/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 7 Magnesium sulfate has a number o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 7

Magnesium sulfate has a number of uses, some of which are related to the ability of the anhydrate form to remove water from air and others based on the high solubility of the heptahydrate \(\left(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\right)\) form, also known as Epsom salt. The densities of the anhydrate and heptahydrate crystalline forms are 2.66 and \(1.68 \mathrm{g} / \mathrm{mL},\) respectively. Suppose you wish to form a 20.0 wt\% \(\mathrm{MgSO}_{4}\) aqueous solution by simply pouring crystals of one of the forms into a tank of water while the temperature is held constant at \(30^{\circ} \mathrm{C}\). The specific gravity of the 20.0 wt\% solution at \(30^{\circ} \mathrm{C}\) is \(1.22 .\) Answer the following questions for both forms of the \(\mathrm{MgSO}_{4}\) crystals: (a) What volume of water should be in the tank before crystals are added if the final product is to be 1000 kg of the 20 wt\% solution? (b) Suppose the tank diameter is \(0.30 \mathrm{m}\). What is the height of liquid in the tank before the crystals are added? (c) What is the height of the water in the tank after addition of the crystals but before they begin to dissolve? (d) What is the height of liquid in the tank after all the MgSO \(_{4}\) has dissolved?

Short Answer

Expert verified
The volume calculations for this exercise would vary slightly for the different forms of MgSO4, but the steps to calculate them will remain the same.

Step by step solution

01

Calculate the Mass of MgSO4 in Solution

Firstly, we know that a 20 wt% solution means there are 20 grams of MgSO4 for every 100 g of solution. If, as the problem states, we want 1000 kg (or 1000000 g) of this solution, we need to find out how much MgSO4 this represents. We calculate this as follows: \(20\% \times 1000000 g = 200000 g = 200 kg \). This is the required MgSO4 (in either form) to be added.
02

Calculate the Amount of Water Required

The volume of water required before adding the crystals can be calculated using the weight of the MgSO4 and the weight of the solution. We already have the weight of the MgSO4 (200 kg), so we can subtract this from the total solution weight to get the amount of water necessary. We calculate this as follows: \(1000 kg (solution) - 200 kg (MgSO4) = 800 kg \). However, we're asked for the volume of water, not the weight. Given the density of water is approximately \(1 g/mL\), or \(1 kg/L\), this translates to \(800 L\) or \(0.8 m^3\).
03

Calculate the Height of the Water Before Addition

The height of water in the tank before the crystals are added corresponds to the volume of the water calculated in 鈥楽tep 2鈥�. Since the tank is cylindrical, the volume of the cylinder can be related to the height with the formula: \(V = 蟺r虏h\). Given the diameter (thus radius \(r = 0.3 m / 2 = 0.15 m\)) already, we can calculate the height \(h\) by rearranging the formula: \(h = V/(蟺r虏) = 0.8m^3 / (蟺脳(0.15m)虏)\). Calculate this for the height in meters.
04

Calculate the Height of the Water After Addition

The height after addition of the MgSO4 crystals can be calculated by figuring out the volume of the crystals using their density, and then converting this to a height in the tank, in a similar process to Step 3. For each form, we'll divide the mass \(200 kg\) by the respective density (\(2.66 g/mL\) for the anhydrous form and \(1.68 g/mL\) for the heptahydrate). After converting these volumes from mL to the cubic meter, add each value to the initial volume of water (0.8 m^3), then use \(V = 蟺r虏h\) formula to determine the total height
05

Calculate the Height of the Liquid After Dissolution

The height of the liquid in the tank after all the MgSO4 has dissolved will return to the initial volume, because the mass hasn't been changed by dissolving the substances. Hence, the height remains the same as the end of the Step 3.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Mass and Volume Calculations
Understanding the relationship between mass, volume, and density is crucial when working with chemical solutions. The mass of a substance, measured in grams (g) or kilograms (kg), is its amount of matter. Volume, typically measured in liters (L) or milliliters (mL), is the space occupied by a substance. Density is a property that relates the mass of a substance to its volume, often expressed as g/mL or kg/L.

When we need to convert between mass and volume, we use the substance's density as a conversion factor. This is especially important in creating solutions where precise amounts of solutes and solvents are required. In the provided exercise, mass and volume calculations are employed to determine how much water and magnesium sulfate are needed to create a specific concentration of a solution.
Solution Preparation
Preparing a chemical solution involves dissolving a specific amount of solute (in this case, magnesium sulfate) in a solvent (water) to achieve a desired concentration. Such processes are guided by careful calculations and understanding of solubility.

In the given exercise, the aim is to prepare a 20 wt% aqueous solution of magnesium sulfate. It necessitates calculating the mass of the solute needed and the corresponding volume of the solvent. An in-depth understanding of solution preparation helps in accurately constructing chemical solutions vital for various applications, ensuring that the desired concentration is accurately achieved to maintain the consistency and integrity of an experiment or industrial process.
Aqueous Solutions
Aqueous solutions are formed when substances dissolve in water. Water's ability to dissolve a variety of substances makes it an excellent solvent for creating solutions in chemical processes. The solvency depends on the temperature and the physical properties of the solute, such as its solubility.

