# Chapter 3: Fundamental Concepts of Stoichiometry (Solution)

**Problem 3.1: **How many grams of NH_{4}Cl are there in 5 mol?

**Problem 3.2: **Convert 750 g CuSO_{4}.5H_{2}O into moles. Find the equivalent mol of CuSO_{4} in the crystals.

**Problem 3.3: **How many kilograms of CS_{2} will contain 3.5 kg-atom carbon?

**Problem 3.4: **How many grams of carbon are present in 264 g of CO_{2}?

**Problem 3.5: **The molecular formula of an organic compound is C_{10}H_{7}Br. Find the weight percentage of carbon, hydrogen, and bromine in the solid.

**Problem 3.6: **Find the equivalents of 3 kmol of FeCl_{3}.

**Problem 3.7: **What is the equivalent weight of Al_{2}(SO_{4})_{3}?

**Problem 3.8: **How many equivalents are there in 500 g KMnO_{4}?

**Problem 3.9: **Calculate the equivalent weight of H_{3}PO_{4} in the reaction

**Problem 3.10: **A certain organic compound is found to contain 81.5 % C, 4.9 % H, and 13.6 % N by weight. If the molecular weight of the compound is 103, determine the molecular formula of the compound.

**Problem 3.11: **Aluminum chloride is made by the chlorination of molten aluminum metal in a furnace:

a) How many kilograms of AlCl_{3} can be made from 100 kg of chlorine? b) How many grams of Al will react with 50 g of chlorine?

**Problem 3.12: **Sodium hydroxide is made by the electrolysis of brine solution. The overall reaction may be written as:

(a) How much NaOH can be made from 1000 kg NaCl (b) How much water is consumed in the production of 500 kg Cl_{2}?

**Problem 3.13: **Sulphur trioxide gas is obtained by the combustion of pyrites (FeS_{2}) according to the following reaction:

The reaction is accompanied by the following side reaction:

4FeS_2+11O_2\rightarrow2{Fe}_2O_3+8{SO}_2Assume that 80 % (weight) of the pyrites charged reacts to give sulphur trioxide and 20 % reacts giving sulphur dioxide. a) How many kilograms of pyrites charged will give 100 kg of SO_{3}? b) How many kilograms of oxygen will be consumed in the reaction?

**Problem 3.14: **Barium chloride reacts with sodium sulfate to precipitate barium sulfate:

a) How many grams of barium chloride is needed to react with 100 g of sodium sulfate? b) For precipitating 50 g of barium sulfate, how many grams of the reactants are consumed? c) How many grams of sodium chloride would be obtained when 50 g of barium sulfate is precipitated?

**Problem 3.15: **Chromite ore analyzed 30.4 % Cr_{2}O_{3}. Determine the theoretical amount of lead chromate (PbCrO_{4}) that can be obtained from 1000 kg of the ore.

**Problem 3.16: **The alloy brass contains lead as an impurity in the form of lead sulfate (PbSO4). By dissolving brass in nitric acid, lead sulfate is precipitated. A sample of brass weighing 5 g is dissolved in nitric acid and 0.03 g of precipitate is formed. Calculate the percentage of lead present in the brass sample.

**Problem 3.17: **How many kilograms of CO_{2} are obtained by the decomposition of 100 kg of limestone containing 94.5 % CaCO_{3}, 4.2 % MgCO_{3,} and 1.3 % inert materials? What is the volume of CO_{2} obtained at STP?

**Problem 3.18: **Sulphur dioxide is obtained by the following reaction

a) When 50 kg Cu dissolves in sulphuric acid what volume of sulfur dioxide is produced at standard conditions? b) How many kilograms of 94 % sulphuric acid will be required for the above reaction?

**Problem 3.19: **Crude calcium carbide, CaC_{2}, is made in an electric furnace by the following reaction.

The product contains 85 % CaC_{2} and 15 % unreacted CaO. a) How much CaO is to be added to the furnace charge for each 1000 kg CaC_{2}? b) How much CaO is to be added to the furnace charge for each 1000 kg of the crude product?

