C4S: ACID BASE EQUILIBRIUM Lesson 3

Transcription

1 C4S: ACID BASE EQUILIBRIUM Lesson 3 Defining ph and poh We already know that in an acidic solution, [H3O + ] is greater than [OH ]. In an alkaline or basic solution, [OH ] is greater than [H3O + ]. If a solution is neutral, that is in pure water, hydronium and hydroxide ion concentrations are equal. Most solutions chemists use have a very small hydronium ion concentration. For example, if you have a swimming pool, you must keep the hydronium ion concentration at around 4 x 10 8 mol/l, about the same as in blood. Even stomach acid is only about 0.01 mol/l HCl. As you can see, using concentration values of hydronium ions or hydroxide ions to describe the acidity or alkalinity of a solution can be quite cumbersome. In 1909, a Danish chemist, named Soren Sorensen ( ), developed a simplified system for referring to the degree of acidity of a solution. He used the ph or the potenz (power) of hydrogen. Therefore, ph describes the concentration of the hydronium or hydrogen ions in solution. ph is defined as the negative logarithm of the hydronium ion concentration, or ph = log[h3o + ] or ph = log[h + ] (We will use the H3O + ion and H + ion interchangeably.) Similarly, poh is defined as the negative logarithm of the hydroxide ion concentration, or poh = log[oh ] Logarithms As with exponents, logarithms, or logs, are a way of working with very large and very small numbers. (If you are familiar with logarithms, this will be a review and you may go to the next page.)

2 A number's base 10 or common logarithm is its exponent when 10 is the base. For example, The logs of other numbers are not whole numbers, but the process is the same: A number greater than one represents a positive log and a number less than one results in a negative log: log(0.001) = 3 or = 10 3 log( ) = or = To calculate "log( )" on your calculator, it depends on the type of calculator you have: press then enter and press "="or enter then press You should try this on your calculator to determine the correct method for the calculator you own. Find the log of each of the following values: a) 1.3 x 10 5 b) 7.2 x c) Answers a) log(1.3 x 10 5 ) = 4.82 b) log(7.2 x ) = c) log(0.0054) = 2.26

3 The ph Scale Values for ph in most solutions range from 0.0 to Pure water is considered to be neutral, or a ph of 7.0. The lower the ph, the more acidic the solution. The higher the ph the more alkaline or basic the solution. ph < 7 ph = 7 ph > 7 acidic neutral basic(alkaline) Below is a ph scale with the ph values of some common solutions. ph Calculations Example 1. Calculate the ph of an HCl solution whose concentration is 5.0 x 10 6 mol/l. Solution HCl is a strong acid. For this lesson, we will assume that all acids and bases completely ionizes or dissociate Therefore the hydronium ion concentration is equal to the concentration of the HCl. Calculate the log of the [H3O + ].

4 ph = log[h3o + ] ph = log(5.0 x 10 6 ) Change the sign to get the negative log. ph = ( 5.30) = 5.30 We will round the log to two decimal places. Example 2. The ph of a solution is Calculate the hydronium ion concentration in the solution. Solution We need to use the opposite of the log, called the antilog or inverse log. On your calculator the antilog function is usually above the log,. [H3O + ] = 10 ph Whencalculating the antilog, be sure to use the "+/ " button to make the negative of the ph value. [H3O + ] = [H3O + ] = 5.6 x 10 4 mol/l We will round the concentrations to one decimal place. ph Calculations Example 1. Calculate the ph of an HCl solution whose concentration is 5.0 x 10 6 mol/l. Solution HCl is a strong acid. For this lesson, we will assume that all acids and bases completely ionizes or dissociate Therefore the hydronium ion concentration is equal to the concentration of the HCl. Calculate the log of the [H3O + ]. ph = log[h3o + ] ph = log(5.0 x 10 6 )

