0.924 mole of A (g) is placed in a 1.00 liter container at 700 ° C, where it is 38.8 % dissociatedwhen equilibrium was established.3 A (g) 5 B (g) + 2 C (g)What is the value of the equilibrium constant, Kc, at the same temperature?
Question
0.924 mole of A (g) is placed in a 1.00 liter container at 700 ° C, where it is 38.8 % dissociatedwhen equilibrium was established.3 A (g) 5 B (g) + 2 C (g)What is the value of the equilibrium constant, Kc, at the same temperature?
Solution
To find the value of the equilibrium constant, Kc, we need to use the given information about the moles of A and the percentage of dissociation.
Step 1: Calculate the initial moles of A: Given that 0.924 mole of A is placed in the 1.00 liter container, the initial moles of A is 0.924 mole.
Step 2: Calculate the moles of A that dissociate: Since the percentage of dissociation is 38.8%, we can calculate the moles of A that dissociate using the equation: Moles of A dissociated = Initial moles of A * Percentage of dissociation Moles of A dissociated = 0.924 mole * 0.388 Moles of A dissociated = 0.358512 mole
Step 3: Calculate the moles of B and C formed: According to the balanced equation, 3 moles of A produce 5 moles of B and 2 moles of C. So, the moles of B formed = Moles of A dissociated * (5/3) Moles of B formed = 0.358512 mole * (5/3) Moles of B formed = 0.59752 mole
Similarly, the moles of C formed = Moles of A dissociated * (2/3) Moles of C formed = 0.358512 mole * (2/3) Moles of C formed = 0.23894 mole
Step 4: Calculate the equilibrium concentrations: The equilibrium concentrations can be calculated by dividing the moles of each species by the volume of the container (1.00 liter).
Concentration of A = Moles of A / Volume of container Concentration of A = 0.924 mole / 1.00 L Concentration of A = 0.924 M
Concentration of B = Moles of B / Volume of container Concentration of B = 0.59752 mole / 1.00 L Concentration of B = 0.59752 M
Concentration of C = Moles of C / Volume of container Concentration of C = 0.23894 mole / 1.00 L Concentration of C = 0.23894 M
Step 5: Calculate the equilibrium constant, Kc: The equilibrium constant, Kc, can be calculated using the concentrations of the products and reactants. According to the balanced equation, the expression for Kc is: Kc = [B]^5 * [C]^2 / [A]^3
Substituting the values: Kc = (0.59752)^5 * (0.23894)^2 / (0.924)^3
Calculating this expression will give you the value of the equilibrium constant, Kc, at the given temperature of 700 °C.
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