**Problem 3.20: **A 1-kg lead ball of density 11.34⨯10^{3} kg/m^{3} is immersed in water. The density of water is 1000 kg/m^{3}. Calculate the buoyant force on the body.

**Problem 3.21: **A body weighs 1.0 kg in air, 0.90 kg in water, and 0.85 kg in liquid. What is the specific gravity of the liquid?

**Problem 3.22: **10 kg of liquid A of specific gravity 1.2 is mixed with 3 kg of liquid B of specific gravity 0.8. Assuming that there is no volume change on mixing, what is the specific gravity of the mixture?

**Problem 3.23: **An alloy contains metals A and B in the ratio of 5:3. If metal A has a specific gravity of 10 and metal B has a specific gravity of 5 in the pure state, what would be the specific gravity of the alloy?

**Problem 3.24: **An aqueous solution of a valuable chemical (molecular weight = 180) leaves the reactor at a rate of 60⨯10^{–3} m^{3}/h. The solution concentration is 40% (weight) and its specific gravity is 1.05. Determine (a) the concentration of the solution in kg/m^{3} and (b) the flow rate in kmol/h.

**Problem 3.25: **A certain solution has a specific gravity of 1.15 at 288.8 K referred to as water at 288.8 K. Express the specific gravity as °Bé and °Tw.

**Problem 3.26: **What is the specific gravity on Baumé scale for a 90 °Tw solution?

**Problem 3.27: **The specific gravity of hydrocarbon oil is 0.88 at 288.8 K. What are the corresponding values in the Baumé and API scales?

**Problem 3.28: **The bulk density of a solid is 1.125 g/mL and the true density is 1.5 g/mL. What is the porosity of the solid?

**Problem 3.29: **500 cubic meters of 30 °API gas oil is blended with 2000 cubic meters of 15 °API fuel oil. What is the density of the resultant mixture in kg/m^{3}? The density of water at 288.5 K = 0.999 g/ml. Assume no volume change on mixing.

**Problem 3.30: **100 liters each of gasoline (55°API), kerosene (40°API), gas oil (31°API), and isopentane (96 °API) are mixed. The density of water at 288.5 K = 0.999 g/mL. (a) Determine the density of the mixture in kg/m^{3} (b) What is the specific gravity in °API? (c) Express the composition of the mixture in weight percent.

**Problem 3.31: **The specific gravity 288.5 K/288.5 K of an ammonia-water solution is 0.9180. What would be the specific gravity 288.5 K/300 K if the density of water at 288.5 K and 300 K are respectively, 0.998 g/mL and 0.989 g/mL?

**Problem 3.32: **An analysis of seawater showed 2.8% NaCl, 0.5% MgCl2 and 0.0085% NaBr by weight. The average specific gravity of the water is 1.03. What mass of magnesium, sodium, and chlorine can be obtained from 100 m3 of seawater?

**Problem 3.33: **What is the weight percentage of CaO in Ca(OH)_{2}?

**Problem 3.34:** Determine the weight percentage of the constituent elements of potassium sulfate.

**Problem 3.35: **What is the percentage of water in Al_{2}(SO_{4})_{3}.17H_{2}O?

**Problem 3.36:** Compare the percentages of iron in ferrous chloride and ferric chloride.

**Problem 3.37:** An aqueous solution contains 40% by weight NaNO_{3}. Determine the composition in mole percent.

**Problem 3.38:** How many kg of Glauber’s salt (Na_{2}SO_{4}.10H_{2}O) will be obtained from 250 kg Na_{2}SO_{4}?

**Problem 3.39: **A sample of urea (NH_{2}CONH_{2}) contains 42.0% nitrogen by weight. What is the percent purity of the sample?

