If \(K_{c}=1\) for the equilibrium \(2 \mathrm{A}(g) \rightleftharpoons \mathrm{B}(g),\) what is the relationship between \([\mathrm{A}]\) and \([\mathrm{B}]\) at equilibrium?

Short Answer

Expert verified
The relationship between the equilibrium concentrations of A and B can be expressed as: \([B] = [A]^2\).

Step by step solution

01

Write the equilibrium expression

For the given reaction, 2 A(g) ⇌ B(g), the equilibrium constant (Kc) can be expressed in terms of the equilibrium concentrations of the reactants and products. The general form of the expression for Kc is: Kc = \(\frac{[Products]}{[Reactants]}\) For this particular reaction, Kc will be: Kc = \(\frac{[B]}{[A]^2}\) We are given that Kc = 1.
02

Substitute Kc into the equilibrium expression and solve for the relationship

Now we can substitute the given Kc value (1) into the equilibrium expression: 1 = \(\frac{[B]}{[A]^2}\) To find the relationship, rearrange the equation to isolate [B] or [A] on one side. In this case, we can isolate [B]: [B] = [A]^2
03

State the relationship between [A] and [B]

At equilibrium, the concentration of B, [B], is equal to the square of the concentration of A, [A]^2. Therefore, the relationship between the equilibrium concentrations of A and B can be expressed as: [B] = [A]^2

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Most popular questions from this chapter

The equilibrium constant for the reaction $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ is \(K_{c}=1.3 \times 10^{-2}\) at 1000 \(\mathrm{K}\) . (a) At this temperature does the equilibrium favor \(\mathrm{NO}\) and \(\mathrm{Br}_{2},\) or does it favor NOBr? (b) Calculate \(K_{c}\) for \(2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)\) (c) Calculate \(K_{c}\) for \(\operatorname{NOBr}(g) \rightleftharpoons \mathrm{NO}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)\)

The reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)\) has \(K_{p}=\) 0.0870 at \(300^{\circ} \mathrm{C} .\) A flask is charged with 0.50 atm \(\mathrm{PCl}_{3}, 0.50 \mathrm{atm} \mathrm{Cl}_{2},\) and 0.20 atm \(\mathrm{PCl}_{5}\) at this temperature. (a) Use the reaction quotient to determine the direction the reaction must proceed to reach equilibrium. (b) Calculate the equilibrium partial pressures of the gases. (c) What effect will increasing the volume of the system have on the mole fraction of \(\mathrm{Cl}_{2}\) in the equilibrium mixture? (d) The reaction is exothermic. What effect will increasing the temperature of the system have on the mole fraction of \(\mathrm{Cl}_{2}\) in the equilibrium mixture?

Consider the hypothetical reaction \(\mathrm{A}(g) \rightleftharpoons 2 \mathrm{B}(g) . \mathrm{A}\) flask is charged with 0.75 atm of pure \(\mathrm{A},\) after which it is allowed to reach equilibrium at \(0^{\circ} \mathrm{C}\) . At equilibrium, the partial pressure of \(\mathrm{A}\) is 0.36 atm. (a) What is the total pressure in the flask at equilibrium? (b) What is the value of \(K_{p} ?(\mathbf{c})\) What could we do to maximize the yield of B?

The equilibrium constant \(K_{c}\) for \(C(s)+\mathrm{CO}_{2}(g) \rightleftharpoons\) 2 \(\mathrm{CO}(g)\) is 1.9 at 1000 \(\mathrm{K}\) and 0.133 at 298 \(\mathrm{K}\) . (a) If excess\(\mathrm{C}\) is allowed to react with 25.0 \(\mathrm{g}\) of \(\mathrm{CO}_{2}\) in a 3.00 -L vessel at \(1000 \mathrm{K},\) how many grams of CO are produced? (b) How many grams of \(\mathrm{C}\) are consumed? (c) If a smaller vessel is used for the reaction, will the yield of CO be greater or smaller? (d) Is the reaction endothermic or exothermic?

Consider the hypothetical reaction \(\mathrm{A}(g)+2 \mathrm{B}(g) \rightleftharpoons\) \(2 \mathrm{C}(g),\) for which \(K_{c}=0.25\) at a certain temperature. A 1.00 -L reaction vessel is loaded with 1.00 mol of compound \(C,\) which is allowed to reach equilibrium. Let the variable \(x\) represent the number of mol/L of compound A present at equilibrium. (a) In terms of \(x,\) what are the equilibrium concentrations of compounds \(\mathrm{B}\) and \(\mathrm{C} ?\) (b) What limits must be placed on the value of \(x\) so that all concentrations are positive? (c) By putting the equilibrium concentrations (in terms of \(x\) ) into the equilibrium-constant expression, derive an equation that can be solved for \(x .(\mathbf{d})\) The equation from part (c) is a cubic equation (one that has the form \(a x^{3}+b x^{2}+c x+d=0 )\) . In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of \(x\) that you specified in part (b). The point at which the cubic equation crosses the \(x\) -axis is the solution. (e) From the plot in part (d), estimate the equilibrium concentrations of \(A, B,\) and C. (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

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