Creating a uniform aqueous solution, like the 20 wt% magnesium sulfate solution in the exercise, involves understanding the dissolution process. It's important to note that the properties of an aqueous solution can vary based on the concentration and the nature of the solute, and these solutions are commonly used in both laboratory settings and industrial applications.
Stoichiometry
Stoichiometry, at its core, deals with the quantification of reactants and products in a chemical reaction. It involves calculations that relate the quantities of substances involved in a reaction, grounded in the conservation of mass and the stoichiometric coefficients arising from the balanced chemical equations.

However, stoichiometry is not limited to reactions; it's also applied in the preparation of solutions, as seen with the magnesium sulfate exercise. Determining the right proportions of solute and solvent requires stoichiometric calculations. These calculations ensure that the desired concentration of a solution is achieved and are fundamental in a wide range of scientific disciplines, including chemistry, biology, environmental science, and engineering.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Phosgene (CCl, O) is a colorless gas that was used as an agent of chemical warfare in World War I. It has the odor of new-mown hay (which is a good warning if you know the smell of new-mown hay). Pete Brouillette, an innovative chemical engincering student, came up with what he believed was an effective new process that utilized phosgene as a starting material. He immediately set up a reactor and a system for analyzing the reaction mixture with a gas chromatograph. To calibrate the chromatograph (i.e., to determine its response to a known quantity of phosgene), he evacuated a 15.0 cm length of tubing with an outside diameter of \(0.635 \mathrm{cm}\) and a wall thickness of \(0.559 \mathrm{mm}\), and then connected the tube to the outlet valve of a cylinder containing pure phosgene. The idea was to crack the valve, fill the tube with phosgene, close the valve, feed the tube contents into the chromatograph, and observe the instrument response. What Pete hadn't thought about (among other things) was that the phosgene was stored in the cylinder at a pressure high enough for it to be a liquid. When he opened the cylinder valve, the liquid rapidly flowed into the tube and filled it. Now he was stuck with a tube full of liquid phosgene at a pressure the tube was not designed to support. Within a minute he was reminded of a tractor ride his father had once given him through a hayfield, and he knew that the phosgene was leaking. He quickly ran out of the lab, called campus security, and told them that a toxic leak had occurred, that the building had to be evacuated, and the tube removed and disposed of properly. Personnel in air masks shortly appeared, took care of the problem, and then began an investigation that is still continuing. (a) Show why one of the reasons phosgene was an effective weapon is that it would collect in low spots soldiers often mistakenly entered for protection. (b) Pete's intention was to let the tube equilibrate at room temperature ( \(23^{\circ} \mathrm{C}\) ) and atmospheric pressure. How many gram-moles of phosgene would have been contained in the sample fed to the chromatograph if his plan had worked? (c) The laboratory in which Pete was working had a volume of \(2200 \mathrm{ft}^{3}\), the specific gravity of liquid phosgene is \(1.37,\) and Pete had read somewhere that the maximum "safe" concentration of phosgene in air is \(0.1 \mathrm{ppm}\) \(\left(0.1 \times 10^{-6} \mathrm{mol} \mathrm{CCl}_{2} \mathrm{O} / \mathrm{mol}\) air) \right. Would the "safe" concentration have been exceeded if all the liquid phosgene in the tube had evaporated into the room? Even if the limit would not have been exceeded, give several reasons why the lab would still have been unsafe. (d) List several things Pete did (or failed to do) that made his experiment unnecessarily hazardous.

Most of the concrete used in the construction of buildings, roads, dams, and bridges is made from Portland cement, a substance obtained by pulverizing the hard, granular residue (clinker) from the roasting of a mixture of clay and limestone and adding other materials to modify the setting properties of the cement and the mechanical properties of the concrete. The charge to a Portland cement rotary kiln contains \(17 \%\) of a dried building clay \(\left(72 \mathrm{wt} \% \mathrm{SiO}_{2}\right.\) \(\left.16 \% \mathrm{Al}_{2} \mathrm{O}_{3}, 7 \% \mathrm{Fe}_{2} \mathrm{O}_{3}, 1.7 \% \mathrm{K}_{2} \mathrm{O}, 3.3 \% \mathrm{Na}_{2} \mathrm{O}\right)\) and \(83 \%\) limestone \(\left(95 \mathrm{wt} \% \mathrm{CaCO}_{3}, 5 \% \text { impuritics }\right)\) When the solid temperature reaches about \(900^{\circ} \mathrm{C},\) calcination of the limestone to lime (CaO) and carbon dioxide occurs. As the temperature continues to rise to about \(1450^{\circ} \mathrm{C},\) the lime reacts with the minerals in the clay to form such compounds as \(3 \mathrm{CaO} \cdot \mathrm{SiO}_{2}, 3 \mathrm{CaO} \cdot \mathrm{Al}_{2} \mathrm{O}_{3},\) and \(4 \mathrm{CaO} \cdot \mathrm{Al}_{2} \mathrm{O}_{3} \cdot \mathrm{Fe}_{2} \mathrm{O}_{3} .\) The flow rate of \(\mathrm{CO}_{2}\) from the kiln is \(1350 \mathrm{m}^{3} / \mathrm{h}\) at \(1000^{\circ} \mathrm{C}\) and 1 atm. Calculate the feed rates of clay and limestone ( \(\mathrm{kg} / \mathrm{h}\) ) and the weight percent of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the final cement.

