/*! 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 51 Dichloromethane, \(\mathrm{CH}_{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 51

Dichloromethane, \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), the solvent used to decaffeinate coffee beans, is prepared by reaction of \(\mathrm{CH}_{4}\) with \(\mathrm{Cl}_{2}\). (a) Write the balanced equation. (HCl is also formed.) (b) How many grams of \(\mathrm{Cl}_{2}\) are needed to react with \(50.0 \mathrm{~g}\) of \(\mathrm{CH}_{4} ?\) (c) How many grams of dichloromethane are formed from \(50.0 \mathrm{~g}\) of \(\mathrm{CH}_{4}\) if the percent yield for the reaction is \(76 \% ?\)

Short Answer

Expert verified
(a) \(\mathrm{CH}_4 + 2\mathrm{Cl}_2 \rightarrow \mathrm{CH}_2\mathrm{Cl}_2 + 2\mathrm{HCl}\); (b) 441.06 g; (c) 201.18 g.

Step by step solution

01

Write the chemical equation

The reaction between methane (\(\mathrm{CH}_4\)) and chlorine (\(\mathrm{Cl}_2\)) to produce dichloromethane (\(\mathrm{CH}_2\mathrm{Cl}_2\)) and hydrogen chloride (\(\mathrm{HCl}\)) can be written as follows:\[\mathrm{CH}_4 + 2\mathrm{Cl}_2 \rightarrow \mathrm{CH}_2\mathrm{Cl}_2 + 2\mathrm{HCl}\]This equation is balanced as it has the same number of each atom on both sides of the equation.
02

Calculate moles of CH4

First, we need to calculate how many moles of methane (\(\mathrm{CH}_4\)) there are in 50.0 g. Using the molar mass of methane, which is approximately 16.05 g/mol, we find the number of moles:\[\text{Moles of \(\mathrm{CH}_4\)} = \frac{50.0 \text{ g}}{16.05 \text{ g/mol}} \approx 3.115 \text{ moles}\]
03

Determine moles of Cl2 needed

According to the balanced equation, 1 mole of \(\mathrm{CH}_4\) requires 2 moles of \(\mathrm{Cl}_2\). Thus, 3.115 moles of \(\mathrm{CH}_4\) will require:\[3.115 \text{ moles } \times 2 \frac{\text{moles of } \mathrm{Cl}_2}{\text{mole of } \mathrm{CH}_4} = 6.230 \text{ moles of } \mathrm{Cl}_2\]
04

Convert moles of Cl2 to grams

Next, we convert moles of \(\mathrm{Cl}_2\) to grams. The molar mass of \(\mathrm{Cl}_2\) is approximately 70.90 g/mol.\[\text{Grams of } \mathrm{Cl}_2 = 6.230 \text{ moles} \times 70.90 \text{ g/mol} \approx 441.06 \text{ g}\]
05

Calculate theoretical yield of CH2Cl2

In ideal conditions (100% yield), the moles of \(\mathrm{CH}_2\mathrm{Cl}_2\) can be determined by the same amount of moles of \(\mathrm{CH}_4\) reacted, which is 3.115 moles. The molar mass of \(\mathrm{CH}_2\mathrm{Cl}_2\) is approximately 84.93 g/mol. The theoretical mass is:\[3.115 \text{ moles} \times 84.93 \text{ g/mol} \approx 264.71 \text{ g}\]
06

Apply percent yield

Given that the actual reaction yield is 76%, we calculate the actual mass of \(\mathrm{CH}_2\mathrm{Cl}_2\) produced:\[\text{Actual mass} = 264.71 \text{ g} \times 0.76 = 201.18 \text{ g}\]

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.