**Problem 3.40: **Determine the mass fraction and mole fraction of chlorine in the substance Ca(ClO)_{2}.

**Problem 3.41: **The strength of phosphoric acid is usually represented as the weight percent of P_{2}O_{5}. A sample of phosphoric acid analyzed 40% P_{2}O_{5}. What is the percent by weight of H_{3}PO_{4} in the sample?

**Problem 3.42: **A blast furnace treats 10^{6} kg per day hematite ore which contains 50% pure ferric oxide. Determine the weight of pig iron produced per day. Pig iron contains 94% iron.

**Problem 3.43: **A liquid mixture contains three components A (MW = 72), B (MW = 58) and C (MW = 56) in which A and B are present in the mole ratio 1.5:1 and the weight percent of B is 25%. A sample of the mixture is found to contain 10 kg of C. Calculate the total number of moles of the mixture.

**Problem 3.44: **A Portland cement sample contained 20% SiO_{2} by weight derived from two silicate compounds, SiO_{2}.2CaO and SiO_{2}.3CaO that are present in the cement in the mole ratio 3:4. Determine the percent by weight of each silicate compound in the cement.

**Problem 3.45: **An ethanol–water mixture forms an azeotrope at 89.43 mole percent ethanol at 101.3 kPa and 351.4 K. What is the composition of the azeotrope in weight percent?

**Problem 3.46: **A 20% (weight) aqueous solution of monoethanolamine (MEA, NH_{2}CH_{2}CH_{2}OH) is used as a solvent for absorbing CO_{2} from a gas stream. The solution leaving contains 0.25 mol CO_{2} per mol MEA. Determine a) the mole percent of CO_{2} in the solution leaving the absorber. b) The mass percent of CO_{2} in the solution.

**Problem 3.47:** A water-soaked cloth is dried from 45% to 9% moisture on dry basis. Find the weight of water removed from 2000 kg of dry fabric.

**Problem 3.48:** A solution of sodium chloride is saturated in water at 289 K. Calculate the weight of salt in kg that can be dissolved in 100 kg of this solution if it is heated to a temperature of 343 K. The solubility of sodium chloride at 289 K = 6.14 kmol/1000 kg water. The solubility at 343 K = 6.39 kmol/1000 kg of water.

**Problem 3.49:** The solubility of benzoic acid (C_{6}H_{5}COOH) is found out to be 66 parts in 100 parts by weight of ether (C_{2}H_{5}OC_{2}H_{5}). Find the mole fraction of benzoic acid in the saturated solution with ether.

**Problem 3.50:** The solubility of benzoic acid (C_{6}H_{5}COOH) in ether (C_{2}H_{5}OC_{2}H_{5}) is found to be 28.59% (by mole). What is the solubility in weight percent? What is the weight ratio of acid to ether in the saturated solution?

**Problem 3.51:** Hydrogen chloride is made by the action of sulphuric acid on sodium chloride. Hydrogen chloride being readily soluble in water forms hydrochloric acid. Calculate the following: (a) The weight in grams of HCl formed by the action of excess sulphuric acid on 1 kg of salt which is 99.5% pure (b) The volume of hydrochloric acid solution (specific gravity 1.2) containing 40% by weight HCl that can be produced (c) The weight in kilograms of sodium sulfate obtained?

**Problem 3.52:** An excess of NaNO_{3} is treated with 25 kg sulphuric acid solution which contains 93.2% by weight of pure H_{2}SO_{4}. Calculate the following: (a) The number of kilomoles of pure nitric acid obtained (b) The mass of nitric acid containing 70% by weight HNO_{3} obtained (c) The number of kilograms of Na_{2}SO_{4} produced?