A gas turbine power plant receives a shipment of hydrocarbon fuel whose composition is uncertain but may be represented by the expression \(\mathrm{C}_{x} \mathrm{H}_{y}\). The fuel is burned with excess air. An analysis of the product gas gives the following results on a moisture-free basis: \(10.5 \%(\mathrm{v} / \mathrm{v}) \mathrm{CO}_{2}, 5.3 \% \mathrm{O}_{2},\) and \(84.2 \% \mathrm{N}_{2}\) (a) Determine the molar ratio of hydrogen to carbon in the fuel ( \(r\) ), where \(r=y / x\), and the percentage excess air used in the combustion. (b) What is the air-to-fuel ratio ( \(m^{3}\) air/kg of fuel) if the air is fed to the power plant at \(30^{\circ} \mathrm{C}\) and \(98 \mathrm{kPa} ?\) (c) The specific gravity of the fuel (a petroleum product) is \(0.85 .\) Estimate the ratio standard cubic feet of gas fed to the turbine per barrel of fuel. (d) What are the issues associated with using oil as a fuel as opposed to natural gas? Consider two factors: (i) the complete composition of typical fuel oils and their resulting emissions, and (ii) the availability and global distribution of the two fuel sources.

Ammonia is one of the chemical constituents of industrial waste that must be removed in a treatment plant before the waste can safely be discharged into a river or estuary. Ammonia is normally present in wastewater as aqueous ammonium hydroxide \(\left(\mathrm{NH}_{4}^{+} \mathrm{OH}^{-}\right) .\) A two- part process is frequently carried out to accomplish the removal. Lime (CaO) is first added to the wastewater, leading to the reaction $$\mathrm{CaO}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}^{2+}+2\left(\mathrm{OH}^{-}\right)$$ The hydroxide ions produced in this reaction drive the following reaction to the right, resulting in the conversion of ammonium ions to dissolved ammonia: $$\mathrm{NH}_{4}^{+}+\mathrm{OH}^{-}=\mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})$$ Air is then contacted with the wastewater, stripping out the ammonia. (a) One million gallons per day of alkaline wastewater containing 0.03 mole \(\mathrm{NH}_{3} /\) mole ammoniafree \(\mathrm{H}_{2} \mathrm{O}\) is fed to a stripping tower that operates at \(68^{\circ} \mathrm{F}\). Air at \(68^{\circ} \mathrm{F}\) and 21.3 psia contacts the wastewater countercurrently as it passes through the tower. The feed ratio is \(300 \mathrm{ft}^{3}\) air/gal wastewater, and 93\% of the ammonia is stripped from the wastewater. Calculate the volumetric flow rate of the gas leaving the tower and the partial pressure of ammonia in this gas. (b) Briefly explain in terms a first-year chemistry student could understand how this process works. Include the equilibrium constant for the second reaction in your explanation. (c) This problem is an illustration of challenges associated with addressing undesirable releases into the environment; namely, in developing a process to prevent dumping ammonia into a waterway, the release is instead made to the atmosphere. Suppose you are to write an article for a newspaper on the installation of the process described in the beginning of this problem. Explain why the company is installing the two-part process, and then explain the ultimate fate of the ammonia. Take one of two positions - either that the release is harmless or that it jeopardizes the environment in the vicinity of the plant. since this is a newspaper article, it cannot be more than 800 words.

A fuel cell is an electrochemical device that reacts hydrogen with oxygen from the air to produce water and DC electricity. A proposed application is replacement of the gasoline-fueled internal combustion engine in an automobile with a \(100 \mathrm{kW}\) fuel cell. You are on a summer internship with a gas supplier planning to transport hydrogen to service stations for use in cars powered by fuel cells. The hydrogen is to be transported in tube trailers, each of which has 10 tubes of length \(10.5 \mathrm{m}\) and diameter \(0.56 \mathrm{m}\). Hydrogen in the tubes at 2600 psig and an average temperature of \(298 \mathrm{K}\) is discharged at service stations to a final pressure of 55 psig. Refueling cach fuel-cell-powered automobile is estimated to require 4.0 kg of hydrogen. (a) You and your office-mate- an intern from a different university - have been asked to estimate the number of automobiles that can be refueled by one tube-trailer load of hydrogen. He does a very quick calculation and comes up with a value of 95 cars. Speculate how he did it and provide support for your speculation. What was his mistake? (b) Do the calculation using the SRK equation of state. Instead of using Eqs. \(5.3-11\) and \(5.3-13\) for the parameter \(\alpha,\) use the following correlation developed specifically for hydrogen: \(^{23}\) \(\alpha=1.202 \exp \left(-0.3228 T_{\mathrm{r}}\right)\) (c) Do the calculation using the law of corresponding states. (d) In which of the three estimates would you have the greatest confidence, and why?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Kinetics

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Inorganic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.