/*! 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 83 When benzene \(\left(\mathrm{C}_... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

When benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) reacts with bromine \(\left(\mathrm{Br}_{2}\right)\), bromobenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}\right)\) is obtained: $$ \mathrm{C}_{6} \mathrm{H}_{6}+\mathrm{Br}_{2} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}+\mathrm{HBr} $$ (a) When \(30.0 \mathrm{~g}\) of benzene reacts with \(65.0 \mathrm{~g}\) of bromine, what is the theoretical yield of bromobenzene? (b) If the actual yield of bromobenzene is \(42.3 \mathrm{~g},\) what is the percentage yield?

Short Answer

Expert verified
Theoretical yield is 60.3 g, and percentage yield is 70.1%.

Step by step solution

01

Calculate Molar Masses

First, we need the molar masses of each reactant and product. The molar mass of benzene (\(\text{C}_6\text{H}_6\)) is calculated as follows:\[ \text{Molar mass of C}_6\text{H}_6 = 6(12.01) + 6(1.008) = 78.11 \, \text{g/mol} \]The molar mass of bromine (\(\text{Br}_2\)) is:\[ \text{Molar mass of Br}_2 = 2(79.904) = 159.81 \, \text{g/mol} \]The molar mass of bromobenzene (\(\text{C}_6\text{H}_5\text{Br}\)) is:\[ \text{Molar mass of C}_6\text{H}_5\text{Br} = 6(12.01) + 5(1.008) + 79.904 = 157.02 \, \text{g/mol} \]
02

Determine the Limiting Reactant

Calculate the moles of benzene and bromine:\[ \text{Moles of C}_6\text{H}_6 = \frac{30.0 \, \text{g}}{78.11 \, \text{g/mol}} = 0.384 \, \text{mol} \]\[ \text{Moles of Br}_2 = \frac{65.0 \, \text{g}}{159.81 \, \text{g/mol}} = 0.407 \, \text{mol} \]According to the balanced equation, 1 mol of \(\text{C}_6\text{H}_6\) reacts with 1 mol of \(\text{Br}_2\). Since both react in a 1:1 ratio, benzene is the limiting reactant because it has fewer moles (0.384 mol) compared to bromine (0.407 mol).
03

Calculate Theoretical Yield

Using benzene as the limiting reactant, calculate the theoretical yield of bromobenzene:\[ \text{Theoretical yield of C}_6\text{H}_5\text{Br} = 0.384 \, \text{mol} \times 157.02 \, \text{g/mol} = 60.3 \, \text{g} \]
04

Calculate Percentage Yield

Percentage yield is calculated using the actual and theoretical yields:\[ \text{Percentage yield} = \left(\frac{\text{Actual yield}}{\text{Theoretical yield}}\right) \times 100\% \]\[ \text{Percentage yield} = \left(\frac{42.3 \, \text{g}}{60.3 \, \text{g}}\right) \times 100\% = 70.1\% \]

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 91Ó°ÊÓ!

Key Concepts

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

Theoretical Yield
In a chemical reaction, the theoretical yield is the maximum amount of product that can be produced from the given amounts of reactants, assuming 100% efficiency in the reaction. To calculate the theoretical yield, you first need to identify the limiting reactant, which is the reactant that is completely consumed first, thus limiting the amount of product formed. In the given exercise, benzene is determined to be the limiting reactant. Once identified, you use its amount to calculate how much of the product, bromobenzene, can theoretically be formed. To do this, convert the mass of the limiting reactant to moles using its molar mass. Then, use the balanced chemical equation to relate the moles of reactants to the moles of products, assuming they react in a 1:1 ratio. Finally, convert the moles of the product back to grams using its molar mass, giving you the theoretical yield. This calculation is crucial in predicting the efficiency and feasibility of a reaction in a real-world setting.
Percentage Yield
The percentage yield is a measure of the efficiency of a chemical reaction, comparing the actual amount of product obtained to the theoretical yield. It's calculated using the formula: \[\text{Percentage yield} = \left(\frac{\text{Actual yield}}{\text{Theoretical yield}}\right) \times 100\%\]In the given exercise, the actual yield of bromobenzene is provided as 42.3 g, and the theoretical yield was previously calculated as 60.3 g. By substituting these values into the formula, the percentage yield is found to be 70.1%.This value reflects how close the reaction arrived at its theoretical potential. A percentage yield of less than 100% typically occurs because of various factors, such as incomplete reactions, side reactions, or loss of product during the purification process. Understanding percentage yield helps chemists optimize reactions, conserve resources, and deliver desired results more reliably.
Molar Mass
Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a chemical substance. It is typically expressed in grams per mole (g/mol). Calculating molar mass is a crucial step in converting between mass and moles, which is an essential operation in stoichiometry.To determine the molar mass of a compound, sum the atomic masses of all the atoms present in one molecule of the compound. For example, to calculate the molar mass of benzene \(\text{C}_6\text{H}_6\),add the atomic masses of six carbon atoms \((6 \times 12.01)\) and six hydrogen atoms \((6 \times 1.008)\), resulting in 78.11 g/mol. Similarly, you calculate molar masses for bromine \(\text{Br}_2\) and bromobenzene \(\text{C}_6\text{H}_5\text{Br}\).Understanding molar mass is vital for quantifying substances in a reaction and converting between different units such as grams and moles. It forms the foundation for determining quantities and yields in chemistry, making accurate calculations essential for successfully executing and evaluating chemical processes.

