Hydronium-ion concentration

Often k" is smaller than k° because attack on the dianion by hydroxide is disfavored. Moreover, the maximum often occurs on the acid side of neutrality. In the pH region near the maximum it will, therefore, often be permissible to set k" = 0 in Eq. (6-80). The result is differentiated and the derivative is set equal to zero, giving, for the hydronium ion concentration at the maximum in the bell. 

Setting the first derivative to zero gives Eq. (6-83) for the hydronium ion concentration at the left-hand minimum. 

EXAMPLE 10.4 Sample exercise Calculating the hydronium ion concentration from the pH... 

STRATEGY Calculate the hydronium ion concentration from the pH and then calculate the value of /C, from the initial concentration of the acid and the hydronium ion concentration. 

All three concentration ratios can he written in terms of the hydronium ion concentration. We simply rearrange the expressions for the first and second acidity constants ... 

In aqueous solutions of very weak acids, the autoprotolysis of water must be taken into account if the hydronium ion concentration is less than 10 6 mol-L The expressions for Kw and Ka are combined with the equations for charge balance and material balance to find the pH. 

A note on good practice Keep in mind the approximations required for the use of the Henderson-Hasselbalch equation (that the concentrations of both the weak acid and its conjugate base are much greater than the hydronium ion concentration). Because the equation uses molar concentration instead of activities, it also ignores the interactions between ions. 

Sulfides with widely different solubilities and solubility products can be selectively precipitated by adding S2 ions to the solution removed from the chlorides in the first step (see Fig. 11.20). Some metal sulfides (such as CuS, HgS, and Sb2S3) have extremely small solubility products and precipitate if there is the merest trace of S2" ions in the solution. Such a very low concentration of S2 ions is achieved by adding hydrogen sulfide, H2S, to an acidified solution. A higher hydronium ion concentration shifts the equilibrium... 

Below is the titration curve for the neutralization of 25 mL of a monoprotic acid with a strong base. Answer the following questions about the reaction and explain your reasoning in each case, (a) Is the acid strong or weak (b) What is the initial hydronium ion concentration of the acid (c) What is K, for the acid (d) What is the initial concentration of the... 

When a pH meter was standardized with a boric acid-borate buffer with a pH of 9.40, the cell emf was +0.060 V. When the buffer was replaced with a solution of unknown hydronium ion concentration, the cell emf was +0.22 V. What is the pH of the solution ... 

There are two solutions to this equation, but one gives a negative value for x. We know that x must be positive, because it represents the increase in hydronium ion concentration. Hence, we... 

The water equilibrium describes an inverse relationship between [H3 0+] eq nd [OH-]gq. When an acid dissolves in water, the hydronium ion concentration increases, so the hydroxide ion concentration must decrease to maintain the product of the concentrations at 1.0 X 10. Similarly, the hydroxide ion concentration increases when a base dissolves in water, so the hydronium ion concentration must decrease. 

As noted in Chapter an acid that quantitatively donates protons to water molecules is called a strong acid. Table lists the six most common strong acids HNO3, HCIO4, H2 SO4, HCl, HBr, and HI. In an aqueous solution of a strong acid, the hydronium ion concentration is equal to the concentration of the acid solution. The... 

This aqueous solution is 5.0 x 10 M HCIO4, so [ H3 O ] = [CIO4 ] = 5.0 x 10 M. The final concentrations are found using an equilibrium analysis. Set up a concentration table for the water dissociation equilibrium, and define the change in hydronium ion concentration as x ... 

In any solution of an acid, the total hydronium and hydroxide ion concentrations include the 10" M contribution from the water reaction. This example illustrates, however, that the change in hydronium ion concentration due specifically to the water equilibrium is negligibly small in an aqueous solution of a strong acid. This is true for any strong acid whose concentration is greater than 10 M. Consequently, the hydronium ion concentration equals... 

Set up a concentration table, defining the change in hydronium ion concentration as x ... 

The hydronium ion concentration in aqueous solution ranges from extremely high to extremely low. Here are three... 

Because hydronium concentrations usually involve negative powers of ten, chemists use a negative log scale in expressing these concentrations. Equation defines the pH scale of acid concentration pH = - log [H3 O ] The pH of a solution is obtained by taking the logarithm of the hydronium ion concentration and then changing the sign. For example, the pH of pure water is pH = - log [H3 O ] = - log (1.0 X 10 ) — -(-7.00) — 7.00 The reverse conversion from pH to [H3 O ] uses powers of 10. For example, lemon juice has a pH of about 2.0 ... 

