Acids & Bases Lesson 5 pH scale

H and OH There is a way we can connect both H and OH together, using what we already know about them. We know: Kw = [H + ][OH - ]= 1.0x

H and OH We can create a scale for the concentrations of H + [H + ] or [H 3 O + ] We can choose to make this scale go from 10 0 to remember; 10 0 = 1

This represents [H + ] going from 1.0 M to 1.0 x M. In other words, going from 1.0 M strong acid to 1.0 M strong base. [OH - ]= 1.0x = 1.0 x = 1.0 M [H + ] 1.0 x Let us simplify those powers of 10 and get them into whole numbers! HCl 1 M H+H+ H 2 O NaCl OH - NaOH 1 M

What if we take the log of -[H + ]? We can call this pH. pH=-Log 10 [H + ] *p comes from “potenz” in German, which means “power” Hence, pH represents powers of 10 of [H + ] We will always use logs to the base 10, and so we will not keep writing 10 as a base anymore. HCl 1 M H+H+ H 2 O NaCl OH - NaOH 1 M

pH=-Log[H + ] Ex: pH = -Log [10 -2 ] = -2 log10= 2 x 1= 2 If I take -Log[H + ] for every value of [H + ], I get the new scale in blue called the pH scale, going from “Nice easy whole numbers” This is the pH scale that goes from 0-14 ( strong acids  strong bases)

pH=-Log[H + ] For each 1 unit change of pH, the [H + ] changes by a factor of 10 x. This is the nature of the logarithm. 1.If [H + ] increases by 100 xpH decreases by 2 2.If [H + ] decreases by 1000 x the pH increases by 3 3.If the pH increases by 2 unitsthe [H + ] decreases by 100 x The pH Scale pH If the pH is lower than 7, the solution is acidic! If the pH is greater than 7, the solution is basic! If the pH is exactly 7, the solution is neutral!

The pH scale has three important end points. pH 0Strong Acid1.0 M HCl 7NeutralH 2 O or NaCl 14Strong Base1.0 M NaOH pH

pH A B C D E Match each letter with a formula. All are 1.0 M NH 3 HCl KOH HF H 2 O weak baseD strong acidA strong baseE weak acidB neutralC

What do we want to take from all of this??

pHEquations You must know the following equations, which are all based on the ionization of water at 25 0 C! H 2 O ⇄ H + +OH - Kw=[H + ][ OH - ]=1.00 x pH=-Log[H + ]OrpOH=-Log[OH - ] pH+pOH=pKw=14.000

Some math stuff! We are gonna get you from here….to here!

OperationInverse - Log x 10 x x ÷ Log= 2 All logs have the base 10. It makes your life easy as we deal with powers of 10’s all the time in our calculations. For ex: log(10 3 ) = log(0.01)= log (10 -2 )= log(10 -5 )=

One more piece of info. needed Log (10 M X l0 Y ) = Log (10 M ) + log (l0 Y ) Very, very important for us… For ex: Log ( 3.94 x ) log ( 3.94 ) + log ( )

Why so important? Most of our calculations will look like this: If [H 3 O + ] = 3.51 x M, what is pH? pH= -log [H + ] or pH= -log [H 3 O + ] pH = -log (3.51 x ) = - log (3.51) + -log ( )

Sig Figs and pH 1.00 x M 3 sig figs-Log 1.00 x = sig figs The 4 is from the which does not count for sig figs For pH or pOH, only digits after the decimal are significant This can also be summarized as: when taking the log of a number, your final answer will have the same number of decimals places as there are significant figures in the original number

Converting from pH to [H ] and [OH - ] Remember, pH= -log [H + ], to get [H + ] we take the anti-log. [H + ]= anti-log (-pH) On your calculator: press 2 nd then log, then enter (-pH) [H + ]= 10 -pH Or [OH - ]= 10 -pOH

Examples: If pH = 3.405, what is [H + ] and [OH - ] ?? [H + ]= 10 -pH [OH - ]= 10 -pOH pH + pOH = pKw =

pHCalculations [H + ][OH - ]pHpOH 2.5 x M Calculation

pHCalculations [H + ][OH - ]pHpOH 2.5 x M CalculationThe number of sig figs are 2 (green)

pHCalculations [H + ][OH - ]pHpOH 2.5 x M CalculationpH = -Log[H + ] pH = -Log[2.5 x ] pH = 3.60 The digit before the decimal does not count as a sig fig. Both digits after the decimal count for 2 sig figs.

pHCalculations [H + ][OH - ]pHpOH 2.5 x M3.60 CalculationpH = -Log[H + ] pH = -Log[2.5 x ] pH = 3.60 keep all digits on the calculator- do not round!

pHCalculations [H + ][OH - ]pHpOH 2.5 x M3.60 CalculationpH + pOH = pOH = pOH = 10.40

pHCalculations [H + ][OH - ]pHpOH 2.5 x M Calculation[OH - ]=10 -pOH [OH - ]= [OH - ]=4.0 x M

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M CalculationNote that all of the entries in the last line have two sig figs!

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M CalculationpH + pOH = pOH = pOH = 4.565

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M Calculation[OH - ]=10 -pOH [OH - ]= [OH - ]=2.72 x M

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M Calculation[H + ][OH - ]=1.00 x [H + ][2.72 x ]=1.00 x [H + ]=3.67 x M

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M CalculationNote that all of the entries in the last line have three sig figs!

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x MTRY CalculationpOH = -Log[OH - ] pOH = -Log[2.6 x ] pOH = 3.59

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M3.59 CalculationpH + pOH = pH = pOH = 10.41

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M Calculation[H + ]=10 -pH [H + ]= [H + ]=3.8 x M

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M 2.6 x M CalculationNote that all of the entries in the last line have two sig figs!

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M 2.6 x M Try

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M 2.6 x M x M8.40

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M 2.6 x M x M8.40

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M 2.6 x M x M4.0 x M8.40

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M 2.6 x M x M4.0 x M

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M x M2.72 x M x M 2.6 x M x M4.0 x M CalculationNote that all of the entries in the last line have two sig figs!

pHCalculations [H + ][OH - ]pHpOH 2.5 x M4.0 x M3.60acid x M2.72 x M9.435basic x M 2.6 x M10.41basic x M4.0 x M5.60 acid8.40 If the pH is lower than 7, the solution is acidic! If the pH is greater than 7, the solution is basic!

Homework Logs and anti-logs p.134 #47 p.135 #48 p. 139 #49, 50 p. 141 #55, 56