Chemistry I

Chapter 1R: Review

Units of Measurement

How do you quantify time? Depends on the application.

  • 30 s (in the microwave)
  • 50 min (of class)
  • 10 h (until bedtime)
  • 7 d (until next Friday)
  • 4 m (until your birthday)
  • 3 y (until graduation)

Measurement System

How do you quantify a length?

Imperial System of Measurement

  • in (relatively small lengths)
  • ft
  • yd
  • mile (relatively big lengths)

Metric System

  • millimeter (relatively small lengths)
  • centimeter
  • meter
  • kilometer (relatively big lengths)

Metric System

Some countries still use the imperial system. Science has adopted the metric system, a system of measurement that uses units with ratios that are multiples of 10.


Source: Wikimedia

SI Base Units

Science uses SI Units (International System of Units) to describe quantities. The base SI units are as follows:


Property Unit Abbreviation

Mass

kilogram

kg

Length

meter

m

Time

second

s

Temperature

kelvin

K

Amount of substance

mole

mol

Electric current

ampere

A

Luminous intensity

candela

cd

Metric Prefixes

Used to modify a basic unit

Prefix Abbeviation Meaning Example

Tera-

T

1012 (trillion)

1 terameter (Gm) = 1×1012 m

Giga-

G

109 (billion)

1 gigameter (Gm) = 1×109 m

Mega-

M

106 (million)

1 megameter (Mm) = 1×106 m

Kilo-

k

103 (thousand)

1 kilometer (km) = 1×103m

Deci-

d

10–1 (one tenth)

1 decimeter (dm) = 1×10–1 m

Centi-

c

10–2 (one hundredth)

1 centimeter (cm) = 1×10–2 m

Milli-

m

10–3 (one thousandth)

1 millimeter (mm) = 1×10–3 m

Micro-

μ

10–6 (one millionth)

1 micrometer (μm) = 1×10–6 m

Nano-

n

10–9 (one billionth)

1 nanometer (nm) = 1×10–9 m

Pico-

p

10–12 (one trillionth)

1 picometer (pm) = 1×10–12 m

Femto-

f

10–15

1 femtometer (fm) = 1×10–16 m

Example

Which quantity would be most appropriate for describing the distance between Athens, GA and Akron, OH (ca. 665 mi)?

  1. 1.07×108 cm (107 million cm)
  2. 1.07×106 m (1.07 million m)
  3. 1,069 km (1.07 thousand km)

Temperature

Relative Scale

Can be less than zero

Absolute Scale

Can never be less than zero

Temperature Scales


Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales are shown. The relative sizes of the scales are also shown.

Source: Openstax

Temperature Conversions

°F → °C

\[t/^{\circ}\mathrm{C} = \dfrac{\left ( t/^{\circ}\mathrm{F} - 32 \right )}{1.8}\]

°C → K

\[t/\mathrm{K} = t/^{\circ}\mathrm{C} + 273.15\]


°C → °F

\[t/^{\circ}\mathrm{F} = \left ( t/^{\circ}\mathrm{C} \times 1.8 \right ) + 32\]

K → °C

\[t/^{\circ}\mathrm{C} = t/\mathrm{K} - 273.15\]

Practice – Temperature

What is 93.0 °F in °C and K?



33.9 °C


307 K

Practice – Temperature

What is absolute zero (0 K) in °C and °F?



–273.15 °C


–459.67 °F

Exponents

\[b^n = \underbrace{b \times b \times \cdots \times b}_{n~\mathrm{times}}\]

\[10^1 = 10 \] \[10^2 = 10 \times 10 = 100\] \[10^3 = 10 \times 10 \times 10 = 1000\]

Exponents

\[b^{-n} = \underbrace{\dfrac{1}{b} \times \dfrac{1}{b} \times \cdots \times \dfrac{1}{b}}_{n~\mathrm{times}}\]

\[10^{-1} = \dfrac{1}{10} = 0.1\] \[10^{-2} = \dfrac{1}{10} \times \dfrac{1}{10} = 0.01\]

\[10^{-3} = \dfrac{1}{10} \times \dfrac{1}{10} \times \dfrac{1}{10} = 0.001\]

Scientific Notation

Used for small and big numbers

\[ 1,234 = 1.234\times 10^1 \times 10^1 \times 10^1 = 1.234\times 10^3 \]


\[ 0.01234 = 1.234 \times 10^{-1} \times 10^{-1} = 1.234\times 10^{-2} \]

or

\[ 0.1234 = \dfrac{1.234}{10^1\times 10^1} = 1.234\times 10^{-2} \]

Practice

Write the following numbers into scientific notation.


