Download Derived SI Units

Derived SI Units.
The units for a number of other quantities can be derived from the SI base units. For example, from the base unit
of length, we can define volume, and from the base units of length, mass, and time, we can define energy. The
following quantities are frequently encountered in the study of chemistry:
Volume. Since volume is length cubed, its SI derived unit is m3. Related units are the cubic centimeter (cm3) and
the cubic decimeter (dm3).
Another common unit of volume is the liter (L). A liter is the volume occupied by one cubic decimeter. One liter
of volume is equal to 1000 mililiters (mL), and one mililiter of volume is equal to one cubic centimeter.
Velocity and Acceleration.
By definition, velocity is the change in distance with elapsed time; that is,
Acceleration is the change in velocity with time; that is,
accelerati on 
velocity 
distance
time
change in velocit y
time
Therefore, velocity has the units of m/s, and acceleration has the units of m/s2. Velocity is needed to define
acceleration, which in turn is required to define force and hence energy. Both force and energy play important
roles in many areas in chemistry.
Force. According to Newton´s second law of motion force = mass x acceleration. In common language, a force
is often regarded as a push or a pull. Chemistry is concerned mainly with the electrical forces that exist among
atoms and molecules. The derived SI unit for force is the newton (N), where 1 N = 1kg m/s2
Pressure is defined as force applied per unit area, that is,
pressure 
force
area
The force experienced by any area exposed to Earth´s atmosphere is equal to the weight of the column of air
above it. The pressure exerted by this column of air is called atmospheric pressure. The actual value of
atmospheric pressure depends on location, temperature, and weather conditions. A common reference pressure
of one atmosphere (10atm) represents the atmospheric pressure exerted by a column of dry air at sea level and
0°C. The derived SI unit of pressure is obtained by applying the derived force unit of one newton over one
square meter, which is the derived unit of area. A pressure of one newton per square meter (1 N/m2) is called a
pascal (Pa).
Energy is the capacity to do work or to produce change. In chemistry, we are interested mainly in energy effects
that result from chemical or physical changes. In mechanics, work is defined as “force x distance”. Since energy
can be measured as work, we can write energy = force x distance. Thus SI derived unit of energy has the units of
newtons x meter or kg m2/s2. This unit is more commonly called a joule (J). Traditionally, chemists have
expressed energy in calories (cal). The calorie is defined by the relationship 1 cal= 4.184 J.
The density of an object is the mass of the object divided by its volume: density 
mass
volume
Note that the density of a given material does not depend on the quantity of mass present. This is because V
increases as m does, so that the ratio of the two quantities always remains the same for the given material. Thus
density is an intensive quantity. The SI derived unit for density is the kilogram per cubic meter (kg/m3). This unit
is awkwardly large for most chemical applications. The unit g/cm3 and its equivalent, g/mL, are more commonly
used for solid and liquid densities. Because gas densities are often very low, we use the units of g/L.
Temperature Scales. Three temperature scales are currently in use. Their units are K (kelvin), °C (degree
Celsius), and °F (degree Fahrenheit). The Fahrenheit scale defines the normal freezing point of water to be
exactly 32°F and boiling point 212°F. It is the most commonly used temperature scale in the US. The Celsius
scale divides the range between the freezing point (0°C) and boiling point (100°C) of water into 100 degrees.
The Celsius scale is the most generally used scale in science. The size of a degree on the Fahrenheit scale is only
100/180, or 5/9 times that on the Celsius grade.
To convert degrees Fahrenheit to degrees Celsius, we To convert degrees Celsius to degrees Fahrenheit, we
write
write
In 1848 Lord Kelvin identified the temperature -273.15°C as theoretically the lowest attainable temperature,
called absolute zero. With absolute zero as a starting point, he set up an absolute temperature scale, now called
the Kelvin temperature scale. One degree Celsius is equal in magnitude to one kelvin. The only difference
between the absolute temperature scale and the Celsius scale is that the zero position is shifted. The relationship
between °C and K is: T (K) = t (°C) + 273.15 °C or K = (°C + 273.15°C)
By convention we use T to denote absolute (kelvin) temperature and t to indicate temperature on the Celsius
scale.
Task 1. A piece of platinum metal of mass 96.4 g has
a volume of 4.49 cm3. Calculate the density of the
element platinum (Pt).
Task 2. The density of ethanol is 0.798 g/ml. Calculate
the mass of 17.4 mL of the liquid.
Task 3. The normal body temperature is 98.6°F. What
is the temperature in degrees Celsius?
Task 4. Calculate the temperature in degrees Celsius
of the following: a) hot summer day of 95°F,
b) a cold winter day of 12°F, c) a fever of 102°F,
d) a furnace operating at 1852°F.
Task 5. What are the units normally used for density?
Task 6. Mercury is the only metal that is a liquid at room temperature. Its density is 13.6 g/mL. How many
grams of mercury will occupy a volume of 95.8 mL?
Task 7. If the temperature is 75°F, what is it in K?