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Determine \(\Delta n_{\text {gas }}\) for each of the following reactions: (a) \(2 \mathrm{KClO}_{3}(s) \rightleftharpoons 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\) (b) \(2 \mathrm{PbO}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{PbO}_{2}(s)\) (c) \(\mathrm{I}_{2}(s)+3 \mathrm{XeF}_{2}(s) \Longrightarrow 2 \mathrm{IF}_{3}(s)+3 \mathrm{Xe}(g)\)

Short Answer

Expert verified
For (a) \( \backslash \Delta n_{\text {gas}} = 3 \), (b) \( \backslash \Delta n_{\text {gas}} = -1 \), (c) \( \backslash \Delta n_{\text {gas}} = 3 \).

Step by step solution

01

Understanding \(\backslash \Delta n_{\text {gas}}\) Concept

\(\backslash \Delta n_{\text {gas}}\) represents the change in the number of moles of gas during a chemical reaction. It is calculated as the difference between the moles of gaseous products and moles of gaseous reactants.
02

Analyzing Reaction (a)

For the reaction \(2 \, \text{KClO}_{3} (s) \rightarrow 2 \, \text{KCl} (s) + 3 \, \text{O}_{2} (g)\), there are no gaseous reactants and 3 moles of \(\text{O}_{2}\) gas as the product. Therefore, \(\backslash \Delta n_{\text {gas}} = 3 - 0 = 3\).
03

Analyzing Reaction (b)

For the reaction \(2 \, \text{PbO} (s) + \text{O}_{2} (g) \rightarrow 2 \, \text{PbO}_{2} (s)\), there is 1 mole of \(\text{O}_{2}\) gas as the reactant and no gaseous products. Therefore, \(\backslash \Delta n_{\text {gas}} = 0 - 1 = -1\).
04

Analyzing Reaction (c)

For the reaction \( \text{I}_{2} (s) + 3 \, \text{XeF}_{2} (s) \rightarrow 2 \, \text{IF}_{3} (s) + 3 \, \text{Xe} (g)\), there are no gaseous reactants and 3 moles of \(\text{Xe}\) gas as the product. Therefore, \(\backslash \Delta n_{\text {gas}} = 3 - 0 = 3\).

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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 reactants into products. These transformations often involve changes in the state of matter, including solids, liquids, and gases. In the context of calculating \( \Delta n_{\text {gas}} \), understanding the state of each substance is crucial.

In the chemical equations given:
  • Reactants are substances that start a reaction.
  • Products are substances formed as a result of the reaction.
  • The states of matter are denoted by (s) for solids, (l) for liquids, (g) for gases, and (aq) for aqueous solutions.
Consider the reaction: \(2 \text{KClO}_{3}(s) \rightarrow 2 \text{KCl}(s) + 3 \text{O}_{2}(g)\). Here, potassium chlorate (\(2 \text{KClO}_{3}\)) breaks down into potassium chloride (\(2 \text{KCl}\)) and oxygen gas (\(3 \text{O}_{2}\)). Understanding each component's state helps in calculating the change in gas moles.

Balancing chemical equations ensures that the same number of each type of atom appears on both sides of the equation, maintaining the law of conservation of mass.
Moles of Gas
Moles measure the amount of a substance. In chemical reactions, particularly those involving gases, counting the moles accurately determines the quantitative outcome of the reaction.

The concept of \( \Delta n_{\text {gas}} \) focuses on the change in the number of moles of gas during a chemical reaction. To calculate \( \Delta n_{\text {gas}} \):
  • Determine the moles of gaseous products (products that are in gas form).
  • Determine the moles of gaseous reactants (reactants that are in gas form).
  • Subtract the moles of gaseous reactants from the moles of gaseous products.
For example, in the reaction \(2 \text{PbO}(s) + \text{O}_{2}(g) \rightarrow 2 \text{PbO}_{2}(s)\), there is 1 mole of \(\text{O}_{2}\) as reactant and no gaseous products. Therefore, \( \Delta n_{\text {gas}} = 0 - 1 = -1\). This indicates a decrease of one mole of gas in the reaction.
Gaseous Products and Reactants
Identifying gaseous products and reactants correctly is essential in calculating \( \Delta n_{\text {gas}} \). The state of reactants and products in a chemical reaction determines whether they are included in the \( \Delta n_{\text {gas}} \) calculation.