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

The reaction between potassium superoxide, \(\mathrm{KO}_{2}\), and \(\mathrm{CO}_{2}\), $$ 4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{~K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2} $$ is used as a source of \(\mathrm{O}_{2}\) and absorber of \(\mathrm{CO}_{2}\) in selfcontained breathing equipment used by rescue workers. (a) How many moles of \(\mathrm{O}_{2}\) are produced when \(0.400 \mathrm{~mol}\) of \(\mathrm{KO}_{2}\) reacts in this fashion? (b) How many grams of \(\mathrm{KO}_{2}\) are needed to form \(7.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) ?

Boron nitride, \(\mathrm{BN},\) is an electrical insulator with remarkable thermal and chemical stability. Its density is \(2.1 \mathrm{~g} / \mathrm{cm}^{3} .\) It can be made by reacting boric acid, \(\mathrm{H}_{3} \mathrm{BO}_{3}\), with ammonia. The other product of the reaction is water. (a) Write a balanced chemical equation for the synthesis of BN. (b) If you made \(225 \mathrm{~g}\) of boric acid react with \(150 \mathrm{~g}\) ammonia, what mass of BN could you make? (c) Which reactant, if any, would be left over, and how many moles of leftover reactant would remain? (d) One application of \(\mathrm{BN}\) is as thin film for electrical insulation. If you take the mass of BN from part (a) and make a \(0.4 \mathrm{~mm}\) thin film from it, what area, in \(\mathrm{cm}^{2}\), would it cover?

Calculate the percentage by mass of oxygen in the following compounds: (a) vanillin, \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3} ;(\mathbf{b})\) isopropyl alcohol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\); (c) acetaminophen, \(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{NO}_{2}\); (d) cyclopropanone, \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O} ;\) (e) dioxin, \(\mathrm{C}_{12} \mathrm{H}_{4} \mathrm{Cl}_{4} \mathrm{O}_{2} ;(\mathbf{f})\) penicillin, \(\mathrm{C}_{16} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{4} \mathrm{~S}\).

Several brands of antacids use \(\mathrm{Al}(\mathrm{OH})_{3}\) to react with stomach acid, which contains primarily HCl: $$ \mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) $$ (a) Balance this equation. (b) Calculate the number of grams of HCl that can react with \(0.500 \mathrm{~g}\) of \(\mathrm{Al}(\mathrm{OH})_{3}\) (c) Calculate the number of grams of \(\mathrm{AlCl}_{3}\) and the number of grams of \(\mathrm{H}_{2} \mathrm{O}\) formed when \(0.500 \mathrm{~g}\) of \(\mathrm{Al}(\mathrm{OH})_{3}\) reacts. (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

(a) What is the mass, in grams, of \(2.50 \times 10^{-3} \mathrm{~mol}\) of ammonium phosphate? (b) How many moles of chloride ions are in \(0.2550 \mathrm{~g}\) of aluminum chloride? (c) What is the mass, in grams, of \(7.70 \times 10^{20}\) molecules of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\) (d) What is the molar mass of cholesterol if 0.00105 mol has a mass of \(0.406 \mathrm{~g}\) ?

See all solutions

Recommended explanations on Chemistry Textbooks

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.