Lecture 1. Introduction and essentials

Tuesday 16 January 2024

Measurement and its units. SI base units and derived units. Density. Unit conversions. Problem-solving strategies.

Reading: Tro NJ. Chemistry: Structure and Properties (3rd ed.) - Ch.E, §E.1-E.9 (pp.3-26).

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Summary

Welcome to this introductory course in general chemistry. Before getting started with the subject matter, a review of the course materials and the big ideas, knowledge, and skills you will gain from this course will be undertaken.

Chemistry is a scientific discipline that bridges the macroscopic world and the nanoscale realm. Atomic theory provides the indispensable framework for this bridge. Atoms are not the indivisible units dreamt of by ancient philosophers pondering the nature of matter and envisioned by John Dalton at the dawn of the 19th century. They are made up of protons and neutrons, together constituting a dense core called the nucleus, and the much smaller and lighter electrons, which somehow occupy most of the volume of the atom. Amazingly, the atom is mostly empty space! Nonetheless, all matter - including our own bodies - is made up of atoms, and from our perceptions seems quite substantial. In contrast to matter, energy seems much less substantial in its various forms. The fascinating interrelation and interplay between matter and energy holds the key to the secrets of the atom and a profound and deep understanding of the physical universe.

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Measurement is absolutely essential to experimental science. Measurement is carried out by observation. In particular, a comparison is made of the object of measurement to a standard. The latter sets the units of the measurement, and the observation is expressed quantitatively, that is as a specific decimal number along with the units. Presumably the measurement is a reasonable attempt to obtain what we can think of as the true value of what is being measured, in other words the measurement is reliable. Inevitably, measurement gives rise to error, which we seek to minimize. In this aim, a distinction is made between random error and systematic error, two ways in which our measurements can differ from the true value. We express numerically the degree of error, or conversely, the reliability of a measurement by first of all specifying the significant figures associated with a measurement. Best practice in writing measurement data (or results of calculations with measurement data as input) is the use of scientific notation.

Precision and accuracy, and types of error

These terms have very specific meanings for the working scientist, despite their being roughly synonymous in everyday use. The shorthand definitions:

• Precision = reproducibility of a measurement
• Accuracy = closeness of measurement to "true" value

The types of experimental error are related to this distinction. Random error is inherent in any experimental measurement, and is reflected in the precision of the measurement (less random error = more precision). Superimposed on random error may be systematic error - the measurement is reproducibly off, or inaccurate, - if the method of making the measurement is flawed.

Significant figures. Counting sig-figs, exact numbers and sig-figs in calculations.

Density as an illustration of:

• the difference between intensive and extensive properties
• determination of density by measurement of mass and volume
• reliability of measurement, experimental error
• significant figures

Energy: Forms and measurement

What is energy, really? When we think of energy, what rapidly spring to mind are its various forms, such as mechanical, electrical, heat, and light. This diversity belies an underlying unity or interconvertability of energy and its quantification and measureability in all these contexts.

Let's adopt the definition of energy from physics as force acting through a distance. Newton's second law, F = ma gives force, F as the product of the mass of an object times its acceleration. This is combined with the work-energy theorem stating that work (force acting through distance) is equivalent to expenditure of energy. Looking at the SI base units involved yields a derived SI unit for energy, the joule (J):

1 J = 1 kg·m² / s²

This is consistent with the definition of kinetic energy, the energy of coherent motion of an object with mass m in motion with a velocity of magnitude v. A first definition for what we term potential energy is a capacity to perform work, such as the work required to accelerate an object at rest up to a certain velocity. An ideal example from mechanics, that of a frictionless pendulum, illuminates the concept of conservation of energy. For the pendulum, its total energy can be assigned to the sum of its kinetic and potential energy. At he highest points of its arc of motion, its velocity (and hence its kinetic energy) is momentarily zero, and its potential energy reaches its maximum. At the bottom of the arc, this potential energy has been converted to the pendulum's maximum velocity and kinetic energy.

Our concern in this course will be with chemical energy, rather than the mechanical energy of a swinging pendulum, and we'll learn more about heat and measuring the energy released or absorbed by a physical process or a chemical reaction. This is known as calorimetry an important experimental method crucial to the development of chemical thermodynamics. This incorporates calorimetric observations into a coherent theory of energy in physical and chemical systems, including a definition for chemical potential energy.

Unit conversions and dimensional analysis

Conversions of the units associated with or derived from measurements is a routine task in problem solving. To perform a conversion of units, an equivalence relation between units must be relied upon. For example, the unit equivalence between inches (in) and centimeters (cm) is

1 in = 2.54 cm

Any such unit equivalence yields two reciprocal, multiplicative conversion factors. A multiplicative conversion factor for inches to centimeters is obtained by dividing both sides of the above equivalence relation by 1 in (the number 1 plus the unit inches):

1 = 2.54 cm/in

Division of both sides of the unit equivalence relation by 2.54 cm yields

(1/2.54) in/cm = 1

the conversion factor (2.54)⁻¹ in/cm, for centimeters to inches on the left-hand side of the equality.

The generation of the above conversion factors illustrates the idea of dimensional analysis. The units are treated in the same manner as numerical or algebraic symbols. The units "in/cm" arise from the division of a quantity expressed in inches by a quantity expressed in cm. The unitless number 1 arises as the ratio of two equal numerical quantities expressed in terms of the same units. When the same units occur in both the numerator and denominator of a ratio, we say that "the units cancel".

The above unit equivalence is an exact one, whereas others are inexact. This distinction, further details and examples can be found on the Conversions topics webpage.