Chapter 1 Scinece and Measurements

Matter and Energy

3 Phases of matter

Matter = has mass and occupies space

Solid -- fixed shape and fixed volume

Liquid -- no fixed shape, but fixed volume

Gas -- sparsely populated (no fixed volume) and no fixed shape

Ice	liquid water	steam

The red spheres represent molecules or atoms.

Energy

In order to convert one phase to another, it requires energy.

Energy is an important concept that allow us to understand many of the phenomena we study in this course.

Energy can be in the form of:

Heat -- In chemistry, we use heat for understanding chemical reactions

Mechanical Work (compression, expansioin, etc)

Units of Measurement

Metric System — Health Professionals use metric system, in particular, SI Unit is adapted as the standard for scientific and medical purposes.

Length

For measurement of length, we use meter, m

Volume

Volume is measured in 3-dimensions (length, height, and width), and we use L (or liter)

Mass

Unit of mass is in SI unit is: kilograms, abbreviated as kg.

Temperature

There are 3 scales: Celsius (°C), Fahrenheit (°F), and Kelvin (K)

0°C = freezing point of water, 100°C = boiling point of water

0°F = freezing point of brine, 100°F = average human body termperature

Kelvin Temp = Celsius Temp. + 273.15

Kelvin is the SI unit of temperature, abbreviated as K.

Time

We know what time is, and we measure time in hours, minutes, seconds, days, months, etc. The SI unit is second, abbreviated as s.

Energy

Unit of energy is: joules, abbreviated as J. We will also see calorie (cal) in this course.

1 cal = 4.184 J

Scientific Notation

It is often encoutered the situation where a number is written in the following way, 0.0000034 g. These leading zeros are cumbersome, and sometimes ambiguity can be introduced when using the floating point (or decimal) notation. So, the standard practice in science is to use scientific notation.

0.0000034 g is written as 3.4 x 10^-6 g .

The scientific notation is separated into two parts as

The first part is a number between 1 to 10, and it also determines how many digits we can trust in our measurements.

The second part is written in powers of 10. In this case, -6 is referred to as exponent. You know that 1/10 is 0.1, and further you know that 1/100 is 0.01. It can be written more mathematically

number	notation & explanation	exponent
1000000	106 $$1000000=10·10·10·10·10·10={10}^6$$	6
100000	105 $$100000=10·10·10·10·10={10}^5$$	5
10000	104 $$10000=10·10·10·10={10}^4$$	4
1000	103 $$1000=10·10·10={10}^3$$	3
100	102 $$100=10·10={10}^2$$	2
10	101	1
1	100	0
0.1	10-1 $$0.1=\frac{1}{10}={10}^{-1}$$	-1
0.01	10-2 $$0.01=\frac{1}{100}=\frac{1}{10·10}=\frac{1}{{10}^2}={10}^{-2}$$	-2
0.001	10-3 $$0.001=\frac{1}{1000}=\frac{1}{10·10·10}=\frac{1}{{10}^3}={10}^{-3}$$	-3
0.0001	10-4 $$0.0001=\frac{1}{10000}=\frac{1}{10·10·10·10}=\frac{1}{{10}^4}={10}^{-4}$$	-4
0.00001	10-5 $$0.00001=\frac{1}{100000}=\frac{1}{10·10·10·10·10}=\frac{1}{{10}^5}={10}^{-5}$$	-5
0.000001	10-6 $$0.000001=\frac{1}{1000000}=\frac{1}{10·10·10·10·10·10}=\frac{1}{{10}^6}={10}^{-6}$$	-6

Hint: It is easy to remember that

For positive exponent, the exponent is the number of zeros after 1
For example: 10⁶ is 1 with 6 zeros after. Hence 1 000 000 (1 million)

For numbers smaller than 1, the exponent is the number of leading zeros before 1, including the zero before decimal point
For example: 10^-5 is 0.000 01, as there are 5 zeros before 1

Measured Numbers & Significant Figures

Measured number always contains uncertainty!

Significant Figure = number of digits that you are able to measure, including last digit with estimation

So, in the following figure, how do you report?

The miniscus (lowest point of the red line) lies between 58 and 59. Therefore, you would report it as 58.5 mL, and reported as having three significan figures. Of course, how much of detail you can read, depends upon how large the scale is made on the instruments.

Since we can report 3 digits, it is said to have 3 significant figures.

Exact Numbers don't have significant figures associated with them. Exact numbers are definitions. For example, we know that 12 in = 1 ft. 1 ft is defined as 12 inches.

Significant Figures in Calculations

If not always, nearly all numbers you measured will be subjected to calculations, so it is quite important to know how to handle significant figures in the calculations.

In order to correctly use significant figures in calculations, you must know three things:

Rounding Off

Multiplication and Division

Adding Significant Zeros

Addition and Subtractions

Rounding Off

Let's say that you have done some calculations, and your calculator reads, 0.98601904761905, and you know you have 2 significant figures. You would then report as 0.99.

Rules for Rounding Off
1. If the first digits to be dropped is 4 or less, then it and all following digits are simply dropped.
2. If the first digit to be dropped is 5 or greater, then the last digits of the number is increased by 1.

Multiplication and Division

When two numbers are multiplied you retain the smaller significant figures of the two numbers.

Adding Significant Zeros

Often you encounter a situation that calculator give a whole number. For example, $$\frac{42.5}{8.5}$$ should give you 5 in the caluclator.

However, the numbers 42.5 has 3 and 8.5 has 2 significant figures. Therefore, overall significant figures in the reporting value is 2 sig. fig. So, you should report the value as 5.0 by adding trailing zero to 5.

