Phosgene (COCl2) is a poisonous gas that dissociates at high temperature into two other poisonous gases, carbon monoxide and chlorine with equilibrium constant Kp = 0.0041 at 600 K. Find the equilibrium composition of the system after 0.124 atm of COCl2 is allowed to reach equilibrium at this temperature in a sealed reaction vessel.
To find the equilibrium composition of the system, we need to calculate the partial pressures of carbon monoxide (CO), chlorine (Cl2), and phosgene (COCl2) at equilibrium.
Let's assume the initial moles of COCl2 is x.
According to the equation, 1 mole of COCl2 dissociates into 1 mole of CO and 1 mole of Cl2.
At equilibrium, the partial pressure of COCl2 can be expressed as (0.124 - x).
Since the equilibrium constant (Kp) is given as 0.0041, we can write the equilibrium expression as:
Kp = (P_CO * P_Cl2) / P_COCl2
Substituting the values, we get:
0.0041 = (P_CO * P_Cl2) / (0.124 - x)
Given that the equilibrium composition of the system is after 0.124 atm of COCl2 is allowed to reach equilibrium, the partial pressure of COCl2 (P_COCl2) is (0.124 - x) atm.
Let's assume the partial pressure of CO is y atm and the partial pressure of Cl2 is z atm.
Hence, the equilibrium expression becomes:
0.0041 = (y * z) / (0.124 - x)
To simplify the calculations, let's assume that x, y, and z are much smaller than 0.124 atm. This allows us to ignore their effect on the initial pressure of COCl2.
Now, let's solve this equation to find the equilibrium composition:
0.0041(0.124 - x) = y * z
Simplifying this equation, we get:
0.0005084 - 0.0041x = y * z
Now, you would need additional information to solve this equation such as the value of x, or the relationship between y and z.
To find the equilibrium composition of the system after 0.124 atm of COCl2 reaches equilibrium, we need to use the equilibrium constant (Kp) and the initial concentration of COCl2.
First, let's start by writing the balanced equation for the dissociation of COCl2:
COCl2 ⇌ CO + Cl2
According to the given equilibrium constant, Kp = 0.0041. This constant is calculated using the partial pressures of the products and reactants at equilibrium.
Kp = (P(CO) * P(Cl2)) / P(COCl2)
Assuming that the initial pressure of CO and Cl2 is negligible compared to COCl2, we can assume their partial pressures at equilibrium are zero.
Therefore, we have the equation:
Kp = (0 * 0) / P(COCl2)
Simplifying further, we get:
Kp = 0
This means that at equilibrium, the partial pressures of CO and Cl2 are both zero. In other words, the dissociation of COCl2 does not occur significantly at this temperature and pressure.
Therefore, the equilibrium composition of the system after 0.124 atm of COCl2 reaches equilibrium will consist almost entirely of undissociated COCl2.
To summarize, because the equilibrium constant is very small (Kp = 0.0041), the dissociation of COCl2 is negligible at this temperature and pressure. As a result, the equilibrium composition will be almost entirely COCl2.
Have you ever heard of ICE charts?
http://www.chem.purdue.edu/gchelp/howtosolveit/Equilibrium/ICEchart.htm