Let's examine the third reaction: \( \text{I}_{2}(s) + 3 \text{XeF}_{2}(s) \rightarrow 2 \text{IF}_{3}(s) + 3 \text{Xe}(g)\).
  • Here, iodine (\(\text{I}_{2}\)) and xenon difluoride (\(3 \text{XeF}_{2}\)) are solid reactants.
  • Iodine trifluoride (\(2 \text{IF}_{3}\)) is a solid product.
  • Xenon (\(3 \text{Xe}\)) is a gaseous product.
By identifying which substances are gases, you can easily calculate \( \Delta n_{\text {gas}} = 3 - 0 = 3\). This increase in gaseous moles shows that more gas is produced than consumed. Keeping track of the states of all reactants and products simplifies these calculations.

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Most popular questions from this chapter

The methane used to obtain \(\mathrm{H}_{2}\) for \(\mathrm{NH}_{3}\) manufacture is impure and usually contains other hydrocarbons, such as propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\). Imagine the reaction of propane occurring in two steps: \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 3 \mathrm{CO}(g)+7 \mathrm{H}_{2}(g)\) $$ \begin{array}{r} K_{\mathrm{p}}=8.175 \times 10^{15} \text { at } 1200 . \mathrm{K} \\ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \\ K_{\mathrm{p}}=0.6944 \text { at } 1200 . \mathrm{K} \end{array} $$ (a) Write the overall equation for the reaction of propane and steam to produce carbon dioxide and hydrogen. (b) Calculate \(K_{p}\) for the overall process at \(1200 .\) K. (c) When 1.00 volume of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and 4.00 volumes of \(\mathrm{H}_{2} \mathrm{O},\) each at \(1200 . \mathrm{K}\) and \(5.0 \mathrm{~atm},\) are mixed in a container, what is the final pressure? Assume the total volume remains constant, that the reaction is essentially complete, and that the gases behave ideally. (d) What percentage of the \(\mathrm{C}_{3} \mathrm{H}_{8}\) remains unreacted?

Ammonium carbamate \(\left(\mathrm{NH}_{2} \mathrm{COONH}_{4}\right)\) is a salt of carbamic acid that is found in the blood and urine of mammals. At \(250 .{ }^{\circ} \mathrm{C}, K_{\mathrm{c}}=1.58 \times 10^{-8}\) for the following equilibrium: $$ \mathrm{NH}_{2} \mathrm{COONH}_{4}(s) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) $$ If \(7.80 \mathrm{~g}\) of \(\mathrm{NH}_{2} \mathrm{COONH}_{4}\) is put into a \(0.500-\mathrm{L}\) evacuated container, what is the total pressure at equilibrium?

Balance each of the following examples of heterogeneous equilibria and write each reaction quotient, \(Q_{c}:\) (a) \(\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) (b) \(\mathrm{KNO}_{3}(s) \rightleftharpoons \mathrm{KNO}_{2}(s)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{S}_{8}(s)+\mathrm{F}_{2}(g) \rightleftharpoons \mathrm{SF}_{6}(g)\)

Consider the formation of ammonia in two experiments. (a) To a 1.00 -L container at \(727^{\circ} \mathrm{C}, 1.30 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) and \(1.65 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) are added. At equilibrium, \(0.100 \mathrm{~mol}\) of \(\mathrm{NH}_{3}\) is present. Calculate the equilibrium concentrations of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\), and find \(K_{\mathrm{c}}\) for the reaction $$ 2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) $$ (b) In a different 1.00 -L container at the same temperature, equilibrium is established with \(8.34 \times 10^{-2} \mathrm{~mol}\) of \(\mathrm{NH}_{3}, 1.50 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) and \(1.25 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) present. Calculate \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{NH}_{3}(g) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) $$ (c) What is the relationship between the \(K_{\mathrm{c}}\) values in parts (a) and (b)? Why aren't these values the same?

Nitrogen dioxide decomposes according to the reaction $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) $$ where \(K_{\mathrm{p}}=4.48 \times 10^{-13}\) at a certain temperature. If \(0.75 \mathrm{~atm}\) of \(\mathrm{NO}_{2}\) is added to a container and allowed to come to equilibrium, what are the equilibrium partial pressures of \(\mathrm{NO}(g)\) and \(\mathrm{O}_{2}(g) ?\)

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