5 Change the sign to get the negative log. ph = ( 5.30) = 5.30 We will round the log to two decimal places. Example 2. The ph of a solution is Calculate the hydronium ion concentration in the solution. Solution We need to use the opposite of the log, called the antilog or inverse log. On your calculator the antilog function is usually above the log,. [H3O + ] = 10 ph Whencalculating the antilog, be sure to use the "+/ " button to make the negative of the ph value. [H3O + ] = [H3O + ] = 5.6 x 10 4 mol/l We will round the concentrations to one decimal place. poh Recall, the ion product for water: KW = [H3O + ][OH ] If we take the negative log of each term, we get logkw = log[h3o + ] + ( log[oh ]) According to the rules of logs, when multiplying terms is equivalent to adding their logs. logkw = ph + poh If we calculate the negative log KW,

6 logkw = log(1.0 x ) = So, ph + poh = poh Recall, the ion product for water: KW = [H3O + ][OH ] If we take the negative log of each term, we get logkw = log[h3o + ] + ( log[oh ]) According to the rules of logs, when multiplying terms is equivalent to adding their logs. logkw = ph + poh If we calculate the negative log KW, So, logkw = log(1.0 x ) = ph + poh = poh Calculations Example 3. The ph of a solution is 10.30, what is the hydroxide ion concentration? Solution

7 Step 1. Find the poh From the previous page, poh = ph poh = = 3.70 Step 2. Convert poh to hydroxide ion concentration using the antilog function. We can make this conversion with poh just as we did with the ph. [OH ] = 10 poh [OH ] = [OH ] = 2.0 x 10 4 mol/l Example 4. What is the ph of a 5.0 x 10 5 mol/l Mg(OH)2 solution? Solution To calculate the ph we need hydronium ion concentration. We can calculate hydronium from the hydroxide ion concentration. Step 1. Calculate hydroxide ion concentration. Mg(OH)2 is an ionic base, so it dissociates completely. Mg(OH)2(s) Mg 2+ (s) + 2 OH (s) [OH ] = 2 x [Mg(OH)2] = 1.0 x 10 4 mol/l Step 2. We can use the ion product of water to calculate hydronium ion concentration. Step 3. Calculate ph ph = log[h3o + ] = log(1.0 x ) = Alternate Method: Determine poh then subtract from 14 to determine ph

8 poh = log[oh ] = log(1.0 x 10 4 ) = 4.00 ph = = Measuring ph There are two ways to measure ph: ph Meters Indicators ph Meters The most important part of the ph meter is the ph probe. The probe consists of two parts: the hydrogen sensitive bulb at the end of the probe and the reference electrode. The H + ion concentration inside the probe is compared to the H + ion concentration outside the probe. The probe acts like a battery whose voltage changes as the ph of the surrounding solution changes. A small electric current is sent to a meter proportional to the hydrogen ion

9 concentration in the solution surrounding the probe. For example, at ph 7.00 the probe produces zero volts. Before it is used, a ph probe must be calibrated. That is, it is inserted in a standard solution, whose ph is known. The meter is adjusted to read the correct ph. ph meters are becoming less expensive as technology improves. They can come in table top models or even small pocket-size meters. ph meters provide an almost instantaneous, accurate ph reading. They are not affected by the colour or cloudiness of the solution. Indicators An acid-base indicator is a weak acid or base that undergoes a colour change when they gain or lose hydrogen ions. The first indicators were dyes from natural sources, such as red cabbage juice, flower petal extracts, teas and fruit extracts. The ionization of the indicator establishes an equilibrium: Adding Acid HIn(aq) + H2O(l) H3O + (aq) + In (aq) colour 1 colour 2 Adding an acid increases [H3O + ]. According to Le Chatelier's Principle, increasing [H3O + ] causes a shift in the equilibrium to the left, in order to use up some of the added product. This decreases the [In (aq)] and increases the [HIn(aq)]. As HIn increases, its colour will increase. As In decreases, its colour decreases. The solution becomes colour 1. Adding Base Adding a base, decreases the [H3O + ]. This is because the OH ions from the base reacts with the H3O + ions from the indicator to form water. According to Le Chatelier's Principle, the equilibrium will shift left to replace the lost product. This increases the [In (aq)] and decreases the [HIn(aq)]. As HIn decreases, its colour will decrease. As In increases, its colour increases. The solution becomes colour 2. Common Indicators

