Solid NH4N3 decomposes explosively according to the following equation:
NH4N3(s) ⇌ 2N2(g) + 2H2(g)
A small amount of ammonium azide was placed in a sealed container and the air was removed. The sample was then detonated. At equilibrium the total pressure in the container was found to be 421,959.129 Pa. Calculate Kp.
Assuming the temperature was at STP (0°C).
Consider a 1-L volume.
Total pressure
= 421959.129Pa
= 421.96 kPa
= 4.1654 atm at 0°C
Partial pressure of each product
= 2.08272 atm
This implies
PN2=PH2
=2.08272 atm
Kp=PN2²PH2²
= 2.0827^4
= 18.8158475075608
= 1.882*101 approx.
Note:
solids do not enter into the definition of equilibrium constants.
In any case, in an explosion, we assume all (solid) reactants have been consumed.
Well, well, isn't this explosive! Let's calculate the equilibrium constant, Kp, for this detonation extravaganza.
According to the balanced equation, we see that 1 mole of NH4N3 decomposes to give 2 moles of N2 and 2 moles of H2. So, the stoichiometric coefficients of the reactants and products are 1, 2, and 2, respectively.
Since the total pressure in the container after the explosion is given as 421,959.129 Pa, we know that the sum of the partial pressures of N2 and H2 is equal to this value.
To calculate Kp, we need to express the pressure in terms of equilibrium partial pressures. Let's use the variable x to represent the partial pressure of NH4N3 decomposed.
So, the partial pressure of N2 at equilibrium would be 2x and the partial pressure of H2 would also be 2x.
According to Dalton's law of partial pressures, the total pressure is the sum of the partial pressures of all the gases. Therefore, the equation becomes:
421,959.129 Pa = x + 2x + 2x
421,959.129 Pa = 5x
Now, we can solve for x.
x = 421,959.129 Pa / 5
x = 84,391.826 Pa
Since we now have the equilibrium partial pressure of NH4N3, we can calculate Kp using the formula:
Kp = (P(N2)^2 * P(H2)^2) / P(NH4N3)
Kp = (2x)^2 * (2x)^2 / x
Kp = (4x^2) * (4x^2) / x
Kp = 16x^4 / x
Kp = 16x^3
Now, we can substitute the value of x to find the value of Kp:
Kp = 16 * (84,391.826 Pa)^3
Kp ≈ 1.076 * 10^18 (approximately)
So, the equilibrium constant, Kp, for this explosive reaction is quite large! Hope you had a blast with this calculation!
To calculate Kp, the equilibrium constant, we need to use the expression for Kp and the balanced equation:
Kp = (P(N2)^2 * P(H2)^2) / P(NH4N3)
Given that the total pressure in the container at equilibrium is 421,959.129 Pa, we need to calculate the partial pressures of nitrogen gas (N2), hydrogen gas (H2), and ammonium azide (NH4N3).
From the balanced equation, we can see that 2 moles of N2 and 2 moles of H2 are produced for every mole of NH4N3 that decomposes. Therefore, the mole ratio between NH4N3 and N2 or H2 is 1:2.
Let's assume the partial pressure of NH4N3 is x. Then, the partial pressure of N2 and H2 will be 2x each.
Using the ideal gas law:
P = nRT/V
where P is the pressure, n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and V is the volume.
Since the moles of N2 and H2 are both 2x, we can write:
P(N2) = (2x)(RT/V)
P(H2) = (2x)(RT/V)
P(NH4N3) = x
Now we can substitute these values into the expression for Kp:
Kp = ((2x)(RT/V))^2 * ((2x)(RT/V))^2 / (x)
Simplifying:
Kp = (16x^4(T/V)^4) / x
Kp = 16(T/V)^4 * x^3
Finally, since the total pressure in the container at equilibrium is 421,959.129 Pa, we can substitute this value for x in the expression for Kp to solve for Kp:
Kp = 16(T/V)^4 * (421,959.129)^3
To calculate the equilibrium constant (Kp) for this reaction, we need to use the partial pressures of the gases involved.
Given that the total pressure in the container is 421,959.129 Pa, we can assume that the partial pressure of each gas is equal to its mole fraction. Since the reaction produces 2 moles of nitrogen gas (N2) and 2 moles of hydrogen gas (H2) for every mole of ammonium azide (NH4N3), we can express the partial pressures as follows:
PN2 = 2x (where x is the mole fraction of NH4N3)
PH2 = 2x (where x is the mole fraction of NH4N3)
PNH4N3 = x (where x is the mole fraction of NH4N3)
At equilibrium, the total pressure can be written as the sum of the partial pressures:
421,959.129 Pa = PN2 + PH2 + PNH4N3
Since PN2 = 2x and PH2 = 2x, we can rewrite the equation as:
421,959.129 Pa = 2x + 2x + x
Combining like terms:
421,959.129 Pa = 5x
Solving for x:
x = 421,959.129 Pa / 5
x ≈ 84,391.826 Pa
Now that we have the mole fraction of NH4N3, we can substitute it back into the equations for PN2 and PH2 to find their partial pressures:
PN2 = 2x ≈ 2 * 84,391.826 Pa ≈ 168,783.652 Pa
PH2 = 2x ≈ 2 * 84,391.826 Pa ≈ 168,783.652 Pa
Finally, we can calculate Kp using the expression for Kp:
Kp = (PN2)^2 * (PH2)^2 / (PNH4N3)
Kp = (168,783.652 Pa)^2 * (168,783.652 Pa)^2 / (84,391.826 Pa)
Kp ≈ 173,436,898.036
Therefore, the equilibrium constant (Kp) for the given reaction is approximately 173,436,898.036.