A change in pH of one unit reflects a tenfold change in hydronium ion concentration Normal rainfall has pH 5, but acid rain has ten times larger hydronium ion concentration, pH 4. 

Figure 17-3 shows the range of pH and hydronium ion concentrations. The measurement of pH is a routine operation in most laboratories. Litmus paper, which turns red when dipped in acidic solution and blue when dipped in basic solution, gives a quick, qualitative indication of acidity. As Figure 17-4 shows, approximate measures of pH can be done using pH paper. Universal pH paper displays a range of colors in response to different pH values and is accurate to about 0.5 pH unit. For quantitative pH determinations, scientists use pH meters. 

A pH around 3 represents an acidic solution, so we expect the hydronium ion concentration to be much larger than the hydroxide ion concentration. Remember that although pH and. w are dimensionless, concentrations of solutes always are expressed In mol/L. Our results have two significant figures because the logarithm has two decimal places. 

A logarithmic scale is useful not only for expressing hydronium ion concentrations, but also for expressing hydroxide ion concentrations and equilibrium constants. That is, the pH definition can be generalized to other quantities pOH = - log [OH ] p Tg = - log Tg p log... 

To find the pH of a solution, first compute [H3 O ] or [OH ] and then apply Equation or. Sodium hydroxide is a strong base, and the water equilibrium provides the link between hydroxide and hydronium ion concentrations. 

Measurements of the pH of solutions of acids show that, except for strong acids, the hydronium ion concentration is smaller than would be expected if proton transfer were quantitative. An acid that reaches equilibrium when only a small fraction of its molecules has transferred protons to water is called a weak acid. One example is benzoic acid, treated in Example. A 0.125 M solution of this acid has [H3 ] = 0.0028 M (pH = 2.55). As... 

Although proton transfer is never complete for a weak acid dissolved in water, some proton transfer always occurs, so the hydronium ion concentration in any solution of a weak acid is greater than that in pure water. Consequently, the pH of an aqueous solution of a weak acid is always less than 7.00. 

We are asked to determine pH, which requires that we find the hydronium ion concentration. 

When a strong acid is added to a buffer solution, the conjugate base A accepts protons from hydronium ions to form the weak acid HA, preventing a large increase in hydronium ion concentration. (All water molecules except those produced in the proton transfer process are omitted for clarity.)... 

At the beginning of the titration, the diprotic acid (represented by H2 A) and H2 O are the only major species in the solution. As we describe in Chapter 17, the hydronium ion concentration can be calculated from the... 

To determine if the overaii caicuiation is reasonable, notice that the hydronium concentration in acid rain is five orders of magnitude higher than in pure water. This increased hydronium ion concentration can convert a substantiai amount of carbonate anions into hydrogen carbonate anions, promoting the soiubiiity of caicium carbonate. The resuiting equiiibrium concentration of caicium cations is about five orders of magnitude iarger than the concentration in a saturated soiution in pure water. 

Contemporary pH meters use single probes that contain two reference electrodes, shown diagrammatically in Figure 19-17Z). One electrode contains a buffer solution of known pH. A glass membrane separates this buffer solution from the solution whose pH is to be measured, so this electrode is called a glass electrode. Because hydronium ions participate in the cell reaction of the glass electrode, the overall cell potential depends on the hydronium ion concentration in the solution whose pH is being measured. 

Glass pH electrodes are simple to use and maintain. They respond selectively to hydronium ion concentration and provide accurate measurements of pH values between about 0 and 10. They can be small enough to be implanted into blood vessels or even inserted into individual living cells. In precision work, these electrodes are calibrated before each use, because their characteristics change somewhat with time and exposure to solutions. The electrode is dipped into a buffer solution of known pH, and the meter is electronically adjusted until it reads the correct value. 

Atmospheric O2 has a partial pressure of 0.20 bar, and atmospheric water vapor is saturated with carbon dioxide. This dissolved CO2 forms carbonic acid, which generates a hydronium ion concentration of about 2.0 X 10 M. The Nemst equation allows calculation of the half-cell potential for the reduction of 02(g) under these... 

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