Kc= 0.040 for the system below at 450oC:
PC15(g)<<==>>PC13(g)+ C12(g) evaluate kp for the reaction at 450oc
We use the relationship:
Kp = Kc(RT)^(∆n)
where ∆n is the change in moles of gas between reactants and products.
We are given Kc = 0.040 at 450°C, but we need to find Kp. We also need to determine the value of ∆n.
Looking at the balanced chemical equation:
PCl5(g) <<==>> PCl3(g) + Cl2(g)
There are 2 moles of gas on the left side (PCl5) and 2 moles of gas on the right side (PCl3 and Cl2). Therefore, ∆n = (2 - 2) = 0.
Now we can use the equation to solve for Kp:
Kp = Kc(RT)^(∆n) = Kc(RT)^0 = Kc
At 450°C, we have:
Kp = Kc = 0.040
Therefore, the value of Kp for the reaction at 450°C is 0.040.
To evaluate Kp for the reaction at 450oC, we need to use the formula relating Kp and Kc for gaseous reactions. The formula is:
Kp = Kc(RT)^(Δn)
Where:
- Kp is the equilibrium constant in terms of partial pressures
- Kc is the equilibrium constant in terms of molar concentrations
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
- Δn is the difference in the number of moles of gaseous products and gaseous reactants
In this case, the reaction is:
PCl5(g) ⇌ PCl3(g) + Cl2(g)
Since the reaction involves the conversion of 1 mole of gaseous reactant (PCl5) into 2 moles of gaseous products (PCl3 and Cl2), Δn = 2 - 1 = 1
We are given Kc = 0.040 at 450oC. To convert the temperature to Kelvin, we add 273 to 450:
T = 450 + 273 = 723 K
Now we can plug the values into the formula to calculate Kp:
Kp = Kc(RT)^(Δn)
= 0.040 (0.0821 L·atm/(mol·K))(723 K)^(1)
= 0.040 (0.0821)(723)
≈ 2.095
Therefore, Kp for the reaction at 450oC is approximately 2.095.
To evaluate Kp for the given reaction at 450°C, we need to use the relationship between Kc and Kp, which is given by the equation:
Kp = Kc * (RT)^(Δn)
Where:
Kp is the equilibrium constant in terms of partial pressures,
Kc is the equilibrium constant in terms of concentrations,
R is the gas constant (8.314 J/(mol·K)),
T is the temperature in Kelvin, and
Δn is the change in the number of moles of gas between the products and reactants.
In the given reaction, the balanced equation is:
PCl5(g) ⇌ PCl3(g) + Cl2(g)
From the balanced equation, we can see that there is no change in the number of moles of gas between the reactants and products. Therefore, Δn = 0.
Given:
Kc = 0.040 at 450°C
To evaluate Kp, we need to convert the given temperature of 450°C to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
T(K) = 450°C + 273.15 = 723.15 K
Now we can calculate Kp by substituting the values into the equation:
Kp = Kc * (RT)^(Δn)
Kp = 0.040 * (8.314 J/(mol·K))^(0) * (723.15 K)^(0)
Since any number raised to the power of zero is always equal to 1, we have:
Kp = 0.040 * 1 * 1 = 0.040
Therefore, the value of Kp for the reaction at 450°C is 0.040.