Foundations of Chemistry. Philippa B. Cranwell

Foundations of Chemistry - Philippa B. Cranwell


Скачать книгу
Symbol Base unit Unit symbol Mass m kilogram kg Length l metre m Time t second s Electrical current I ampere A Temperature T kelvin K Amount of substance n mole mol

      This defines the unit of speed as metre per second or m/s. In chemistry, as in most other scientific subjects, this would be written as: m s−1, where the superscript ‘−1’ means ‘per second’.

      Dealing with exponents

      Exponents tell us how many times a number should be multiplied by itself. For example:

      

A special case is a0 = 1 To multiply quantities with exponents just add the exponents together:
To divide quantities with exponents subtract the exponents:

Quantity Unit name Symbol and base units
Area square metre m2
Volume cubic metre m3
Velocity (speed) metre per second m s−1
Acceleration metre per second squared m s−2
Density kilogram per cubic metre kg m−3
Concentration mole per cubic metre mol m−3
Energy joule J = kg m2 s−2
Force newton N = J m−1 = kg m s−2
Pressure pascal Pa = N m−2 = kg m−1 s−2
Frequency hertz Hz = s−1

      It is very important when carrying out calculations to keep track of the units, as you will be expected to quote the units of your answers. Units of each value in a calculation multiply or cancel with each other, as shown in the example here:

       Acceleration is defined as the change in velocity (speed) divided by the time taken and can be represented by this equation: acceleration = .

       Replacing the quantities with their units, we obtain: acceleration = .

       The unit can also be written as s−1, so the units for acceleration are m s−1 × s−1.

       To multiply s−1 by s−1, we simply add the −1 superscripts: acceleration = m s−1 × s−1 = m s−2.

       If we know the speed of an object and wish to determine how far it travels in a certain time, we multiply the speed by the time: distance = speed × time.

       Inserting the units for speed and time gives us the unit for distance = m s−1 × s.

       To multiply s−1 by s, again we add the superscripts: distance = m s−1 × s = m. This gives us the answer for distance in the correct units of metres. You should always check your answer when doing calculations to make sure that the value you obtain and the units are sensible.

      Worked Example 0.1

      Determine the derived units for the following quantities using the definitions given:

      1 density =

      2 entropy =

      3 pressure =

      4 power =

       Solution

      1 density = = kg m−3

      2 entropy = = = kg m2 s−2 K−1

      3 pressure = = = = kg m s−2 × m−2 = kg m−1 s−2

      4 power = = = = kg m2 s−2 × s−1 = kg m2 s−3


Скачать книгу