# Scientific Notation

Scientific notation is used by biochemists to work with very small numbers. We write the first digit of a number followed by a decimal and then the rest of the number times 10 to the appropriate power.

^{-7}

This number could also be written as 523 X 10 ^{–9} or 52.3 X 10 ^{–8}. However, using scientific notation, we put the decimal after the first digit.

When we multiply two numbers using scientific notation, multiply the first numbers in each expression and add the exponents of 10.

For Example, multiply (5 X 10 ^{–7})(2 X 10 ^{–7}):

multiply (5)(2) = 10 and (10 ^{–7}) (10 ^{–7}) = (10 ^{–14})

The result is 10 X 10 ^{–14} or 1 X 10^{-13}

For example, divide 1 X 10^{-13} by 2 X 10^{ –7}:

First, divide ½ = 0.5

Next, subtract the exponent –7 from the exponent –13 = -6

The result is 0.5 X 10 ^{–6} or 5 X 10 ^{–7}.

# Ion Product of Water

Define the ion product for water! Given any hydroxide ion concentration, determine the hydrogen ion concentration and visa versa. Note!, this problem was not shown in class. Note!, the brackets designate concentration.

First Problem: The [H^{+}] of a solution is 5 X 10^{-5} M. What is the [OH^{-}]?

^{-14}= [H

^{+}] [OH

^{-}] = 5 X 10

^{-5}[OH

^{-}]

Since 1 X 10

^{-14 }= 10 X 10

^{-15}

[OH

^{-}] = (10 X 10

^{-15}) / (5 X 10

^{-5}) = 2 X 10

^{-10}

To check the problem:

(5 X 10^{-5})(2 X 10

^{-10}) = 10 X 10

^{-15}= 1 X 10

^{-14}

Second Problem: If you decreased the pH from 7.0 to 6.0, what would be the final hydroxide ion concentration of the solution?

^{-6}M.

Kw = 1 X 10^{-14} = [H^{+}] [OH^{-}]. or

[OH^{-}] = (1 X 10^{-14})/[H^{+}] = (1 X 10^{-14})/[1 X 10^{-6}] = 1 X 10^{-8}