Determine Kc at 298 K for the reaction 1/2 N2(g0 + 1/2 O2(g) + 1/2 Cl2(g)--> NOCl(g), given the following data at 298 K
1/2 N2(g) + O2(g)--> NO2(g) Kp= 1.0 x 10^-9
NOCl(g) + 1/2 O2(g)-->NO2Cl(g) Kp= 1.1 x 10^2
NO2(g) + 1/2 Cl2(g)--> NO2Cl(g) Kp= 0.3
Jamaal
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To determine Kc at 298 K for the reaction 1/2 N2(g) + 1/2 O2(g) + 1/2 Cl2(g) --> NOCl(g), we can use the given data for Kp values and the relationship between Kp and Kc.
Firstly, let's write the overall balanced equation for the reaction:
1/2 N2(g) + 1/2 O2(g) + 1/2 Cl2(g) --> NOCl(g)
Now, we need to consider the individual reactions and their corresponding Kp values to find the overall Kc for the reaction.
The given data includes three reactions:
1) 1/2 N2(g) + O2(g) --> NO2(g) (Kp = 1.0 x 10^-9)
2) NOCl(g) + 1/2 O2(g) --> NO2Cl(g) (Kp = 1.1 x 10^2)
3) NO2(g) + 1/2 Cl2(g) --> NO2Cl(g) (Kp = 0.3)
We need to manipulate these three reactions to obtain the desired reaction: 1/2 N2(g) + 1/2 O2(g) + 1/2 Cl2(g) --> NOCl(g)
From these three reactions, we can combine them to form the desired reaction by adding the corresponding equations. However, before adding the equations, we need to multiply them to obtain the coefficients matching the desired reaction.
1/2 N2(g) + O2(g) --> NO2(g) (Kp = 1.0 x 10^-9) [Multiply by 2]
2 NOCl(g) + O2(g) --> 2NO2Cl(g) (Kp = 1.1 x 10^2) [Multiply by 1/2]
NO2(g) + 1/2 Cl2(g) --> NO2Cl(g) (Kp = 0.3) [Multiply by 1/2]
After multiplying the equations, we can add them together:
N2(g) + O2(g) --> 2NO2(g) (Kp = 2.0 x 10^-9)
NOCl(g) + O2(g) --> NO2Cl(g) (Kp = 5.5 x 10^1)
NO2(g) + Cl2(g) --> NO2Cl(g) (Kp = 0.15)
Finally, we sum up the equations to obtain the desired reaction:
2N2(g) + 2O2(g) + 2Cl2(g) --> 4NOCl(g) (Kp = 2.0 x 10^-9 * 5.5 x 10^1 * 0.15)
Now, we can calculate Kc using the relationship between Kp and Kc:
Kp = Kc(RT)^(∆n)
Where:
- Kp is the equilibrium constant in terms of partial pressures
- Kc is the equilibrium constant in terms of molar concentrations
- R is the gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in kelvin (298 K)
- ∆n is the change in the number of moles of gas (products - reactants)
Since the reaction has no change in the number of moles of gas (∆n = 0), Kp and Kc are the same. Therefore:
Kc = 2.0 x 10^-9 * 5.5 x 10^1 * 0.15
Now, you can calculate the value of Kc using a calculator or by multiplying the numbers:
Kc = 1.65 x 10^-7.