**Problem 3.53:** A liquid mixture contains three components A (MW = 72), B (MW = 58), and C (MW = 56) in which A and B are present in the mole ratio 1.5:1 and the weight percent of B is 25%. The specific gravities of the pure liquids are 0.67, 0.60, and 0.58 respectively, for A, B, and C and there is no volume change on mixing. Calculate the following: (a) The analysis of the mixture in mole percent (b) The molecular weight of the mixture (c) The volume percent of C on a B-free basis (d) The specific gravity of the mixture?

**Problem 3.54:** An alcohol–water solution contains 20% (volume) ethanol at 300 K. The densities of ethanol and water at 300 K are 0.798 g/mL and 0.998 g/mL respectively. What is the weight percent of alcohol?

**Problem 3.55:** Calculate the concentration in mol/L of pure methanol at 298 K if the density of methanol at 298 K is 0.9842 g/mL.

**Problem 3.56:** A company has a contract to buy NaCl of 98 percent purity for Rs 300 per 1000 kg salt delivered. Its last shipment of 1000 kg was only of 90% purity. How much they should pay for the shipment?

**Problem 3.57:** A compound is found to contain 62.4% Ca and 37.6% C. (a) How many gram atoms of Ca and C are present in 100 g of the compound (b) Suggest an empirical formula for the compound?

**Problem 3.58:** It is desired to prepare a 40% solution of NaCl in water at 300 K. (a) How many kg of anhydrous sodium chloride should be added to 0.05 cubic meters of pure water having a density of 0.998 g/mL at 300 K (b) If the salt contains 10% water, how many kg of salt is required?

**Problem 3.59:** Absolute humidity of air is 0.02 kg water vapor/kg dry air. Assuming the average molecular weight of air to be 29, calculate the following: (a) The mole percent of water vapor in the air (b) The molal absolute humidity, which is the same as the mole ratio of water vapor to dry air.

**Problem 3.60:** Assuming that dry air contains 21% oxygen and 79% nitrogen, calculate the following: (a) The composition in weight percent (b) The average molecular weight of dry air.

**Problem 3.61:** By electrolyzing brine, a mixture of gases is obtained at the cathode having the following composition by weight: chlorine 67%, bromine 28%, and oxygen 5%. Calculate the composition of gases by volume.

**Problem 3.62:** Determine the weight percent of NaOH in an aqueous solution of molality 2.

**Problem 3.63:** Calculate the molality of a solution of 93% H_{2}SO_{4} (W/V). The density of the solution is 1840 kg/m^{3}.

**Problem 3.64:** A 6.9 molar solution of KOH in water contains 30% by weight of KOH. Calculate the density of the solution.

**Problem 3.65:** The concentration of SO_{2} in the flue gases from a boiler is found to be 0.2 kg/m^{3} at STP. Determine the concentration of SO_{2} in parts per million by volume at STP. Assume that the gases are perfect.

**Problem 3.66:** A benzene solution of an organic compound A analyses 10% of A. The molality of the solution is reported to be 0.62. Calculate the following: (a) The molecular weight of the compound (b) The mole fraction of the compound in the solution.

**Problem 3.67:** An aqueous solution of NaCl contains 20% NaCl. The density of the solution is 1.16 g/mL. 500 ml water of density 1 g/mL is added to 1 liter of the solution. What will be the molality and molarity of the resulting solution?

**Problem 3.68:** A solution of ZnBr_{2} in water contains 130 g salt per 100 mL solution at 293 K. The specific gravity of the solution is 2.00. Calculate the following: (a) The concentration of ZnBr_{2} in mole percent (b) The concentration of ZnBr_{2} in weight percent (c) The molarity (d) The molality?

**Problem 3.69:** The molality of an aqueous solution of LiCl in water is 10. The density of the solution is 1.16 g/mL at 350 K. Determine the following: (a) The weight percent of LiCl in the solution (b) The molarity of the solution at 350 K (c) The normality of the solution at 350 K (d) The composition of the solution in mole percent?

