These all stumped me I'll ask my tutor if you dont answer (find partial pressure of I2)

Question

Honestly for 5 hours now I give up on them. Need help. Okay:

Hydrogen iodide undergoes decomposition according to the equation

2HI(g) H2(g) I2(g)

The equilibrium constant Kp at 500 K for this equilibrium is 0.060. Suppose 0.621 mol of HI is placed in a 9.00-L container at 500 K. What is the equilibrium partial pressure of I2(g)?

(R = 0.0821 L · atm/(K · mol))

A.

0.069 atm

B.

0.035 atm

C.

0.12 atm

D.

0.014 atm

E.

0.56 atm

I didnt even get close does Kp = Kc(RT)raised to power of delta moles and solve for kc, take the square root of that to find I2 pressure give me my answer?

Answer 1

Since:

2HI (g) --> H2 (g) + I2 (g)

Kp = P(H2) * P(I2) / P(HI)^2

We know the pressure of HI from the ideal gas law:

PV=nRT

P=nRT/V=(0.621 mol * 0.08206 L*Atm/K*mol *500 K)/9.00 L

P = 2.83 Atm

Now, we need to define a change, we'll call x, in terms of the equilibrium expression Kp.  We start with 2.83 atm of HI, and then equilibrium needs to occur causing the change of 2.83 atm of HI into two gases (x).  So the change in HI is 2.83 - x and the change in the other two gases is +x.  This is called construction of an ICE (Initial-Change-Equilibrium) table, look that up for more in depth explanation.

0.06 = (x * x)/ (2.83 - x)^2:

x=0.557 atm =  approximately 0.56 atm

So the answer is E. 0.56 atm

Answer 2

"Kp = Kc(RT)raised to power of delta moles"

deltaN = 0 so Kp=Kc

pH2*pI2/pHI^2 = 0.06

Now we started out with 0.621mol of HI. Let's convert that to a pressure.

pHI =nRT/V = ( 0.621)(0.0821)500/9 = 2.832 atm

This is the initial pressure of HI. It will decompose into [H2] and [I2] but the total number of moles and the total pressure will remain constant.The initial pH2 and pI2 are both zero. x is the change in partial pressure as the reaction goes to equilibrium.

(0 + x)(0 + x)/(2.832 - x)^2 = 0.060

or

x^2/(2.832 - x)^2 = 0.060

We can solve this by taking the square root of both sides.

x/(2.832 - x) = sqrt(0.060) = 0.2449

Now we solve for x

x = 0.2449(2.832 - x)

x(1+ 0.2449) = 0.2449(2.832)

x =0.557atm = 0.56 atm

The answer is E.