Worked examples concentration

Worked Example 5.7 What is the concentration of molecular oxygen in water at 25 °C The atmosphere above the water has a pressure of 105 Pa and contains 21 per cent of oxygen. 

Worked Example 6.1 What is the concentration of the solvated proton in super-pure... 

Worked Example 6.2 What is the pH of bench nitric acid having a concentration of 0.25 mol dm-3 ... 

Worked Example 6.3 What is the concentration of nitric acid having a pH of 3.5 Inserting values into Equation (6.21) ... 

Worked Example 6.4 Without using a calculator, what is the concentration of HNO3 solution if its pH is 4 ... 

Worked Example 6.5 What is the pH of a solution of sodium hydroxide of concentration 0.02 mol dm-3 Assume the temperature is 298 K. 

At first sight, this problem appears to be identical to those in previous Worked Examples, but we soon appreciate how it is complicated because we need first to calculate the concentration of the free protons before we can convert to a pH. However, if we know the concentration of the alkali, we can calculate the pH thus ... 

Equation (6.27) demonstrated how the concentration of the solvated protons equates to the concentration of a mono-protic acid from which it derived but, from Equation (6.28), the concentration of the solvated protons will be twice the concentration if the parent acid is di-protic. These different stoichiometries affect the pH, as demonstrated now by Worked Examples 6.6 and 6.7. 

Worked Example 6.6 Nitric acid of concentration 0.01 mol dm 3 is dissolved in water. What is its pH ... 

Worked Example 6.7 What is the pH of sulphuric acid having the same concentration in water as the nitric acid in Worked Example 6.6 ... 

A medicine or skin lotion is often described as pH neutral as though it was obviously a good thing. A solution is defined as neutral if it contains neither an excess of solvated protons nor an excess of hydroxide ions. Equation (6.4) tells us the autoprotolysis constant Kw of super-pure water (water containing no additional solute) is 10-14 (moldm-3)2. Furthermore, we saw in Worked Example 6.1 how the concentration of the solvated protons was 10-7 mol dm-3 at 298 K. 

By considering both the definition of pH in Equation (6.20) and the concentration of the solvated protons from Worked Example 6.1, we see how a sample of super-pure water - which is neutral - has a pH of 7 at 298 K. We now go further and say all neutral solutions have a pH of 7. By corollary, we need to appreciate how an acidic solution always has a pH less than 7. If the pH is exactly 7, then the solution is neutral. 

Worked Example 6.10 The methanoic acid from a nettle sting is extracted into 50 cm3 of water and neutralized in the laboratory by titrating with sodium hydroxide solution. The concentration of NaOH is 0.010 mol dm 3. The volume of NaOH solution needed to neutralize the acid is 34.2 cm3. What is the concentration c of the acid ... 

Unlike the Worked Example 6.9, we do not know the number of moles n of either reactant, we only know the volumes of each. But we do know one of the concentrations. 

Worked Example 6.11 A titration is performed with 25 cm3 of NaOH neutralizing 29.4 cm3 of nitric acid. The concentration of NaOH is 0.02 mol dm-3. Calculate the concentration of the acid. 

In practice, we obtain the end point by extrapolating the two linear regions of the pH curve (the extrapolants should be parallel). A third parallel line is drawn, positioned exactly midway between the two extrapolants. The volume at which this third line crosses the pH curve indicates the end point. Knowing the volume V(end point) > we can calculate the concentration of the acid via a calculation similar to Worked Example 6.11. 

Worked Example 6.12 We need to prepare a buffer of pH 9.8 by mixing solutions of ammonia and ammonium chloride solution. What volumes of each are required Take the Ka of the ammonium ion as 6 x 10 l0. Assume the two solutions have the same concentration before mixing. 

Worked Example 6.13 Consider the so-called acetate buffer , made with equal volumes of sodium ethanoate and ethanoic acid solutions. The concentration of each solution is 0.1 mol dm-3. A small volume (10 cm3) of strong acid (HC1 of concentration 1 mol dm 3) is added to a litre of this buffer. The pH before adding HC1 is 4.70. What is its new pH ... 

SAQ 6.14 Consider the ammonia-ammonium buffer in Worked Example 6.12. Starting with 1 dm3 of buffer solution containing 0.05 mol dm-3 each of NH3 and NH4CI, calculate the pH after adding 8 cm3 of NaOH solution of concentration 0.1 mol dm 3. 

The flask will contain a known volume of acid of unknown concentration, and we add alkali from a burette. We know we have reached neutralization when the Litmus changes from red (acid in excess) and just starts changing to blue. We know the pH of the solution is exactly 7 when neutralization is complete, and then note the volume of the alkali, and perform a calculation similar to Worked Example 6.11. 

Worked Example 7.12 Calculate the ionic strength of a simple 1 1 electrolyte, such as NaCl, that has a concentration of c = 0.01 mol dm ... 

