# Chemistry and the Scientific Method | General Chemistry 1

## Scientific Method and Notation

**The scientific method:**

An empirical method in which observations give rise to laws, data give rise to hypotheses, hypotheses are tested with experiments, data are collected, conclusions are drawn and successful hypotheses give rise to theories

**Scientific notation:**

A way of writing extremely large or extremelly small numbers. A number is written in scientific notation when expressed as *N* x 10* ^{n}* where

*N*is a number between 1 and 10 and

*n*is a positive or negative integer

850,000,000 = 8.5 x 10

^{8}in scientific notation

0.0000023 = 2.3 x 10^{-6 }in scientific notation

## The Properties of Matter

Chemistry is the study of matter and the changes that matter undergoes. The properties of a substance may be quantitative (measured and expressed with a number) or qualitative (not involving numbers)

**Physical vs. chemical properties**

Physical property is a property that can be determined without changing the identity of a substance

Chemical property is a property that are determined only as the result of a chemical process. The original substance is converted to a different substance

Physical properties: color, physical state, melting point, boiling point

Chemical properties: flammability, combustibility, oxidation states, enthalpy of formation

**Intensive vs. extensive properties**

Intensive property is a property independent of the amount of a substance

Extensive property is a property directly proportional to the amount of matter

Intensive properties: density, color, temperature, hardness, melting point

Extensive properties: masse, volume, weight, length

## States of Matter

**States of matter:**

The 3 physical states of matter are:

- Solid: fixed volume and fixed shape. Particles form an ordered lattice of atoms or molecules
- Liquid: definite volume but no specific shape. Particles are held together by forces but are still free to randomly move
- Gas: it fills the entire volume of the container (no definite shape). Particles move quickly over the entire volume of the container

**Phase changes:**

gas → liquid: condensation

gas → solid: deposition

liquid → solid: freezing

liquid → gas: boiling

solid → gas: sublimation

solid → liquid: melting

## The International System of Units

**SI base units**

The preferred system of units used in scientific work is the metric system. All measurements are expressed in terms of one set of metric units called SI units (International System of units). There are 7 base SI units:

- length ⇒ meter = m
- mass ⇒ kilogram = kg
- temperature ⇒ kelvin = K
- time ⇒ second = s
- electric current ⇒ ampere = A
- amount of substance ⇒ mole = mol
- luminous intensity ⇒ candela = cd

**Prefixes used with SI units**

In the metric system, the designations of multiples and subdivisions of any unit can be obtained by adding a prefix to the name of the unit. The common prefixes for SI units are:

peta- (= P) ⇒ 10^{15}

tera- (= T) ⇒ 10^{12}

giga- (= G) ⇒ 10^{9}

mega- (= M) ⇒ 10^{6}

kilo- (= k) ⇒ 10^{3}

hecto- (= h) ⇒ 10^{2}

deca- (= da) ⇒ 10^{1}

deci- (= d) ⇒ 10^{-1}

centi- (= c) ⇒ 10^{-2}

milli- (= m) ⇒ 10^{-3}

micro- (= m) ⇒ 10^{-6}

nano- (= n) ⇒ 10^{-9}

pico- (= p) ⇒ 10^{-12}

femto- (= f) ⇒ 10^{-15}

## Scientific Measurement

**Temperature (T)**

2 temperature scales are used in chemistry: the Kelvin scale (SI unit K) and the Celsius scale (°C). Outside of scientific circles, the Fahrenheit scale is the one most used in US

T (in K) = T (in °C) + 273.15

T (in °F) = $\frac{9}{5}$ x T (in °C) + 32.0

**Volume (V) and density ( d)**

The derived SI unit for volume is the cubic meter (m^{3}) but a more convenient measure of volume is liter (L)

1L = 1 dm^{3} and 1 m^{3} = 1000 L

Density is the ratio of mass to volume and is usually expressed in kg.m^{-3}

*d* = $\frac{\mathrm{m}}{\mathrm{V}}$

m = mass (in kg)

V = volume (in m^{3})