Chemical Reactions
A chemical reaction involves the transformation of substances through breaking and forming of chemical bonds. When methane (\(\mathrm{CH}_4\)) reacts with chlorine (\(\mathrm{Cl}_2\)), it leads to the formation of new substances: dichloromethane (\(\mathrm{CH}_2\mathrm{Cl}_2\)) and hydrogen chloride (\(\mathrm{HCl}\)).
  • The initial substances (reactants) used here are methane and chlorine.
  • The products, what are produced as a result of the reaction, are dichloromethane and hydrogen chloride.
Understanding this transformation is key to stoichiometry, which is the area of chemistry focused on the quantitative relationships between reactants and products in chemical reactions.The chemical reaction can be visually represented in a chemical equation, which shows the reactants changing into products.
Molar Mass Calculations
Molar mass is the mass of one mole of a substance. It is a crucial component of stoichiometry as it allows us to convert between the mass of a substance and the amount in moles.To calculate molar mass:
  • Add the atomic masses of all atoms in a molecule. For example, methane (\(\mathrm{CH}_4\)) consists of one carbon atom (12.01 g/mol) and four hydrogen atoms (each 1.01 g/mol), totaling approximately 16.05 g/mol.
  • This unit, grams per mole, helps us relate the mass of a sample to the number of molecules it contains.
In the exercise, the molar mass of \(\mathrm{Cl}_2\) is 70.90 g/mol. Calculating how many grams or moles are needed is essential to moving forward with solving how much product will be formed.
Percent Yield
Percent yield tells us how efficient a chemical reaction is in producing the desired product. In almost all practical scenarios, reactions yield less than 100% due to various factors such as incomplete reactions or side reactions.
  • It is calculated using the formula: \(\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\% \)
  • In this exercise, with a theoretical yield of 264.71 grams of \(\mathrm{CH}_2\mathrm{Cl}_2\), the actual yield, considering a 76% efficiency, is 201.18 grams.
Understanding percent yield lets us estimate the actual results from a chemical reaction under non-ideal conditions.
Balancing Chemical Equations
Balancing chemical equations is a vital skill in chemistry, ensuring that the same number of each kind of atom appears on both sides of the equation.The exercise illustrates this by balancing the reaction:\[\mathrm{CH}_4 + 2\mathrm{Cl}_2 \rightarrow \mathrm{CH}_2\mathrm{Cl}_2 + 2\mathrm{HCl}\]
  • First, count the number of each type of atom on both sides of the equation.
  • Adjust coefficients (the numbers in front of compounds) to make sure each type of atom has the same count on either side.
Knowing how to properly balance equations is crucial in stoichiometry, as it allows you to use the correct mole ratios in calculations, ensuring precise results pertaining to reactants and products.

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

Although Cu is not sufficiently active to react with acids, it can be dissolved by concentrated nitric acid, which functions as an oxidizing agent according to the following equation: \(\mathrm{Cu}(s)+4 \mathrm{HNO}_{3}(a q) \longrightarrow\) $$\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2 \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ (a) Write the net ionic equation for this process. (b) Is \(35.0 \mathrm{~g}\) of \(\mathrm{HNO}_{3}\) sufficient to dissolve \(5.00 \mathrm{~g}\) of copper?

The active ingredient in milk of magnesia (an antacid) is magnesium hydroxide, \(\mathrm{Mg}(\mathrm{OH})_{2}\). A typical dose (one tablespoon) contains \(1.2 \mathrm{~g}\) of \(\mathrm{Mg}(\mathrm{OH})_{2} .\) Calculate (a) the molar mass of magnesium hydroxide and (b) the amount of magnesium hydroxide (in moles) in one tablespoon.

What is the theoretical yield of chloroethane in the reaction of \(19.4 \mathrm{~g}\) of ethene with \(50 \mathrm{~g}\) of hydrogen chloride? What is the percent yield if \(25.5 \mathrm{~g}\) of chloroethane is actually formed? (For ethene, molecular mass \(=28.0\) amu; for hydrogen chloride, molecular mass \(=36.5\) amu; for chloroethane, molecular mass \(=64.5\) amu. \()\) \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}+\mathrm{HCl} \longrightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}\)

How many moles of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O},\) are in a \(10.0 \mathrm{~g}\) sample? How many grams are in a \(0.10 \mathrm{~mol}\) sample of ethanol?

Acetylsalicylic acid, the active ingredient in aspirin, is prepared from salicylic acid by reaction with acetic anhydride. $$\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \quad \longrightarrow \quad \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \quad+\quad \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$ (salicylic acid) (acetic anhydride) (acetylsalicylic acid) (acetic acid) (a) Calculate the theoretical yield if \(47 \mathrm{~g}\) of salicylic acid is reacted with \(25 \mathrm{~g}\) of acetic anhydride. (b) What is the percent yield if only \(35 \mathrm{~g}\) is obtained?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Kinetics

Read Explanation

Chemistry Branches

Read Explanation

Chemical Reactions

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Physical Chemistry

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.