Respuesta :
Answer:
a. Kp=1.4
[tex]P_{A}=0.2215 atm[/tex]
[tex]P_{B}=0.556 atm[/tex]
b.Kp=2.0 * 10^-4
[tex]P_{A}=0.495atm[/tex]
[tex]P_{B}=0.00995 atm[/tex]
c.Kp=2.0 * 10^5
[tex]P_{A}=5*10^{-6}atm[/tex]
[tex]P_{B}=0.9999 atm[/tex]
Explanation:
For the reaction
A(g)⇌2B(g)
Kp is defined as:
[tex]Kp=\frac{(P_{B})^{2}}{P_{A}}[/tex]
The conditions in the system are:
A B
initial 0 1 atm
equilibrium x 1atm-2x
At the beginning, we don’t have any A in the system, so B starts to react to produce A until the system reaches the equilibrium producing x amount of A. From the stoichiometric relationship in the reaction we get that to produce x amount of A we need to 2x amount of B so in the equilibrium we will have 1 atm – 2x of B, as it is showed in the table.
Replacing these values in the expression for Kp we get:
[tex]Kp=\frac{(1-2x)^{2}}{x}[/tex]
Working with this equation:
[tex]x*Kp=(1-2x)^{2} - -> x*Kp=4x^{2}-4x+1- - >4x^{2}-(4+Kp)*x+1=0[/tex]
This last expression is quadratic expression with a=4, b=-(4+Kp) and c=1
The general expression to solve these kinds of equations is:
[tex]x=\frac{-b(+-)*\sqrt{(b^{2}-4ac)}}{2a}[/tex] (equation 1)
We just take the positive values from the solution since negative partial pressures don´t make physical sense.
Kp = 1.4
[tex]x_{1}=\frac{(1.4+4)+\sqrt{(-(1.4+4)^{2}-4*4*1)}}{2*4}=1.128[/tex]
[tex]x_{1}=\frac{(1.4+4)-\sqrt{(-(1.4+4)^{2}-4*4*1)}}{2*4}=0.2215[/tex]
With x1 we get a partial pressure of:
[tex]P_{A}=1.128 atm[/tex]
[tex]P_{B}=1-2*1.128 = -1.256 atm[/tex]
Since negative partial pressure don´t make physical sense x1 is not the solution for the system.
With x2 we get:
[tex]P_{A}=0.2215 atm[/tex]
[tex]P_{B}=1-2*0.2215 = 0.556 atm[/tex]
These partial pressures make sense so x2 is the solution for the equation.
We follow the same analysis for the other values of Kp.
Kp=2*10^-4
X1=0.505
X2=0.495
With x1
[tex]P_{A}=0.505atm[/tex]
[tex]P_{B}=1-2*0.505 = -0.01005 atm[/tex]
Not sense.
With x2
[tex]P_{A}=0.495atm[/tex]
[tex]P_{B}=1-2*0.495 = 0.00995 atm[/tex]
X2 is the solution for this equation.
Kp=2*10^5
X1=50001
[tex]X2=5*10^{-6}[/tex]
With x1
[tex]P_{A}=50001atm[/tex]
[tex]P_{B}=1-2*50001=-100001atm[/tex]
Not sense.
With x2
[tex]P_{A}= 5*10^{-6}atm[/tex]
[tex]P_{B}=1-2*5*10^{-6}= 0.9999 atm[/tex]
X2 is the solution for this equation.
The study of chemicals and bonds is called chemistry. The state at which the formation of the reactant and the products are equal is called the equilibrium state.
The correct answer is mentioned below.
Equilibrium constant.
- The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium
- A state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change
The reaction involved in the question is as follows:-
[tex]A <-----> 2B[/tex]
The formula used to solve the question is as follows:-
[tex]K_P=\frac{P_a^2}{P_b}[/tex]
In the beginning, we don’t have an A in the system, so B starts to react to produce A until the system reaches the equilibrium producing x amount of A.
From the stoichiometric relationship in the reaction, we get that to produce x amount of A we need to 2x amount of B so in the equilibrium we will have 1 atm – 2x of B.
placed the value in the equation and solve the question.
[tex]K_p =\frac{(1-2x)^2}{x}[/tex]
After solving the equation the value of x will be:-
[tex]4x^2- (4+K_P)*x+1[/tex]
Use the algebraic method to find the value of x, the value is:-
The value of kp is 1.4
[tex]x_1= \frac{[1.4+4]+\sqrt{-[1.4+4]^2-(4*4*1)} }{2*4}\\=1.128[/tex]
hence,
[tex]P_A =1.128atm\\P_b =1-2*1.128 =-1.256[/tex]
For x2 the value will be:-
[tex]P_b =1-2*0.2215 = 0.556atm[/tex]
The value of kp is given in the question that is
- [tex]2*10^{-4}[/tex]
- [tex]X_1=0.505[/tex]
- [tex]X_2=0.495[/tex]
After solving all the equations, the value of Pb for X1 will be:-
[tex]P_B = 1-2*0.505 = -0.01005atm[/tex]
After solving all the equations, the value of Pb for X2 will be:-
[tex]P_b = 1-2*0.495=0.00995atm[/tex]
The value of Pb will get after solving the question is:-
[tex]P_a = 5*10^{-6}\\P_b = 1-2*5*10^{-6}[/tex]
hence, the solution to the question is mentioned above.
For more information on this question, refer to the link:-
https://brainly.com/question/9552459
