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Chapter 13: Problem 73

For the following reactions, predict whether the mole fraction of the reactants or products increases or remains the same when the volume of the reaction vessel is increased. a. $\operatorname{Br}_{2}(g)+\mathrm{H}_{2}(g) \leftrightharpoons 2 \mathrm{HBr}(g)$ b. $2 \mathrm{CH}_{4}(g) \leftrightharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g)$ c. \(2 \mathrm{HI}(g) \leftrightharpoons \mathrm{I}_{2}(s)+\mathrm{H}_{2}(g)\)

Short Answer

Expert verified
For each reaction: a. The mole fraction of reactants and products remains the same. b. The mole fraction of reactants decreases, while the mole fraction of products increases. c. The mole fraction of reactants increases, while the mole fraction of products decreases.

Step by step solution

01

(Balancing the equation)

First, we need to make sure the given equation is balanced: \[ \mathrm{Br}_{2}(g)+\mathrm{H}_{2}(g) \leftrightharpoons 2 \mathrm{HBr}(g) \] Here, the reaction is already balanced.
02

(Identifying the number of gas moles)

Now, we must identify the number of gas moles on both sides of the equation. On the reactant side, there are 2 moles of gas molecules (1 mole of Br2 and 1 mole of H2). On the product side, there are 2 moles of gas molecules (2 moles of HBr).
03

(Predicting the reaction direction)

When we increase the volume of the reaction vessel, the pressure decreases. From Le Chatelier's principle, the reaction will shift its equilibrium in the direction that has more gas moles. In this case, both sides have the same number of gas moles, so the reaction will be unaffected, and the mole fraction of the reactants and products will remain the same. #b. Reaction 2:
04

(Balancing the equation)

First, we need to make sure the given equation is balanced: \[ 2 \mathrm{CH}_{4}(g) \leftrightharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g) \] Here, the reaction is already balanced.
05

(Identifying the number of gas moles)

Now, we must identify the number of gas moles on both sides of the equation. On the reactant side, there are 2 moles of gas molecules (2 moles of CH4). On the product side, there are 4 moles of gas molecules (1 mole of C2H2 and 3 moles of H2).
06

(Predicting the reaction direction)

When we increase the volume of the reaction vessel, the pressure decreases. From Le Chatelier's principle, the reaction will shift its equilibrium in the direction that has more gas moles. In this case, the reaction will shift to the right (toward the products). So, the mole fraction of the reactants will decrease, while the mole fraction of the products will increase. #c. Reaction 3:
07

(Balancing the equation)

First, we need to make sure the given equation is balanced: \[ 2 \mathrm{HI}(g) \leftrightharpoons \mathrm{I}_{2}(s)+\mathrm{H}_{2}(g) \] Here, the reaction is already balanced.
08

(Identifying the number of gas moles)

Now, we must identify the number of gas moles on both sides of the equation. On the reactant side, there are 2 moles of gas molecules (2 moles of HI). On the product side, there is 1 mole of gas molecule (1 mole of H2; note that I2 is a solid and thus not included in gas mole counting).
09

(Predicting the reaction direction)

When we increase the volume of the reaction vessel, the pressure decreases. From Le Chatelier's principle, the reaction will shift its equilibrium in the direction that has more gas moles. In this case, the reaction will shift to the left (toward the reactants). So, the mole fraction of the reactants will increase, while the mole fraction of the products will decrease.

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Most popular questions from this chapter

The equilibrium constant \(K_{\mathrm{p}}\) is \(2.4 \times 10^{3}\) at a certain temperature for the reaction $$2 \mathrm{NO}(g) \leftrightharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)$$ For which of the following sets of conditions is the system at equilibrium? For those not at equilibrium, in which direction will the system shift? a. $P_{\mathrm{NO}}=0.012 \mathrm{atm}, P_{\mathrm{N}_{2}}=0.11 \mathrm{atm}, P_{\mathrm{O}_{2}}=2.0 \mathrm{atm}$ b. $P_{\mathrm{NO}}=0.0078 \mathrm{atm}, P_{\mathrm{N}_{2}}=0.36 \mathrm{atm}, P_{\mathrm{O}_{2}}=0.67 \mathrm{atm}$ c. $P_{\mathrm{NO}}=0.0062 \mathrm{atm}, P_{\mathrm{N}_{2}}=0.51 \mathrm{atm}, P_{\mathrm{O}_{2}}=0.18 \mathrm{atm}$

The gas arsine, \(\mathrm{AsH}_{3},\) decomposes as follows: $$2 \mathrm{AsH}_{3}(g) \rightleftharpoons 2 \mathrm{As}(s)+3 \mathrm{H}_{2}(g)$$ In an experiment at a certain temperature, pure \(\mathrm{AsH}_{3}(g)\) was placed in an empty, rigid, sealed flask at a pressure of 392.0 torr. After 48 hours the pressure in the flask was observed to be constant at 488.0 torr. a. Calculate the equilibrium pressure of \(\mathrm{H}_{2}(g)\) b. Calculate \(K_{\mathrm{p}}\) for this reaction.

The partial pressures of an equilibrium mixture of $\mathrm{N}_{2} \mathrm{O}_{4}(g)\( and \)\mathrm{NO}_{2}(g)\( are \)P_{\mathrm{N}_{2} \mathrm{O}_{4}}=0.34\( atm and \)P_{\mathrm{NO}_{2}}=1.20 \mathrm{atm}$ at a certain temperature. The volume of the container is doubled. Calculate the partial pressures of the two gases when a new equilibrium is established.

Consider the following exothermic reaction at equilibrium: $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$ Predict how the following changes affect the number of moles of each component of the system after equilibrium is reestablished by completing the table below. Complete the table with the terms increase, decrease, or no change.

Consider the following reaction: $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$ Amounts of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2},\) and \(\mathrm{CO}_{2}\) are put into a flask so that the composition corresponds to an equilibrium position. If the CO placed in the flask is labeled with radioactive \(^{14} \mathrm{C}\) will \(^{14} \mathrm{C}\) be found only in \(\mathrm{CO}\) molecules for an indefinite period of time? Explain.
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