Worked Example 7.14 Calculate the ionic strength of the 1 2 electrolyte Q1CI2, again of concentration 0.01 mol dm-3. 

Worked Example 7.15 What is the activity coefficient of copper in a solution of copper sulphate of concentration 10-4 mol dm 3 7... 

Worked Example 7.16 What is the activity coefficient of a solution of CuSC>4 of concentration 10 2 mol dm 3 ... 

A good example of a concentration cell would be the iron system in the worked example above, in which a(R) = a.cui = U accordingly, for simplicity here, we will assume that the reduced form of the couple is a pure solid. 

Worked Example 8.2 yields a value for the rate constant k, but an alternative and usually more accurate way of obtaining k is to prepare a series of solutions, and to measure the rate of each reaction. A graph is then plotted of reaction rate (as y ) against concentration(s) of reactants (as V) to yield a linear graph of gradient equal to k. 

Worked Example 8.7 Methyl ethanoate is hydrolysed when dissolved in excess hydrochloric acid at 298 K. The ester s concentration was 0.01 mol dm-3 at the start of the reaction, but 8.09 x 10 2 after 21 min. What is the value of the first-order rate constant k ... 

Worked Example 8.11 We encountered the dimerization of methyl viologen radical cation MV+ in Equation (8.6) and Worked Example 8.4. Calculate the value of the second-order rate constant k2 if the initial concentration of MV+ was 0.001 mol dm-3 and the concentration dropped to 4 x 10-4 mol dm-3 after 0.02 s. (The temperature was 298 K.)... 

Worked Example 8.12 Consider the data below, which relate to the second-order racem-ization of a glucose in aqueous hydrochloric acid at 17 °C. The concentrations of glucose and hydrochloric acid are the same, [A] . 

Worked Example 8.16 The reaction of the ester ethyl methanoate and sodium hydroxide in water is performed with NaOH in great excess ([NaOH]o = 0.23 mol dm-3). The reaction has a half-life that is independent of the initial concentration of ester present. 13.2 per cent of the ester remains after 14 min and 12 s. What is the second-order rate constant of reaction k2l... 

One of the most basic requirements in analytical chemistry is the ability to make up solutions to the required strength, and to be able to interpret the various ways of defining concentration in solution and solids. For solution-based methods, it is vital to be able to accurately prepare known-strength solutions in order to calibrate analytical instruments. By way of background to this, we introduce some elementary chemical thermodynamics - the equilibrium constant of a reversible reaction, and the solubility and solubility product of compounds. More information, and considerably more detail, on this topic can be found in Garrels and Christ (1965), as well as many more recent geochemistry texts. We then give some worked examples to show how... 

Worked Example 3.4. A sample of iron-containing ore is crushed and the powder extracted to form a clear aqueous solution. A clean iron rod is immersed into the solution and the cell Fe Fe " (aq) 11 SCE is therefore made. The emf at equilibrium was measured as 0.714 V at 298 K, and the SCE was the positive electrode. What is the concentration of the iron (Assume that all the iron exists as a simple aquo ion in the -1-2 oxidation state and that the solution is quiet .)... 

Worked Example 3.6. An old medicine bottle is discovered that once contained tincture of iodine. The bottle still contains a trace of solid iodine. Some of the solid is dissolved in an aqueous solution of potassium iodide of concentration 0.1 mol dm . The electrode potential of the I2,1 couple was determined at a platinum electrode immersed in the solution. If = —0.54 V and i,i for the resultant solution is —0.60 V, what is the concentration of the iodine Ignore the presence of the brown 13 ion. 

Worked Example 3.7. What is the ionic strength / of a 1 1 electrolyte such as NaCl, at a concentration of c ... 

Worked Example 3.10. Here, we will consider a real situation. There is thought to be contamination from a zinc smelting plant, so a sample of soil from near the smelter is collected and digested in sulfuric acid (of concentration 0.01 mol dm in order to leach out the soluble zinc as the sulfate salt. 

A lot, particularly at higher concentrations and higher ionic strengths This can be seen by considering the following worked example. 

Worked Example 3.11. We know the concentration of copper sulfate to be 0.01 mol dm from other experiments, and so we also know (from suitable tables) that the mean ionic activity coefficient of the copper sulfate solution is 0.404. The measured electrode potential was Ec j+ — 0.269 V and = 0.340 V. We will calculate the... 

Worked Example 6.2. Cadmium ion is reduced at a DME and the diffusion current measured as 24.3 pA. Previously, a sample of 2.0 x 10" mol dm" Cd was analysed at the same DME with the same drop time, and the diffusion current was then found to be 15.2 pA. What is the concentration of the sample (Assume that the residual current was known, and has been subtracted for both samples.)... 

Following the worked example above, what Is the concentration of diffusion current is 9.04 pA ... 

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