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Chapter 3: Problem 122

Consider the following reaction: $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ If a container were to have 10 molecules of \(\mathrm{O}_{2}\) and 10 molecules of \(\mathrm{NH}_{3}\) initially, how many total molecules (reactants plus products) would be present in the container after this reaction goes to completion?

Short Answer

Expert verified
The limiting reactant in the given reaction is O₂. When the reaction goes to completion, there will be 8 molecules of NO, 12 molecules of H₂O, and 2 remaining molecules of NH₃. So, the total number of molecules present in the container will be 22.

Step by step solution

01

Identify the limiting reactant

To identify the limiting reactant, compare the mole ratios of the given reactants to the balanced equation. Using the balanced equation: 4 NH₃ + 5 O₂ → 4 NO + 6 H₂O We have 10 molecules of NH₃ and 10 molecules of O₂. To find out which reactant will run out first, let's divide the number of molecules by their respective coefficients from the balanced equation. For NH₃: \( \frac{10}{4} \) = 2.5 For O₂: \( \frac{10}{5} \) = 2 Since the value for O₂ is smaller, it will be the limiting reactant and will determine the amount of products formed.
02

Determine the moles of products formed

Using the mole ratios in the balanced equation, we will calculate the amount of NO and H₂O produced when all the O₂ molecules react: For NO The mole ratio of O₂ to NO is \( \frac{5}{4} \). So, using the limiting reactant O₂, we can calculate the number of NO molecules formed: \(NO\, molecules = \frac{4}{5} \times 10 = 8\, molecules\) For H₂O The mole ratio of O₂ to H₂O is \( \frac{5}{6} \). So, using the limiting reactant O₂, we can calculate the amount of H₂O molecules formed: \(H_2O\, molecules = \frac{6}{5} \times 10 = 12\, molecules\)
03

Determine the remaining moles of NH₃

Now, we need to determine how many NH₃ molecules are left after the reaction goes to completion. To do this, we will use the mole ratio of NH₃ to O₂ from the balanced equation, which is \( \frac{4}{5} \): \(Used\, NH_3\, molecules = \frac{4}{5} \times 10 = 8\, molecules\) Thus, the remaining NH₃ molecules: \(Remaining\, NH_3\, molecules = 10 - 8 = 2\, molecules\)
04

Calculate the total number of molecules present after the reaction

Finally, we can calculate the total number of molecules present in the container after the reaction goes to completion by adding the moles of the remaining reactant (NH₃) and the products formed (NO and H₂O): Total molecules = Remaining NH₃ molecules + NO molecules + H₂O molecules Total molecules = 2 + 8 + 12 Total molecules = 22 Therefore, there will be 22 total molecules present in the container after the reaction goes to completion.

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Most popular questions from this chapter

Which of the following statements about chemical equations is(are) true? a. When balancing a chemical equation, you can never change the coefficient in front of any chemical formula. b. The coefficients in a balanced chemical equation refer to the number of grams of reactants and products. c. In a chemical equation, the reactants are on the right and the products are on the left. d. When balancing a chemical equation, you can never change the subscripts of any chemical formula. e. In chemical reactions, matter is neither created nor destroyed so a chemical equation must have the same number of atoms on both sides of the equation.

Elixirs such as Alka-Seltzer use the reaction of sodium bicarbonate with citric acid in aqueous solution to produce a fizz: $$ 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q) \longrightarrow $$ $$ 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) $$ a. What mass of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used for every \(1.0 \times 10^{2} \mathrm{mg} \mathrm{NaHCO}_{3} ?\) b. What mass of \(\mathrm{CO}_{2}(g)\) could be produced from such a mixture?

Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

A sample of a hydrocarbon (a compound consisting of only carbon and hydrogen contains \(2.59 \times 10^{23}\) atoms of hydrogen and is 17.3\(\%\) hydrogen by mass. If the molar mass of the hydrocarbon is between 55 and 65 g/mol, what amount (moles) of compound is present, and what is the mass of the sample?

Vitamin A has a molar mass of 286.4 \(\mathrm{g} / \mathrm{mol}\) and a general molecular formula of \(\mathrm{C}_{x} \mathrm{H}, \mathrm{E}\) , where \(\mathrm{E}\) is an unknown element. If vitamin \(\mathrm{A}\) is 83.86$\% \mathrm{C}\( and 10.56\)\% \mathrm{H}$ by mass, what is the molecular formula of vitamin A?
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