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Chapter 6: Problem 80

The solubility of sodium bicarbonate in water is \(11.1 \mathrm{g} \mathrm{NaHCO}_{3} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) at \(30^{\circ} \mathrm{C}\) and \(16.4 \mathrm{g}\) \(\mathrm{NaHCO}_{3} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) at \(60^{\circ} \mathrm{C} .\) If a saturated solution of \(\mathrm{NaHCO}_{3}\) at \(60^{\circ} \mathrm{C}\) is cooled and comes to equilibrium at \(30^{\circ} \mathrm{C},\) what percentage of the dissolved salt crystallizes?

Short Answer

Expert verified
Approximately 32.32% of the dissolved salt crystallizes.

Step by step solution

01

Determine the initial amount of dissolved sodium bicarbonate

At 60掳C, the solubility of sodium bicarbonate is given as 16.4 g per 100 g of water. Given the solution described is saturated, this means that there are 16.4 g of sodium bicarbonate for every 100 g of water.
02

Determine the final amount of dissolved sodium bicarbonate

At 30掳C, the solubility of sodium bicarbonate is given as 11.1 g per 100g of water. This means that when cooled to 30掳C, only this amount of sodium bicarbonate can remain dissolved in 100g of water. The rest will crystallize.
03

Determine the amount of sodium bicarbonate that crystallizes

Subtract the final amount of dissolved sodium bicarbonate from the initial amount to determine how much sodium bicarbonate crystallizes. \[Crystallized = Initial - Final = 16.4g - 11.1g = 5.3g \]
04

Determine the percentage of sodium bicarbonate that crystallizes

The percentage of sodium bicarbonate that crystallizes can be determined by dividing the amount that crystallizes by the initial amount and multiplying by 100. \[Percentage = \frac{crystallized}{initial} * 100 = \frac{5.3g}{16.4g} * 100 鈮� 32.32% \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sodium Bicarbonate Crystallization
Sodium bicarbonate, commonly known as baking soda, is a compound that can dissolve in water to a certain extent. This solubility is not fixed and varies with changes in temperature. When a saturated solution of sodium bicarbonate is cooled, the amount of compound that water can hold in solution decreases.

This change leads to a process called crystallization, where the dissolved substance forms solid crystals. In the exercise, the crystallization occurs when the saturated solution at 60掳C is cooled to 30掳C. Since solubility decreases, the sodium bicarbonate that can no longer be kept in solution forms solid crystals.

Through crystallization, the solid sodium bicarbonate gets deposited, often adhering to a surface or forming at the bottom of the container. It's interesting to note that the purity of the crystallized substance is often high because typically, only the pure compound crystallizes out of the solution.
Temperature Effect on Solubility
Temperature is one of the key factors that affect the solubility of substances. The rule of thumb is that solubility of solids in liquids, such as sodium bicarbonate in water, generally increases with an increase in temperature.

Therefore, when the temperature of the solution is raised from 30掳C to 60掳C, as presented in the exercise, more sodium bicarbonate can dissolve. Conversely, when the solution is cooled, the solubility decreases which is why we observe crystallization of the excess sodium bicarbonate.

This relationship between temperature and solubility is crucial in many practical applications, such as in cooking, chemical synthesis, and preservation processes. Understanding this concept helps to manipulate conditions to either dissolve more of a substance or to crystallize it out from a solution.
Chemical Equilibrium
Chemical equilibrium refers to the state where the rate of the forward chemical reaction equals the rate of the reverse reaction, resulting in no net change in the amounts of reactants and products. It's a dynamic state where reactions are still occurring, but there's no observable change over time.

In the context of solubility, equilibrium is reached when the process of the substance dissolving is balanced with the process of the substance crystallizing. When the saturated solution of sodium bicarbonate is at equilibrium, the rate at which sodium bicarbonate dissolves in water equals the rate at which it crystallizes from the solution.

Whenever the conditions like temperature change, the solubility equilibrium is disturbed, initiating the process to re-establish a new equilibrium at the new temperature. This can result in either more of the solid dissolving or crystallizing out, as observed with the temperature-induced crystallization of sodium bicarbonate.

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Most popular questions from this chapter

