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Chapter 4: Problem 41

Chloroform, \(\mathrm{CHCl}_{3}\), is prepared industrially by the reaction of methane with chlorine. How many grams of \(\mathrm{Cl}_{2}\) are needed to produce 1.50 moles of chloroform? \(\mathrm{CH}_{4}(\mathrm{g})+3 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{CHCl}_{3}(\ell)+3 \mathrm{HCl}(\mathrm{g})\)

Short Answer

Expert verified
319.05 grams of \( \mathrm{Cl}_2 \) are needed.

Step by step solution

01

Understand the Balanced Equation

The balanced chemical equation for the reaction is \( \mathrm{CH}_4(\mathrm{g}) + 3 \mathrm{Cl}_2(\mathrm{g}) \rightarrow \mathrm{CHCl}_3(\ell) + 3 \mathrm{HCl}(\mathrm{g}) \). This tells us that 3 moles of chlorine gas \( \mathrm{Cl}_2 \) are needed to produce 1 mole of chloroform \( \mathrm{CHCl}_3 \).
02

Set Up the Mole Ratio

From the balanced equation, the mole ratio of \( \mathrm{Cl}_2 \) to \( \mathrm{CHCl}_3 \) is 3:1. This implies that to produce 1.50 moles of \( \mathrm{CHCl}_3 \), we need \( 1.50 \times 3 = 4.50 \) moles of \( \mathrm{Cl}_2 \).
03

Convert Moles of \( \mathrm{Cl}_2 \) to Grams

The molar mass of \( \mathrm{Cl}_2 \) is \( 2 \times 35.45 = 70.90 \ \mathrm{g/mol} \) (since the atomic mass of \( \mathrm{Cl} \) is 35.45). To find the mass in grams, we use the formula: \( \text{mass} = \text{moles} \times \text{molar mass} \). Substituting in the values gives \( 4.50 \times 70.90 = 319.05 \ \mathrm{g} \).

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Key Concepts

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

Understanding the Chemical Equation
A chemical equation provides a symbolic representation of a chemical reaction. In our example, the equation is \( \mathrm{CH}_{4} + 3 \mathrm{Cl}_{2} \rightarrow \mathrm{CHCl}_{3} + 3 \mathrm{HCl} \). This equation is balanced, which means the number of atoms for each element is conserved on both sides of the equation. This is crucial for understanding how reactants transform into products.
  • The equation tells us one molecule of methane (\( \mathrm{CH}_4 \)) reacts with three molecules of chlorine gas (\( \mathrm{Cl}_2 \)).
  • This produces one molecule of chloroform (\( \mathrm{CHCl}_3 \)) and three molecules of hydrogen chloride (\( \mathrm{HCl} \)).
The balanced chemical equation is fundamental for determining the relationship between reactants and products, allowing us to calculate quantities such as moles and mass accurately.
The Importance of Mole Ratio
The mole ratio derived from the balanced chemical equation is a crucial concept in stoichiometry. It relates the amounts of each substance involved in the reaction.
In our chemical equation, the mole ratio is expressed between \( \mathrm{Cl}_2 \) and \( \mathrm{CHCl}_3 \) as 3:1. This ratio tells us that three moles of chlorine are required to produce one mole of chloroform.
Given that we want to produce 1.50 moles of chloroform, the mole ratio helps us calculate the moles of chlorine needed:
  • Multiply the moles of chloroform by the mole ratio: \( 1.50 \times 3 = 4.50 \) moles of \( \mathrm{Cl}_2 \).
This step is vital for moving from theoretical ratios to practical quantities, ensuring we have enough reactants to complete the reaction.
Calculating Molar Mass and Mass
Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is used to convert between moles of a substance and its mass.
For chlorine gas \( \mathrm{Cl}_2 \), each chlorine atom has an atomic mass of 35.45. Therefore, the molar mass of \( \mathrm{Cl}_2 \) is calculated as follows:
  • Multiply the atomic mass of chlorine by 2 (since there are two chlorine atoms in each molecule): \( 2 \times 35.45 = 70.90 \ \text{g/mol} \).
To find the mass of chlorine needed, use the formula:
  • \( \text{mass} = \text{moles} \times \text{molar mass} \).
  • Substituting known values gives: \( 4.50 \times 70.90 = 319.05 \ \text{g} \).
This calculation converts theoretical mole quantities into practical mass measures, allowing chemists to accurately determine the amount of chemical substances required for reactions.

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Most popular questions from this chapter

What is the difference between exothermic and endothermic reactions?

Chlorine dioxide, \(\mathrm{ClO}_{2}\), is used for bleaching paper. It is also the gas used to kill the anthrax spores that contaminated the Hart Senate Office Building in the fall of 2001 . Chlorine dioxide is prepared by treating sodium chlorite with chlorine gas. \(\mathrm{NaClO}_{2}(\mathrm{aq})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{ClO}_{2}(\mathrm{g})+\mathrm{NaCl}(\mathrm{aq})\) (a) Balance the equation for the preparation of chlorine dioxide (b) Calculate the weight of chlorine dioxide that can be prepared from \(5.50 \mathrm{kg}\) of sodium chlorite.

Assume the gasoline in an automobile is composed completely of octane, \(C_{8} H_{18}(\ell),\) with a density of \(0.69 \mathrm{g} / \mathrm{mL} .\) If the automobile travels 168 miles with a gas mileage of \(21.2 \mathrm{mi} / \mathrm{gal}\), how many kg of \(\mathrm{CO}_{2}\) are produced assuming complete combustion of octane and excess oxygen?

The active ingredient in an analgesic tablet is \(488 \mathrm{mg}\) of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{5}\). How many moles of aspirin does the tablet contain?

Answer true or false. (a) Heat of reaction is the heat given off or absorbed by a chemical reaction. (b) An endothermic reaction is one that gives off heat. (c) If a chemical reaction is endothermic, the reverse reaction is exothermic. (d) All combustion reactions are exothermic. (e) If the reaction of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) and \(\mathrm{O}_{2}\) in the body to give \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) is an exothermic reaction, then photosynthesis in green plants (the reaction of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) to give glucose and \(\mathrm{O}_{2}\) ) is an endothermic process. (f) The energy required to drive photosynthesis comes from the sun in the form of electromagnetic radiation.
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