**Energy (E) and Power**

Energy can be defined as the ability to cause a change in a physical system. This quantity is expressed in joule (J) which is equivalent to kg.m^{2}.s^{-2}

Law of conservation of energy: E_{total} = E_{k} + E_{p} = constant

Kinetic Energy (E_{k}): energy associated with a moving object

E_{k} = $\frac{1}{2}$ mv^{2}

m =mass of the object (in kg)

v = velocity of the object (in m.s^{-1})

Potential Energy (E_{p}): energy of an object due to its location relative to a reference point. If the ground is the reference point:

E_{p} = mgh

m = mass (in kg)

g = the gravitational acceleration constant = 9.81 m.s^{-2} (on Earth)

h = the height (in m)

Power can be defined as the rate at which energy is produced or utilized. This quantity is expressed in watt (W) which is equivalent to J.s^{-1}

## Uncertainty in Measurement

**Precision vs. accuracy**

Precision refers to how close a series of replicate measurements are to one another

Accuracy refers to how close a measurement/result is to the actual value. Percentage error can be used to measure accuracy:

% error = $\left|\frac{\mathrm{average}\mathrm{value}-\mathrm{true}\mathrm{value}}{\mathrm{true}\mathrm{value}}\right|\times 100$

**Significant Figures:**

Meaningful digits in a measured or calculated value that specify the uncertainty of the mesurement. The rules for determining the number of significant figures are:

- Non-zero digits are always significant
- Any zeros between two significant digits are significant
- Zeros to the left of the first non-zero digit are not significant
- Zeros to the right of the last non-zero digit are significant if the number contains a decimal point
- Zeros to the right of the last non-zero digit in a number without a decimal point may or may not be significant ⇒ scientific notation should be used to avoid ambiguity in such cases

0.0

51has 2 significant figures

0.0510has 3 significant figures

5.100x 10^{3}has 4 significant figures

Numbers that can be counted exactly are considered exact numbers. They have no limit to their precision (may be treated as having an infinite number of significant figures) and do not limit the number of significant figures in a calculated result

10 persons in a room ⇒ exact number ⇒ infinite number of significant figures

## Calculated Numerical Results

**Addition and subtraction:**

- Count the number of significant figures in the decimal portion of each number
- Add or subtract in the normal fashion
- The final answer cannot have more significant figures to the right of the decimal point than any of the original numbers

5.05 – 3.229 = 1.821

5.05 ⇒ 2 digits after the decimal point

3.229 ⇒ 3 digits after the decimal point

The final answer cannot have more than 2 digits after the decimal point and is therefore rounded to 1.82

**Multiplication and division:**

- Count the number of significant figures of each number
- Multiply or divide in the normal fashion
- The number of significant figures in the final answer is determined by the original number that has the smallest number of significant figures

2.1 x 0.0568 = 0.11928

2.1 ⇒ 2 significant figures

0.0568 ⇒ 3 significant figures

The final answer must have 2 significant figures and is therefore rounded to 0.12

## Dimensional Analysis

**Conversion factor:**

A fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. Because the numerator and denominator express the same quantity, this fraction is equal to 1

$\frac{3600\mathrm{s}}{1\mathrm{hour}}$ is the conversion factor to convert hours to seconds

**Dimensional analysis:**

The use of conversion factors in problem solving to convert one type of unit to another, while keeping the same quantity

Convert 2.0 m^{3}in liters:Conversion factors: $\frac{1000{\mathrm{dm}}^{3}}{1{\mathrm{m}}^{3}}$ and $\frac{1\mathrm{L}}{1{\mathrm{dm}}^{3}}$

Dimensional analysis: 2.0 m

^{3}x $\frac{1000{\mathrm{dm}}^{3}}{1{\mathrm{m}}^{3}}$ x $\frac{1\mathrm{L}}{1{\mathrm{dm}}^{3}}$ = 2000 L

Answer: 2.0 m^{3}= 2000 L

Convert 50 miles.hour^{-1}in m.s^{-1}:Conversion factors: $\frac{1.61\mathrm{km}}{1\mathrm{mile}}$ ; $\frac{1000\mathrm{m}}{1\mathrm{km}}$ ; $\frac{1\mathrm{hour}}{3600\mathrm{s}}$