Nitric acid is a chemical intermediate primarily used in the synthesis of ammonium nitrate, which is used in the manufacture of fertilizers. The acid also is important in the production of other nitrates and in the separation of metals from ores. Nitric acid may be produced by oxidizing ammonia to nitric oxide over a platinum-rhodium catalyst, then oxidizing the nitric oxide to nitrogen dioxide in a separate unit where it is absorbed in water to form an aqueous solution of nitric acid.The reaction sequence is as follows:$$\begin{aligned} 4 \mathrm{NH}_{3}+5 \mathrm{O}_{2} & \rightarrow 4 \mathrm{NO}+6 \mathrm{H}_{2} \mathrm{O} \\\4 \mathrm{NO}+2 \mathrm{O}_{2} & \rightarrow 4 \mathrm{NO}_{2} \\\4 \mathrm{NO}_{2}+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{O}_{2} & \rightarrow 4 \mathrm{HNO}_{3}(\mathrm{aq}) \end{aligned}$$.Ammonia vapor produced by vaporizing pure liquid ammonia at 820 kPa absolute is mixed with air, and the combined stream enters the ammonia oxidation unit. Air at \(30^{\circ} \mathrm{C}, 1\) atm absolute, and \(50 \%\) relative humidity is compressed and fed to the process. A fraction of the air is sent to the cooling and hydration units, while the remainder is passed through a heat exchanger and mixed with the ammonia. The total oxygen fed to the process is the amount stoichiometrically required to convert all of the ammonia to HNO \(_{3},\) while the fraction sent to the ammonia oxidizer corresponds to the stoichiometric amount required to convert ammonia to NO.The ammonia reacts completely in the oxidizer, with \(97 \%\) forming NO and the rest forming \(\mathrm{N}_{2}\). Only a negligible amount of \(\mathrm{NO}_{2}\) is formed in the oxidizer. However, the gas leaving the oxidizer is subjected to a series of cooling and hydration steps in which the NO is completely oxidized to \(\mathrm{NO}_{2}\) which in turn combines with water (some of which is present in the gas from the oxidizer and the rest is added) to form a 55 wt\% aqueous solution of nitric acid. The product gas from the process may be taken to contain only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\). (a) Taking a basis of \(100 \mathrm{kmol}\) of ammonia fed to the process, calculate (i) the volumes \(\left(\mathrm{m}^{3}\right)\) of the ammonia vapor and air fed to the process using the compressibility-factor equation of state; (ii) the amount (kmol) and composition (in mole fractions) of the gas leaving the oxidation unit; (iii) the required volume of liquid water \(\left(\mathrm{m}^{3}\right)\) that must be fed to the cooling and hydration units; and (iv) the fraction of the air fed to the ammonia oxidizer. (b) Scale the results from Part (a) to a new basis of 100 metric tons per hour of 55\% nitric acid solution.(c) Nitrogen oxides (collectively referred to as \(\mathrm{NO}_{x}\) ) are a category of pollutants that are formed in many ways, including processes like that described in this problem. List the annual emission rates of the three largest sources of \(\mathrm{NO}_{x}\) emissions in your home region. What are the effects of exposure to excessive concentrations of \(\mathrm{NO}_{x} ?\) (d) A platinum-rhodium catalyst is used in ammonia oxidation. Fxplain the function of the catalyst, describe its structure, and explain the relationship of the structure to the function.

You were recently hired as a process engineer by a pulp and paper manufacturing firm. Your new boss calls you in and tells you about a pulp dryer designed to reduce the moisture content of \(1500 \mathrm{kg} / \mathrm{min}\) of wet pulp from \(0.9 \mathrm{kg} \mathrm{H}_{2} \mathrm{O} / \mathrm{kg}\) dry pulp to \(0.15 \mathrm{wt} \% \mathrm{H}_{2} \mathrm{O}\). The design called for drawing atmospheric air at \(90 \%\) relative humidity, \(25^{\circ} \mathrm{C}, 760 \mathrm{mm}\) Hg into a blower that forces the air through a heater and into the dryer. When the operation was put into service, weather conditions were exactly as assumed in the design, and measurements showed that the air leaving the dryer was at \(80^{\circ} \mathrm{C}\) and a gauge pressure of \(10 \mathrm{mm}\) Hg. However, there was no way to check the operation of the blower to see if it was delivering the specified volumetric flow rate of air. Your boss wants to check that value and asks you to devise a method for doing so. You go back to your office, sketch the process, and determine that you can estimate the air flow rate from the given information if you also know the moisture content of the air leaving the dryer.(a) Propose a method to estimate the moisture content of the exit air. (b) Suppose your measurement is carried out and you learn that the exit air at \(10 \mathrm{mm}\) Hg gauge has a dew point of \(40^{\circ} \mathrm{C}\). Use that information and the mass of water removed from the wet pulp to determine the volumetric flow rate ( \(\mathrm{m}^{3} / \mathrm{min}\) ) of air entering the system.

A storage tank for liquid \(n\) -octane has a diameter of \(30 \mathrm{ft}\) and a height of \(20 \mathrm{ft}\). During a typical \(24-\mathrm{h}\) period the level of liquid octane falls from 18 ft to 8 ft, after which fresh octane is pumped into the tank to return the level to \(18 \mathrm{ft}\). As the level in the tank falls, nitrogen is fed into the free space to maintain the pressure at 16 psia; when the tank is being refilled, the pressure is maintained at 16 psia by discharging gas from the vapor space to the environment. The nitrogen in the tank may be considered saturated with octane vapor at all times. The average tank temperature is \(90^{\circ} \mathrm{F}\). (a) What is the daily rate, in gallons and \(1 \mathrm{b}_{\mathrm{m}}\), at which octane is used? (b) What is the variation in absolute pressure at the bottom of the tank in inches of mercury? (c) How much octane is lost to the environment during a 24 -h period? (d) Why is nitrogen used in the vapor space of the tank when air would be cheaper? (e) Suggest a means by which the octane can be recovered from the gas stream discharged to the atmosphere.