Additon and Subtraction

Keep the least significant decimal places.

Say you are adding the following numbers, 4.111, 0.011, 2.01, and 2.2. So,

4.111	3 places after decimal point
0.011	3 places after decimal point
2.01	2 places
2.2	1 places ← least decimal place!
8.332
8.3	is the reported value

Significant Figures in Calculations

Often times, it is very cumbersome to write 0.0005 g of prescription drug, many times over. So we can use milligram instead. Milli is a prefix to the gram quantity, and it means 0.001 or one thousand^th. So, 0.0005 g = 0.5 mg. Easier to see, harder for workers to make mistakes.

You may know already some of the prefixes. How many bytes of disk do you have on your computer? If your computer is a laptop and relatively new, you may have 500 gigabytes (or Gb). Here giga is the prefix to byte, and it means 10⁹, so 500 Gb = 500 000 000 000 bytes!!

Another example may be much more to our everyday life. You know 100 pennies will make a dollar. Therefore, 100 cent = 1 dollar, then 1 cent = 1/100 dollar.

Similarly, 100 cm (centimeter) = 1 m, and centi is the prefix to meter. The followingi table gives you the necessary prefixes.

Prefix	Symbol	Multiplier
giga	G	1 000 000 000 = 109
mega	M	1 000 000 = 106
kilo	k	1 000 = 103
hecto	h	100 = 102
deka	da	10 = 101
		1 = 100
deci	d	0.1 = 10-1
centi	c	0.01 = 10-2
milli	m	0.001 = 10-3
micro	μ	0.000 001 = 10-6
nano	n	0.000 000 001 = 10-9
pico	p	0.000 000 000 001 = 10-12
femto	f	0.000 000 000 000 001 = 10-15

Measuring Length

In measuring anything, we tend to use appropriate unit. For example, we use cm for height. We measure the direct distance from LIU Brooklyn campus to Statue of Liberty by km. A nurse may measure the length of skin lesion with cm scale. These are appropriate for its size, but you should know how to convert between m to the cm, km, etc.

Measuring Volume

Volume is a cube of length, meaning that (side) x (depth) x (height) = volume and 1 cm³ = 1 mL = 10^-3 L is the starting point for conversions.

Measuring Mass

A body weight in metric system is generally obtained by using kg. 1 kg = 1000 g or 1 g = 10^-3 kg. Medicine and its active ingredients are measured often by mg.

Writing Conversion Factors

Conversion Factor is a number associated with two units. For example, speed is a conversion factor between distance (miles) and time (hour). We write the highway speed limit in much of NJ is 55 miles/hr (miles per hour), as you know. What it really means is that for a car traveling 55 mi/hr, 1 hour is equivalent to 55 mi of distance. Thus, 55 mi = 1 hr.

What about 1 year? 1 year is defined as one circulation of Earth, which takes 365 days to complete. Further 1 day is defined as 1 rotation of Earth, which takes 24 hours. Hence 1 year = 365 days, 1 day = 24 hrs.

Above shows how we calculate intuitively. However, if the calculation involves little more twist, it is not easy to come up with the answer. So, here we'll show you how to do this more systematically.

Dimensional Analysis (takes thinking away from calculations!)

I mean it. When you get used to this type of calculations, you don't have to think hard to arrive at answers. By simply setting up a calculation, as prescribed below, you get to do conversions in no time!

Metric Conversion Factors

Above mentioned prefixes is used to convert within metric system. So, for example, 1 km = 1000 m, 100 cm = 1 m, 1 μm = 10^-6 m, etc.

Metric-US System Conversion Facotrs

Here in the table below, common units we use and their conversion factors are listed.

Density, Specific Gravity, and Specific Heat

Density is given as the ratio between mass and volume, given by the following: $$d=\frac{m}{v}$$

Density can have many different units, g/mL, g/L, kg/L, μg/mL, g/cc, etc.

Water has density of about 1 g/mL, depending on temperature. Generally, solid has higher density than water, therefore when a metallic object is placed in water, it sinks.

What abou ice? Ice is the frozen or solid form of water. Water is peculiar because the solid is less dense than its liquid form. This is why ice floats on top of water.

Generally, specific gravity is measured by a hydrometer, looks like the following picture.

Density of Solid

You can measure density of solid substance in few different ways.

If the substance has definite shape or you can mold into some shape that you can measure, then you can measure the sides, for example, to obtain its volume. The mass can be always measured by using a balance.

If the substance has no definite shape, then you can use a graduated cylinder.

You can first weigh the sample on a balance to record its mass.

You fill water to a graduated cylinder to some amount, and record.

Place the substance in to the graduated cylinder, and re-measure the volume.

The difference between the two volumes gives the volume of the substance.

Calculations involving density.

Specific Gravity

Specific Gravity is the ratio of density of some substance with density of water. Density of water is about 1 g/mL depending on the temperature. $$sp·gr=\frac{densit{y}_{sample}}{densit{y}_{water}}$$ Hydrometer measures the specific gravity of substance. You may have seen it in homebrewer's shop. It is basically to measure the alcohol content of in the fermentation process.

Specific Heat

Specific heat is the amount of heat energy required to raise the temperature of 1 gram of the substance by 1°C.

Usually, we use the specific heat of water to be: $$H_{sp}\left(water\right)=\frac{1cal}{°C·g}$$ Calculations involving specific heat.

Temperature Conversions

You can use either $$T\left({}^{\circ }F\right)=\left(1.8·T\left({}^{\circ }C\right)\right)+32$$ or $$T\left({}^{\circ }C\right)=\frac{T\left({}^{\circ }F\right)-32}{1.8}$$ for conversions.

Extra Questions