\[502\]

\[1,535,234\]

\[0.00008753\]

\[5.02\times 10^2\]

\[1.535234 \times 10^{6}\]

\[8.753\times 10^{-5}\]

Sci. Notation: Add and Subtract

\[3.4\times 10^{4} + 9.7\times 10^{5}\]

Transform each number into the same power of 10.

\[0.34\times 10^{5} + 9.7\times 10^{5}\]

Add or subtract the numbers.

\[10.04\]

Rewrite in scientific notation.

\[10.04 \times 10^{5} = 1.004 \times 10^6\]

Sci. Notation: Multiplying

Powers of 10 get added.

\[200 \times 100 = 20,000 = 2.00\times 10^{4}\]


\[\begin{align*} \left (2.00\times 10^{2} \right) \times \left (1.00 \times 10^{2}\right) &= \\[2ex] \left (2.00\times 1.00 \times 10^{2} \times 10^{2} \right) &= 2.00\times 10^4 \end{align*}\]

Sci. Notation: Dividing

Powers of 10 get subtracted.

\[\begin{align*} \dfrac{200}{100} = 2 &= 2\times 10^{0} \\[4ex] \dfrac{2.00\times 10^{2}}{1.00 \times 10^{2}} &= 2\times 10^0 = 2 \end{align*}\]

Significant Figures (digits)

Not all digits are significant. Here, the graduated cylinder is a “measuring stick” for volume. How accurate are we able to make a reading?

Significant Figures (digits)

We know by inspection that the water is clearly greater than 21 mL but less than 22 mL. We estimate that the water is perhaps 21.6 mL (at the meniscus).

The “2” and the “1” are certain but the 0.6 is uncertain. All certain/exact digits as well as the first uncertain/inexact digit are considered significant. Our measurement has three significant figures.

Source: Openstax

Significant Figures

The numbers you use in this class are treated as exact (infinite sig. figs.) or inexact numbers.

Exact

Obtained through counting

  • 3 pennies
  • 15 puppies
  • 130 students

Inexact

Obtained through measurement

  • length
  • mass
  • volume
  • temperature

See Significant Figures Rules

Unit Conversions

Imperial-to-metric conversions

  • Hard – inexact; conversion
  • Soft – exact; substitution

See table for some official SI Units and Conversions

For this class, treat all imperial-to-metric conversions as being exact.

See Conversions notes.

Measurements

Precision - indicates how well several measurements agree

Accuracy - the agreement of a measurement with the accepted value


Source: Openstax

Error

Measurements have error.


Experimental Error

“Error in measurement” can be an average value of n measurements.

\[\mathrm{error~in~measurement} = \mathrm{measured~value} - \mathrm{accepted~value}\]

Percent Error

\[ \%~\mathrm{error} = \dfrac{\mathrm{error~in~measurement}}{\mathrm{accepted~value}}\times 100\% \]

Practice

A coin has a diameter of 28.054 mm. Two people make a series of measurements (reported in mm). What is the average diameter and percent error obtained in each case? Which person was more accurate on average?


Person 1 Person 2

28.246

27.9

28.244

28.0

28.246

27.8

28.248

28.1

Person 1

Average: 28.246 mm

\[\begin{align*} \mathrm{\%~error} &= \dfrac{28.246~\mathrm{mm} - \mathrm{28.054~\mathrm{mm}}}{28.054~\mathrm{mm}}\\[1.5ex] &~~~~\times 100\% \\[1.5ex] &= 0.684\% \end{align*}\]

Person 2

Average: 27.95 mm

\[\begin{align*} \mathrm{\%~error} &= \dfrac{27.\bar{9}5~\mathrm{mm} - \mathrm{28.054~\mathrm{mm}}}{28.054~\mathrm{mm}}\\[1.5ex] &~~~~\times 100\% \\[1.5ex] &= -0.4\% \end{align*}\]

Person 2 was more accurate.

Types of Error

Determinate

identifiable; can be avoided

  • using impure reagents
  • underwashing glassware
  • overwashing precipitates
  • careless measuring

Indeterminate

random; arises from uncertainties in measurements

  • random fluctuations in measuring devices (e.g. background noise from signals)

Standard Deviation

The std. dev. of a series of measurements is equal to the

  1. square root of the sum (\(\Sigma\)) of the squares of the deviations (\(\left ( x_i - \bar{x} \right )^2\)) for each measurement (\(x_i\)) from the average (\(\bar{x}\))
  2. divided by one less than the number, N, of measurements

\[\mathrm{std.~dev.} = \sqrt{\dfrac{\sum{\left(x_i - \bar{x}\right)^2}}{N-1}}\]