The feed to a distillation column (sketched below) is a 45.0 mole\% \(n\) -pentane- 55.0 mole\% n-hexane liquid mixture. The vapor stream leaving the top of the column, which contains 98.0 mole\% pentane and the balance hexane, goes to a total condenser (which means all the vapor is condensed). Half of the liquid condensate is returned to the top of the column as reflux and the rest is withdrawn as overhead product (distillate) at a rate of \(85.0 \mathrm{kmol} / \mathrm{h}\). The distillate contains \(95.0 \%\) of the pentane fed to the column. The liquid stream leaving the bottom of the column goes to a reboiler. Part of the stream is vaporized; the vapor is returned to the bottom of the column as boilup, and the residual liquid is withdrawn as bottoms product.(a) Calculate the molar flow rate of the feed stream and the molar flow rate and composition of the bottoms product stream. (b) Estimate the temperature of the vapor entering the condenser, assuming that it is saturated (at its dew point) at an absolute pressure of 1 atm and that Raoult's law applies to both pentane and hexane. Then estimate the volumetric flow rates of the vapor stream leaving the column and of the liquid distillate product. State any assumptions you make. (c) Estimate the temperature of the reboiler and the composition of the vapor boilup, again assuming operation at 1 atm.(d) Calculate the minimum diameter of the pipe connecting the column and the condenser if the maximum allowable vapor velocity in the pipe is \(10 \mathrm{m} / \mathrm{s}\). Then list all the assumptions underlying the calculation of that number.

An aqueous waste stream leaving a process contains 10.0 wt\% sulfuric acid and 1 kg nitric acid per \(\mathrm{kg}\) sulfuric acid. The flow rate of sulfuric acid in the waste stream is \(1000 \mathrm{kg} / \mathrm{h}\). The acids are neutralized before being sent to a wastewater treatment facility by combining the waste stream with an aqueous slurry of solid calcium carbonate that contains 2 kg of recycled liquid per \(\mathrm{kg}\) solid calcium carbonate. (The source of the recycled liquid will be given later in the process description.) The following neutralization reactions occur in the reactor:$$\begin{array}{l} \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{CaSO}_{4}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \\ \mathrm{CaCO}_{3}+2 \mathrm{HNO}_{3} \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \end{array}$$,The sulfuric and nitric acids and calcium carbonate fed to the reactor are completely consumed. The carbon dioxide leaving the reactor is compressed to 30 atm absolute and \(40^{\circ} \mathrm{C}\) and sent elsewhere in the plant. The remaining reactor effluents are sent to a crystallizer operating at \(30^{\circ} \mathrm{C},\) at which temperature the solubility of calcium sulfate is \(2.0 \mathrm{g} \mathrm{CaSO}_{4} / 1000 \mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) Calcium sulfate crystals form in the crystallizer and all other species remain in solution.The slurry leaving the crystallizer is filtered to produce (i) a filter cake containing \(96 \%\) calcium sulfate crystals and the remainder entrained saturated calcium sulfate solution, and (ii) a filtrate solution saturated with \(\mathrm{CaSO}_{4}\) at \(30^{\circ} \mathrm{C}\) that also contains dissolved calcium nitrate. The filtrate is split, with a portion being recycled to mix with the solid calcium carbonate to form the slurry fed to the reactor, and the remainder being sent to the wastewater treatment facility.(a) Draw and completely label a flowchart for this process. (b) Speculate on why the acids must be neutralized before being sent to the wastewater treatment facility.(c) Calculate the mass flow rates ( \(\mathrm{kg} / \mathrm{h}\) ) of the calcium carbonate fed to the process and of the filter cake; also determine the mass flow rates and compositions of the solution sent to the wastewater facility and of the recycle stream. (Caution: If you write a water balance around the reactor or the overall system, remember that water is a reaction product and not just an inert solvent.)(d) Calculate the volumetric flow rate ( \(L / h\) ) of the carbon dioxide leaving the process at 30 atm absolute and 40^0 C. Do not assume ideal-gas behavior. (e) The solubility of \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) at \(30^{\circ} \mathrm{C}\) is \(152.6 \mathrm{kg} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) per \(100 \mathrm{kg} \mathrm{H}_{2} \mathrm{O}\). What is the maximum ratio of nitric acid to sulfuric acid in the feed that can be tolerated without encountering difficulties associated with contamination of the calcium sulfate by-product by \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} ?\)
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