Phosgene is a potent chemical warfare agent that is now outlawed by international agreement. It decomposes by the reaction CoCl2(g)=>Co(g) + Cl2(g), Kc=8.3×10^-4.calculate [CoCl2] when 0.100mol CoCl2 decomposes and reach equilibrium in a 10L flask
kc=x^2/(.1/10 -x)
so you get a quadratic.
.01*8.3E-4 -8.3xE-4= x^2
x^2+ 8.3xE-4 -8.3E-6 =0
solve for x
I get two roots:
-0.014161118818594, 0.0058611188185937
ignore the negative root, so the conc is 5.86E-3 moles/liter
check my work https://www.mathsisfun.com/quadratic-equation-solver.html
To calculate the concentration of CoCl2 at equilibrium, we can use the equation for the equilibrium constant (Kc) and the stoichiometry of the reaction.
The balanced equation for the decomposition of phosgene (CoCl2) is:
CoCl2(g) ⇌ Co(g) + Cl2(g)
Using the stoichiometry of the equation, we know that for every 1 mole of CoCl2 that decomposes, 1 mole of Co and 1 mole of Cl2 are produced.
In this case, we are given that 0.100 mol of CoCl2 decomposes.
Since the volume of the flask is 10 L, we can use the equation:
Kc = [Co][Cl2] / [CoCl2]
We can assume that at the start, the concentration of Co and Cl2 is zero, and the entire 0.100 mol of CoCl2 is present.
So, at equilibrium, the change in CoCl2 concentration will be -0.100 mol.
Now, let's calculate the concentration of CoCl2 at equilibrium.
First, substitute the given values into the equation:
8.3 × 10^-4 = [Co][Cl2] / (0.100 - 0.100)
8.3 × 10^-4 = [Co][Cl2] / 0.100
Next, let's assume x is the concentration of CoCl2 at equilibrium.
Therefore, the concentration of Cl2 and Co will also be x, using the stoichiometry.
Now, substitute these values into the equation:
8.3 × 10^-4 = (x)(x) / 0.100
Simplifying the equation:
8.3 × 10^-4 × 0.100 = x^2
0.083 × 10^-4 = x^2
Taking the square root of both sides of the equation:
x = √(0.083 × 10^-4)
x = 2.88 × 10^-3
Therefore, the concentration of CoCl2 at equilibrium is 2.88 × 10^-3 mol/L.
To calculate the concentration of CoCl2 at equilibrium, we can use the equilibrium expression and stoichiometry of the reaction.
The given equilibrium expression is:
CoCl2(g) <=> Co(g) + Cl2(g)
The equilibrium constant, Kc, for the reaction is 8.3×10^-4.
Let's assume that at equilibrium, the concentration of CoCl2 is x mol/L. The concentration of Co(g) and Cl2(g) would also be x mol/L each since the stoichiometry of the balanced equation is 1:1:1 for CoCl2, Co, and Cl2.
Therefore, we can set up an expression for the equilibrium constant using the given concentrations:
Kc = [Co][Cl2] / [CoCl2]
Substituting the values:
8.3×10^-4 = (x)(x) / (0.100 - x)
Now, we can solve this equation to find the value of x, which represents the concentration of CoCl2 at equilibrium.
1. Multiply both sides of the equation by (0.100 - x):
8.3×10^-4 * (0.100 - x) = x^2
2. Distribute the left side:
8.3×10^-4 * 0.100 - 8.3×10^-4 * x = x^2
3. Rearrange the equation and set it to zero:
x^2 + 8.3×10^-4 * x - 8.3×10^-4 * 0.100 = 0
Now, we have a quadratic equation. We can solve it using quadratic formula or factoring. In this case, let's use the quadratic formula.
Quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a)
In the equation: x^2 + 8.3×10^-4 * x - 8.3×10^-4 * 0.100 = 0
a = 1, b = 8.3×10^-4, c = -8.3×10^-4 * 0.100
Plugging these values into the quadratic formula, we can calculate the two possible values of x.
x = (-8.3×10^-4 ± √((8.3×10^-4)^2 - 4(1)(-8.3×10^-4 * 0.100))) / (2(1))
After solving this equation, you will obtain two values for x. However, since we are considering the decomposition of CoCl2, the value of x should be less than 0.100 mol/L, which was the initial concentration.
Therefore, only the positive solution that satisfies 0 < x < 0.100 is the concentration of CoCl2 at equilibrium.