10 Indicators are a convenient and inexpensive way to measure ph. The colour of each indicator can be coordinated with the ph. The colour of the indicator can be compared to a standard to determine the ph of the solution. Often, an indicator (or a combination of several indicators) can be incorporated into paper or plastic strips, making their use more convenient. You just dip the strip into the solution and the strip changes colour, depending on the indicators used and the ph of the solution. Using an indicator is not as accurate as a ph meter. Indicators are also affected by the colour of the solution. But, their ease of use and convenience makes them an invaluable tool in the lab. In fact, those of you with pools or hot tubs at home probably use a kit, that contains an acid-base indicator, to determine the water's ph. Here is a table of some common indicators and the ph range they measure:

11 Exercise Answer the following questions. Besure to show all your work. 1. Determine the ph of each of the following values a. [H + ] = b. [H + +] = c. [OH ] = d. [OH ] = e. [H + ] = f. [H + ] = g. [OH ] = h. [OH ] = Determine the concentration of [H + ] of each of the following. a. ph = 7.00 b. poh = 5.00 c. ph = d. poh = e. ph = 3.40 f. poh = 6.10 g. ph = 8.90 h. poh = Determine the poh of the following if the ph is given a. ph = 5.40 b. ph = 8.60 c. ph = 2.90 d. ph = Determine the concentration of the OH ions in the solutions with the following ph values. a. ph = 4.10 b. ph = 5.10 c. ph = 1.60 d. ph = Calculate ph of each of the following solutions. a mol/l HCl b mol/l NaOH c mol/l Ba(OH)2 d mol/l HNO3

12 Answer Key 1. Determine the ph of each of the following values a. ph = log[h + ] = log( ) = 6.00 b. ph = log[h + ] = log( ) = 8.00 c. poh = log[oh ] = log( ) = 2.00 ph = 14 poh = = d. d) poh = log[oh ] = log( ) = 5.00 ph = 14 poh = = 9.00 e. ph = log[h + ] = log( ) = 2.70 f. ph = log[h + ] = log( ) = 3.46 g. poh = log[oh ] = log( ) = 6.12 ph = 14 poh = = 7.88 h. poh = log[oh ] = log( ) = 8.05 ph = 14 poh = = Determine the concentration of [H + ] of each of the following. a. [H3O + ] = 10 ph = 10 7 = mol/l H3O + b. ph = 14 poh = = 9.00 [H3O + ] = 10 ph = 10 9 = mol/l H3O + c. [H3O + ] = 10 ph = = mol/l H3O + d. ph = 14 poh = = 3.00 [H3O + ] = 10 ph = 10 3 = mol/l H3O + e. [H3O + ] = 10 ph = = mol/l H3O +

13 f. ph = 14 poh = = 7.90 [H3O + ] = 10 ph = = mol/l H3O + g. [H3O + ] = 10 ph = = mol/l H3O + h. ph = 14 poh = = 0.20 [H3O + ] = 10 ph = = 0.63 mol/l H3O + 3. Determine the poh of the following if the ph is given a. poh = 14 ph = = 8.60 b. poh = 14 ph = = 5.40 c. poh = 14 ph = = d. poh = 14 ph = = Determine the concentration of the OH ions in the solutions with the following ph values. a. poh = 14 ph = = 9.90 [OH ] = 10 poh = = mol/l OH b. poh = 14 ph = = 8.90 [OH ] = 10 poh = = mol/l OH c. poh = 14 ph = = [OH ] = 10 poh = = mol/l OH d. poh = 14 ph = = 4.80 [OH ] = 10 poh = = mol/l OH 5. Calculate ph of each of the following solutions. a. a) HCl + H2O H3O + + Cl [H3O + ] = mol/l ph = log[h3o + ] = log(0.0020) = 2.70 b. b) NaOH Na + + OH [OH ] = 0.50 mol/l

14 ph = log[h3o + ] = log( ) = c. Ba(OH)2 Ba OH [OH ] = 2( mol/l) = mol/l ph = log[h3o + ] = log( ) = d. HNO3 + H2O H3O NO3 [H3O + ] = 0.50 mol/l ph = log[h3o + ] = log(0.50) = 0.30