/*! 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 66 Certain race cars use methanol (... [FREE SOLUTION] | 91Ó°ÊÓ

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Certain race cars use methanol (CH \(_{3} \mathrm{OH}\), also called wood alcohol) as a fuel. The combustion of methanol occurs according to the following equation:$$2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)$$In a particular reaction, 9.8 moles of \(\mathrm{CH}_{3} \mathrm{OH}\) are reacted with an excess of \(\mathrm{O}_{2}\). Calculate the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) formed.

Short Answer

Expert verified
The number of moles of \(\mathrm{H}_{2} \mathrm{O}\) formed is 19.6

Step by step solution

01

Identify the relevant stoichiometric ratio

From the balanced chemical equation, you can see that the ratio between the moles of methanol (\(\mathrm{CH}_{3} \mathrm{OH}\)) and water (\(\mathrm{H}_{2} \mathrm{O}\)) is 2 : 4, or simplifying, 1 : 2. It means for every 1 mole of methanol reacted, 2 moles of water are formed.
02

Use the identified ratio to compute the moles of water

We know that there are 9.8 moles of methanol reacted. We use our ratio to calculate the quantity of water produced. By multiplying the 9.8 moles of methanol by the stoichiometric ratio of 2 moles of water per mole of methanol, we get the number of moles of water produced.
03

Calculation

The calculation becomes \(9.8 \: \text{moles CH}_{3} \text{OH} \times \frac{2 \: \text{moles H}_{2} \text{O}}{1 \: \text{mole CH}_{3} \text{OH}} = 19.6 \: \text{moles H}_{2} \text{O}\).

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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 one or more substances into new substances. Each reaction follows a specific pattern, represented by a chemical equation. In these equations, reactants are substances that undergo change, while products are the new substances formed.

Every chemical equation must be balanced, meaning that the number of atoms for each element in the reaction must be the same on both sides of the equation. This reflects the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. Balance ensures that the quantities of reactants and products are in the right proportions.
  • In a balanced chemical reaction, coefficients are used to ensure the same number of each type of atom appears on both sides.
  • The equation given for the combustion of methanol is an example of a balanced chemical equation: \[ 2 \mathrm{CH}_{3} \mathrm{OH}(l) + 3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2} \mathrm{O}(l) \]
Understanding these coefficients is crucial, as they help in calculating the amounts of products formed from given reactants.
Mole Concept
The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. One mole of any substance contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). This concept enables chemists to count particles by weighing them.

In stoichiometry, the mole concept is crucial as it connects the macroscopic world (grams, liters) to the microscopic world (atoms, molecules, ions). It serves as the bridge between balanced chemical equations and real-world reactions.
  • For instance, in the methanol combustion reaction, the mole ratio is used to relate moles of methanol to moles of water formed.
  • This allows the calculation of the amount of product (water) from a given amount of reactant (methanol).
The key is to use the balanced chemical equation, which tells how many moles of one substance react with how many moles of another substance. This ensures precise calculations in chemical processes.
Combustion Reaction
Combustion reactions are a type of chemical reaction where a substance combines with oxygen to release energy. They are essential in various applications, such as powering engines or heating homes.

A common example of combustion is the burning of fuels, like in the reaction of methanol as demonstrated here. Combustion typically produces carbon dioxide and water as byproducts when a hydrocarbon or alcohol is burned in the presence of oxygen.
  • The general form of a combustion reaction can be shown as: \[ \text{Fuel} + \text{Oxygen} \rightarrow \text{Carbon Dioxide} + \text{Water} \]
  • Specific to the methanol example: \[ 2 \mathrm{CH}_{3} \mathrm{OH} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O} \]
In this case, the methanol serves as the fuel. The reaction with oxygen, a combustion reaction, results in energy, carbon dioxide, and water, consistent with many real-world applications of combustion.

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Most popular questions from this chapter

A certain metal oxide has the formula \(\mathrm{MO},\) where \(\mathrm{M}\) denotes the metal. A \(39.46-\mathrm{g}\) sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, \(31.70 \mathrm{~g}\) of the metal is left over. If \(\mathrm{O}\) has an atomic mass of 16.00 amu, calculate the atomic mass of \(\mathrm{M}\) and identify the element.

In the formation of carbon monoxide, CO, it is found that \(2.445 \mathrm{~g}\) of carbon combine with \(3.257 \mathrm{~g}\) of oxygen. What is the atomic mass of oxygen if the atomic mass of carbon is 12.01 amu?

Titanium(IV) oxide \(\left(\mathrm{TiO}_{2}\right)\) is a white substance produced by the action of sulfuric acid on the mineral ilmenite \(\left(\mathrm{FeTiO}_{3}\right)\) $$\mathrm{FeTiO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow\mathrm{TiO}_{2}+\mathrm{FeSO}_{4}+\mathrm{H}_{2} \mathrm{O}$$Its opaque and nontoxic properties make it suitable as a pigment in plastics and paints. In one process, \(8.00 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{FeTiO}_{3}\) yielded \(3.67 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{TiO}_{2} .\) What is the percent yield of the reaction?

Allicin is the compound responsible for the characteristic smell of garlic. An analysis of the compound gives the following percent composition by mass: C: 44.4 percent, \(\mathrm{H}: 6.21\) percent, \(\mathrm{S}: 39.5\) percent, \(\mathrm{O}:\) 9.86 percent. Calculate its empirical formula. What is its molecular formula given that its molar mass is about \(162 \mathrm{~g}\) ?

A certain metal M forms a bromide containing 53.79 percent Br by mass. What is the chemical formula of the compound?

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