Halogen lamps are ordinary tungsten filament lamps in which the lamp bulb contains a small amount of a halogen (often bromine). At the high temperatures of the lamp, the halogens dissociate and exist as single atoms.(c) When the WBr41g2 diffuses back toward the filament, it decomposes, depositing tungsten back onto the fila- ment. Show quantitatively that the pressure of WBr4 from part (a) will cause the reaction in part (a) to go in reverse direction at 2800 K. [The pressure of Br1g2 is still 0.010 atm.] Thus, tungsten is continually recycled from the walls of the bulb back to the filament, allow-ing the bulb to last longer and burn brighter.
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1
Identify the reaction from part (a) and write the balanced chemical equation for the decomposition of \( \text{WBr}_4 \) into \( \text{W} \) and \( \text{Br}_2 \).
Use the given temperature (2800 K) and the pressure of \( \text{Br}_2 \) (0.010 atm) to calculate the equilibrium constant \( K_p \) for the reverse reaction using the equation \( K_p = \frac{P_{\text{products}}}{P_{\text{reactants}}} \).
Determine the partial pressure of \( \text{WBr}_4 \) from part (a) and use it to calculate the reaction quotient \( Q_p \) for the reverse reaction.
Compare \( Q_p \) with \( K_p \) to determine the direction of the reaction. If \( Q_p > K_p \), the reaction will proceed in the reverse direction.
Conclude that the pressure of \( \text{WBr}_4 \) is sufficient to drive the reaction in the reverse direction, allowing tungsten to be deposited back onto the filament.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Chemical Equilibrium
Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In the context of the halogen lamp, understanding how changes in pressure affect the equilibrium position is crucial. According to Le Chatelier's principle, increasing the pressure of a gaseous reactant will shift the equilibrium towards the side with fewer gas molecules, which is essential for analyzing the reaction involving WBr4.
Gibbs free energy (G) is a thermodynamic potential that helps predict the direction of chemical reactions. A negative change in Gibbs free energy (ΔG) indicates that a reaction is spontaneous. At high temperatures, the relationship between Gibbs free energy, enthalpy, and entropy becomes significant, as it can determine whether the decomposition of WBr4 is favorable under the given conditions, such as 2800 K.
Partial pressure refers to the pressure exerted by a single component of a gas mixture. Dalton's Law states that the total pressure of a gas mixture is the sum of the partial pressures of its individual components. In this scenario, understanding how the partial pressure of Br2 and WBr4 influences the overall reaction is vital for determining the conditions under which the tungsten recycling process occurs effectively.
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