Dimensional analysis: 50 miles.hour

Answer: 50 miles.hour^{-1}= $\frac{50\mathrm{miles}}{1\mathrm{hour}}$ x $\frac{1.61\mathrm{km}}{1\mathrm{mile}}$ x $\frac{1000\mathrm{m}}{1\mathrm{km}}$ x $\frac{1\mathrm{hour}}{3600\mathrm{s}}$ = 22.4 m.s^{-1}^{-1}= 22.4 m.s^{-1}

### Check your knowledge about this Chapter

Multiply the decimal number by 10 raised to the power indicated.

1.23 x 10^{3} = 1.23 x 1,000 = 1,230

1.23 x 10^{-3} = 1.23 x 0.001 = 0.00123

When adding or subtracting numbers in scientific notation, the exponents must be the same.

Step 1: adjust the powers of 10 in the 2 numbers so that they have the same exponent.

Step 2: add or subtract the decimal parts.

Step 3: rewrite the result in scientific notation.

Step 1: group the decimal parts and multiply them.

Step 2: add the exponents.

Step 3: rewrite the result in scientific notation.

Step 1: group the decimal parts and divide them.

Step 2: add the exponents of the numerators, subtract the result by the exponents of the denominators.

Step 3: rewrite the result in scientific notation.

The 2 temperature scales used in chemistry are the Celsius scale (°C), and the absolute or Kelvin scale (K). Outside of scientific circles, the Fahrenheit temperature scale is the most widely used in the United States.

We use the following equation to convert a temperature from units of degrees Celsius to Kelvins: K = °C + 273.15

Density is the ratio of mass to volume.

The volume of a substance is equal to the mass divided by the density of the substance.

The SI unit of mass is kg, that of volume is m^{3}, and that of density is kg.m^{-3}.

A joule (J) is equivalent to kg.m^{2}.s^{-2} in SI units.

The kinetic energy of an object is equal to half of its mass multiplied by the velocity squared.

The potential energy of an object relative to a reference point is equal to its mass (in kg) multiplied by the gravitational acceleration constant (9.81 m.s^{-2} on Earth) multiplied by the height of the object relative to the reference point (in m).

During any process, energy is neither created nor destroyed. Energy can be converted from one form to another or transferred from one system to another, but the total amount of energy never changes.

Due to the law of conservation of energy, E_{total} = E_{kinetic} + E_{potential} = constant

Power can be defined as the rate at which energy is produced or used. This quantity is expressed in watt (W) which is equivalent to J.s^{-1}.

Accuracy refers to how close a measurement/result is to the actual value while precision refers to how close a series of replicate measurements are to one another.

- Non-zero digits are always significant
- Any zeros between two significant digits are significant
- Zeros to the left of the first non-zero digit are not significant
- Zeros to the right of the last non-zero digit are significant if the number contains a decimal point

- Count the number of significant figures in the decimal portion of each number
- Add or subtract in the normal fashion
- The final answer cannot have more significant figures to the right of the decimal point than any of the original numbers

- Count the number of significant figures of each number
- Multiply or divide in the normal fashion
- The number of significant figures in the final answer is determined by the original number that has the smallest number of significant figures

Dimensional analysis is a technique used to convert the value of a physical quantity from one system of units to another system of units, while keeping the same quantity.

There are 7 fundamental dimensions in terms of which the dimensions of all other physical and chemical quantities may be expressed: length, mass, temperature, time, electric current, amount of substance, and luminous intensity.

- 2 physical quantities can only be compared if they have the same dimension
- 2 physical quantities can only be added or subtracted if they have the same dimensions
- The dimensions of the multiplication or division of 2 quantities are given by the multiplication or division of their dimensions of these 2 quantities

The principle of homogeneity states that the terms of an equation will have the same dimension on both sides. This principle is based on the fact that only physical quantities having the same dimension can be compared, added or subtracted.

A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. It is used to change one set of units into another without changing the value.

Since the numerator and denominator of conversion factor express the same quantity, this fraction is always equal to 1.