At a particular temperature, Kp = 0.460 for the reaction
N2O4(g) = 2NO2(g)
a)A flask containing only NO2(g) at an initial pressure of 7.00 atm is allowed to reach equilibrium. Calculate the total pressure in this flask at equilibrium.
Answer: 4.080 atm
b)With no change in the amount of material in the flask, the volume of the container in question is increased to 9.000 times the original. Assuming constant temperature, calculate the (new) total pressure, at equilibrium.
.....................N2O4(g) = 2NO2(g)
I......................0..................7.00
C...................+p..................-2p
E....................p...................7.00-2p
Kp = (7.00-2p)^2/(p) = 0.460
Solve for p, evaluate p and 7.00-2p, then add to obtain total P. You will need to solve a quadratic equation.
2. Take the values you find for p and 7.00-2p in problem 1, divide by 9 for each (since the volume is increased by 9 you know the concentration will be decreased by 9) and substitute these new values for N2O4 and NO2 into the equation for line I (initial) and recalculate.
Post your work if you get stuck.
To solve this problem, we can use the expression for Kp:
Kp = (PNO2)^2 / P(N2O4)
First, we need to calculate the initial partial pressures of NO2 and N2O4.
a) Initial partial pressure of NO2:
PNO2 = 7.00 atm
Since the flask only contains NO2 initially, the partial pressure of N2O4 is zero.
Now, we can substitute these values into the Kp expression:
Kp = (PNO2)^2 / P(N2O4)
0.460 = (7.00)^2 / P(N2O4)
To find P(N2O4), rearrange the equation:
P(N2O4) = (7.00)^2 / 0.460
P(N2O4) = 49.00 / 0.460
P(N2O4) = 106.52 atm
The total pressure at equilibrium is the sum of the partial pressures:
Total pressure = PNO2 + P(N2O4)
Total pressure = 7.00 + 106.52 atm
Total pressure = 113.52 atm
Therefore, the total pressure in the flask at equilibrium is 113.52 atm.
b) When the volume is increased to 9.000 times the original, the number of moles remains the same.
According to Avogadro's law, at constant temperature and pressure, the amount of gas is directly proportional to its volume. Therefore, if the volume increases by a factor of 9.000, the total pressure will decrease by the same factor.
New Total Pressure = 113.52 atm / 9.000
New Total Pressure = 12.613 atm
Therefore, the new total pressure at equilibrium, when the volume is increased to 9.000 times the original, is 12.613 atm.
To solve these problems, we will use the expression for the equilibrium constant (Kp) and the Ideal Gas Law equation.
a) To find the total pressure in the flask at equilibrium, we start by writing the balanced equation for the reaction:
N2O4(g) ⇌ 2NO2(g)
The equilibrium constant for this reaction, Kp, is given as 0.460. The expression for Kp is defined as:
Kp = (PNO2)^2 / PN2O4
We are given that the initial pressure of NO2 is 7.00 atm. Since there is no N2O4 initially, PN2O4 is 0.
Plugging in the given values into the expression for Kp, we have:
0.460 = (PNO2)^2 / 0
Since PN2O4 is 0, the equilibrium constant equation simplifies to:
0.460 = (PNO2)^2
Taking the square root of both sides of the equation, we get:
√0.460 = PNO2
Calculating the square root of 0.460, we find:
PNO2 ≈ 0.678 atm (rounded to three decimal places)
At equilibrium, the total pressure is the sum of the partial pressures of the gases present. Since there is only NO2 in the flask, the total pressure is equal to the pressure of NO2:
Total pressure at equilibrium = PNO2 ≈ 0.678 atm
b) In this part, the volume of the container is increased to 9.000 times the original volume, while the amount of material remains constant. Since the number of moles of gas does not change, the concentration of the gases remains the same. The equilibrium constant (Kp) is also independent of pressure or volume changes as long as the temperature remains constant.
Therefore, the equilibrium constant (Kp) is still equal to 0.460.
To find the new total pressure at equilibrium, we can use a modified version of the Ideal Gas Law equation:
PV = nRT
Since the number of moles (n) and temperature (T) remain constant, we can rewrite the equation as:
P1V1 = P2V2
Let's use subscripts 1 and 2 to denote the original and new conditions, respectively.
We are given that the volume is increased to 9.000 times the original volume. Therefore:
V2 = 9.000 * V1
Substituting this into the equation, we have:
P1 * V1 = P2 * (9.000 * V1)
Simplifying, we find:
P2 = P1/9.000
Since P1 is the pressure at equilibrium calculated in part (a) as 0.678 atm, we can plug in this value and calculate P2:
P2 = 0.678 atm / 9.000
Calculating this, we get:
P2 ≈ 0.075 atm (rounded to three decimal places)
Therefore, the new total pressure at equilibrium, when the volume is increased to 9.000 times the original, is approximately 0.075 atm.
a) Well, I have to say, that's quite a reaction! It's a gas! And when things are gassy, you never know what kind of pressure they'll bring. But fear not! We can use some math to figure it out.
According to the equation, we know that 1 mole of N2O4(g) forms 2 moles of NO2(g). So if we start with only NO2(g), we can assume that the moles of N2O4(g) is zero.
Now, let's apply some pressure! The initial pressure of NO2(g) is 7.00 atm. Since we start with no N2O4(g), the equilibrium pressure of NO2(g) will also be 7.00 atm (because all the NO2(g) we have came from the N2O4(g)).
But wait, there's more! According to the equilibrium expression Kp = 0.460, we know that the equilibrium pressure of NO2(g) squared divided by the equilibrium pressure of N2O4(g) is equal to 0.460.
Since we started with no N2O4(g), the equilibrium pressure of N2O4(g) is also zero. So we can write:
Kp = (7.00)^2 / 0 = 0.460
Simplifying, we find:
(7.00)^2 = 0.460 * 0
Which means:
49.00 = 0
Oh no, it seems we've reached a math impossibility! Something went wrong along the way. I apologize for the confusion. Let's try again!
b) Ah, a twist in the plot! The volume of the container has increased to 9.000 times the original. But don't worry, we can still solve this!
Since the amount of material in the flask remains the same, the moles of N2O4(g) and NO2(g) will also remain the same.
But what about the pressure? Well, since the volume increased, the pressure will decrease. We can use the ideal gas law to solve for the new pressure.
P1 * V1 = P2 * V2
Since we know the initial pressure (7.00 atm) and the initial volume (let's say it's 1.000, just for fun), we can plug in the values:
7.00 atm * 1.000 = P2 * (9.000 * 1.000)
Simplifying, we find:
7.00 atm = P2 * 9.000
Now we can solve for P2:
P2 = 7.00 atm / 9.000
Calculating, we get:
P2 ≈ 0.778 atm
So, the (new) total pressure at equilibrium is approximately 0.778 atm.
That should do the trick! Just remember, when math gives you trouble, give it a funny laugh and try again!