**Problem 3.70:** The molarity of an aqueous solution of MgCl_{2} at 300 K is 4.0. The specific gravity of the solution is 1.3 at 300 K. Determine the following: (a) The concentration of MgCl_{2} in weight fraction (b) The concentration of MgCl_{2} in mole fraction (c) The molality of the solution (d) The normality of the solution at 300 K?

**Problem 3.71:** Pure water and alcohol are mixed to get a 50 % alcohol solution. The density (g/mL) of water, alcohol, and the solution may be taken to be 0.998, 0.780, and 0.914, respectively at 293 K. Calculate the following: (a) The volume percent of ethanol in the solution at 293 K (b) The molarity (c) The molality?

**Problem 3.72:** A solution of potassium chloride in water contains 384 g KCl per liter of the solution at 300 K. The specific gravity of the solution is 1.6. Determine the following: (a) The concentration in weight percent (b) The mole fraction of KCl (c) The molarity of the solution (d) The molality of the solution.

**Problem 3.73:** Silver nitrate reacts with metallic Zn depositing silver according to the reaction

With 0.05 kg metallic Zn is added to 10^{–3} m^{3} of silver nitrate solution, it was found that after all silver in the solution is deposited in metallic form some Zn metal is left unreacted. The total weight of the unreacted Zn and deposited silver was found to be 0.07 kg. Determine the following: (a) The mass of silver deposited (b) The molarity of the silver nitrate solution.

**Problem 3.74:** 1 kg nitrogen is mixed with 3.5 m^{3} of hydrogen at 300 K and 101.3 kPa and sent to the ammonia converter. The product leaving the converter analyzed 13.7% ammonia, 70.32% hydrogen, and 15.98% nitrogen. (a) Identify the limiting reactant. (b) What is the percent excess of the excess reactant (c) What is the percent conversion of the limiting reactant?

**Problem 3.75:** In the chlorination of ethylene to dichloroethane, the conversion of ethylene is 99.0%. If 94 mol of dichloroethylene is produced per 100 mol of ethylene fed, calculate the overall yield and the reactor yield based on ethylene.

**Problem 3.76:** In the manufacture of methanol by the reaction of carbon monoxide and hydrogen, some formaldehyde is also formed as a by-product.

A mixture consisting of CO and H_{2} is allowed to react and the product analyzed 2.92% CO, 19.71% methanol, 6.57% formaldehyde, and 70.80% hydrogen. Calculate the following: (a) The percent conversion of the limiting reactant (b) The percent excess of any reactant (b) the Percent yield of methanol.

**Problem 3.77: **Water vapor decomposes according to the following reaction

What is the mole fraction of oxygen in the reaction mixture in terms of the extent of reaction if the system contained n_{0} moles of water vapor initially?

**Problem 3.78: **The following reaction occurs in a mixture consisting of 2 mol methane, 1 mol water, 1 mol carbon monoxide, and 4 mol hydrogen initially.

What is the mole fraction of hydrogen in the reaction mixture in terms of the extent of the reaction?

**Problem 3.79: **A system consisting of 2 mol methane and 3 mol water is undergoing the following reaction:

Derive expressions for the mole fraction of hydrogen in terms of the extent of reactions.

**Problem 3.80: **The following gas-phase reactions occur in a mixture initially containing 3 mol ethylene and 2 mol oxygen.

Derive an expression for the mole fraction of ethylene in terms of the extent of reactions.

**Problem 3.81: **In the vapor-phase hydration of ethylene to ethanol, diethyl ether is obtained as a by-product.

A feed mixture consisting of 55% ethylene, 5% inerts, and 40% water is sent to the reactor. The products analyzed were 52.26% ethylene, 5.49% ethanol, 0.16% ether, 36.81% water, and 5.28% inerts. Calculate the conversion of ethylene, yield of ethanol, and ether based on ethylene.

