Respuesta :
Answer:
[tex]\large \boxed{0.0106}[/tex]
Explanation:
We have three equations:
1. M(g) ⇌ Z(g); Kc₁ = 3.15
2. 6R(g) ⇌ 2N(g) + 4Z(g); Kc₂ = 0.509
3. 3X(g) + 3Q(g) ⇌ 9R(g); Kc₃ = 12.5
From these, we must devise the target equation:
4. Q(g) + X(g) ⇌ 2M(g) + N(g); Kc = ?
The target equation has Q(g) on the left, so you divide Equation 1 by 3.
When you divide an equation by 3, you take the cube root of its Kc.
5. X(g) + Q(g) ⇌ 3R(g): K₅ = ∛(Kc₃)
Equation 5 has 3R on the right, and that is not in the target equation.
You need an equation with 3R on the left, so you divide Equation 2 by 2.
When you divide an equation by 2, you take the square root of its Kc.
6. 3R(g) ⇌ N(g) + 2Z(g); K₆ = √ (Kc₂)
Equation 6 has 2Z on the right, and that is not in the target equation.
You need an equation with 2Z on the left, so you reverse Equation 2 by and double it.
When you reverse an equation, you take the reciprocal of its K.
When you double an equation, you square its K.
7. 2Z(g) ⇌ 2M(g); K₇ = (1/Kc₁)²
Now, you add equations 5, 6, and 7, cancelling species that appear on opposite sides of the reaction arrows.
When you add equations, you multiply their K values.
You get the target equation 4:
5. X(g) + Q(g) ⇌ 3R(g); K₅ = ∛(Kc₃)
6. 3R(g) ⇌ N(g) + 2Z(g); K₆ = √(Kc₂)
7. 2Z(g) ⇌ 2M(g); K₇ = (1/Kc₁)²
4. Q(g) + X(g) ⇌ 2M(g) + N(g); Kc = K₅K₆K₇ = [∛(Kc₃)√(Kc₂)]/(Kc₁)²
Kc = [∛(12.5)√(0.509)]/(12.5)² = (2.321 × 0.7120)/156.2 = 0.0106
[tex]K_{c} \text{ for the reaction is $\large \boxed{\mathbf{0.0106}}$}[/tex]
Answer:
The value of the equilibrium constant is 0.167
Explanation:
Step 1: The target equation
Q(g) + X(g) ⇔ 2M(g) + N(g)
Given is:
(1) M(g)⇔Z(g) c1=3.15
(2) 6R(g) ⇔ 2N(g) + 4Z(g) c2=0.509
(3) 3X(g) +3Q(g) ⇔ 9R(g) c3=12.5
Step 2: Rearange the equation
We have to rearange the equation to come to the final result
This is Hess' Law
In the target equation we have Q(g) + X(g)
In (3) we have 3X(g) +3Q(g) ⇔ 9R(g)
To get the target of Q(g) + X(g) we have to divide (3) by 3. This will give us:
X(g) +Q(g) ⇔ 3R(g) Kc = ∛12.5 = 2.32 (Note: to get Kc of the target equation we use cube root)
The target equation has as product 2M(g) + N(g)
To get M(g) we will use the (1) equation
Since M(g) is a product and not a reactant, we have to reverse the equation. Next to that we also have to double the equation because we need 2M(g) and not M(g)
2Z(g) ⇔ 2M(g) Kc = 1/(3.15)² = 0.101 (Note: to get Kc' after reversing the equation we calculate 1/Kc. To get Kc'' after doubling and reversing the equation we calculate 1/(Kc²)
To get N(g) we will use (2) 6R(g) ⇔ 2N(g) + 4Z(g)
Since we only need N(g) we will divide this equation by 2. This will get us:
3R(g) ⇔ N(g) + 2Z(g) Kc = √0.509 = 0.713 (Note: if we divide the equation by 2, to calculate Kc' we use square root)
Now we have all the components we will add the 3 equations:
X(g) +Q(g) + 2Z(g) + 3R(g)⇔ 3R(g) + 2M(g) + N(g) + 2Z(g)
We will simplify this equation:
X(g) +Q(g) ⇔ 2M(g) + N(g) this is our target equation
The value of the equilibrium constant, Kc is:
Kc = 2.32 * 0.101*0.713
Kc = 0.167
Note: to calculate Kc after adding several equations,we'll multiply Kc1* Kc2 * Kc3 etc...
The value of the equilibrium constant is 0.167
