precise method gives consistent results, even if they are not close to the true value (precision is about repeatability, not accuracy).

ii) Standard solution

A standard solution is a solution of known, precisely determined concentration. It is used in analytical procedures (like titrations) to determine the concentration of an unknown analyte. Standard solutions can be primary (prepared from a pure, stable substance, e.g., KHP for acid-base titrations) or secondary (standardized against a primary standard).

iii) Accuracy

Accuracy is the degree of agreement between a measured value and the true (or accepted reference) value of the quantity being measured. It reflects how close the measured result is to the actual value, and is affected by systematic errors (which precision is not). A method can be precise but inaccurate (if systematic errors exist) or accurate and precise (if both random and systematic errors are minimized).

iv) Outlier

An outlier is a data point in a set of measurements that differs significantly from the other data points. Outliers can arise from experimental errors (e.g., a spilled sample, or a miscalculation during measurement) or rare, legitimate variations. They are often identified using statistical tests (e.g., Grubbs’ test) and may be excluded from data analysis if they are confirmed to be errors.

Part (c) - i) Mean

To calculate the mean (\(\bar{x}\)) of a set of values, we use the formula:
$$\bar{x} = \frac{\sum_{i = 1}^{n} x_i}{n}$$
where \(x_i\) are the individual measurements, and \(n\) is the number of measurements.

Step 1: Identify the values and \(n\)

The values are \(0.442\), \(0.446\), \(0.442\), \(0.441\), and \(0.440\) ppm. So, \(n = 5\).

Step 2: Sum the values

$$\sum_{i = 1}^{5} x_i = 0.442 + 0.446 + 0.442 + 0.441 + 0.440$$
$$= (0.442 + 0.442) + 0.446 + (0.441 + 0.440)$$
$$= 0.884 + 0.446 + 0.881$$
$$= 0.884 + 0.446 = 1.33; \quad 1.33 + 0.881 = 2.211$$

Step 3: Calculate the mean

$$\bar{x} = \frac{2.211}{5} = 0.4422$$

Final Answers

a) (i), (ii), (iii) – Explanations as above.
b) (i), (ii), (iii), (iv) – Explanations as above.
c) i) The mean iron content is \(\boldsymbol{0.4422}\) ppm (or rounded to appropriate significant figures, e.g., \(0.442\) ppm if considering the precision of the measurements).