**Problem 3.82: **Elemental phosphorous is produced from phosphate rock in an electric furnace by the following reaction:

The furnace is fed with 1000 kg phosphate. Carbon charged is 25% in excess and silica charged is 50% in excess. The reaction goes to 95% completion. The unconverted reactants along with the calcium silicate formed constitute the slag. Calculate the following: (a) The mass of carbon and silica charged (in kilograms) (b) The amount of phosphorous obtained (in kilograms) (c) The mass of slag produced (in kilograms)

**Problem 3.83: **Iron pyrites is burned in 50% excess air. The following reaction occurs:

For 100 kg of iron pyrites charged, calculate the following: (a) The amount of air supplied (in kilograms) (b) The composition of exit gases if the percent conversion of iron pyrites is 80%

**Problem 3.84: **Ammonia reacts with sulphuric acid giving ammonium sulfate:

(a) 20 m^{3} of ammonia at 1.2 bar and 300 K reacts with 40 kg of sulphuric acid. Which is the excess reactant and what is the percent excess? (b) How much ammonium sulfate is obtained?

**Problem 3.85: **Sulphur dioxide reacts with oxygen producing sulfur trioxide:

In order to ensure a complete reaction, twice as much oxygen is supplied than that required theoretically. However, only 60% conversion is obtained. The pressure was 500 kPa and the temperature was 800 K. 100 kg of SO_{2} is charged to the converter. Determine the following: (a) The volume of pure oxygen supplied at 1.5 bar and 300 K (b) The volume of sulfur trioxide produced (c) The volume of gases leaving the converter (d) The composition of gases leaving the converter (e) The average molecular weight of the gas leaving the converter.

**Problem 3.86: **Nitrogen dioxide shows a tendency to associate and form nitrogen tetroxide.

One cubic meter of nitrogen dioxide at 100 kPa and 300 K is taken in a closed rigid container and allowed to attain equilibrium at constant temperature and volume. The pressure inside the container has fallen to 85 kPa at equilibrium. (a) What is the degree of association? (b) What is the partial pressure of N_{2}O_{4} in the final mixture?

**Problem 3.87:** Ammonium chloride in the vapor phase dissociates into ammonia and hydrogen chloride according to

10.7 g of ammonium chloride is taken in a container. When dissociation is complete and equilibrium has attained the pressure, the volume and temperature of the gas mixture were measured to be 1.2 bar, 7.764⨯10–3 m3, and 400 K, respectively. Determine the following: (a) The fraction of ammonium chloride dissociated (b) The partial pressure of HCl in the products

**Problem 3.88: **A gaseous mixture consisting of 50% hydrogen and 50% acetaldehyde (C_{2}H_{4}O) is initially contained in a rigid vessel at a total pressure of 1.0 bar. Methanol is formed according to

After a time, it was found that the total pressure in the vessel has fallen to 0.9 bar while the temperature was the same as that of the initial mixture. Assuming that the products are still in the vapor phase, calculate the degree of completion of the reaction.

**Problem 3.89: **Ammonia is made by the reaction between hydrogen and nitrogen according to the following reaction:

(a) For the complete conversion of 100 cubic meters of nitrogen at 20 bar and 350 K, what volume of hydrogen at the same conditions of temperature and pressure is theoretically required? (b) If hydrogen is available at 5 bar and 290 K, what is the volume required which is stoichiometrically equivalent to 100 m^{3} of nitrogen at 20 bar and 350 K? (c) If the reaction is carried out at 50 bar and 600 K, what volumes of nitrogen and hydrogen at these conditions are theoretically required for producing 1000 kg ammonia and what will be the volume of ammonia produced at the reactor conditions?

**Problem 3.90: **Carbon dioxide dissociates into carbon monoxide and oxygen at 1 bar and 3500 K.

25 L of CO_{2} at 1 bar and 300 K is heated to 3500 K at constant pressure. If all gases behave ideally, determine the following: (a) The final volume of the gas if no dissociation is occurred (b) The fraction of CO2 is dissociated if the final volume is found to be 0.35 m^{3}.