how do you calculate the equilibrium constant K for a reaction given only the equilibruim pressure for the sample...i thought u needed partial pressures for all substances involved.
They just tell me the eq pressure is 3 atm for the sample and ask for Keq.
Here's the rxn...
NH2COONH4(s) --> 2NH3(g) + CO2(g)
Choices...
A)4
B)1/27
C)4/27
D)27
See my response to your post above.
To calculate the equilibrium constant (K) for a reaction given only the equilibrium pressure, you can use the ideal gas law and the equation relating the partial pressure of a gas to its molar amount.
In this case, the equation is:
NH2COONH4(s) --> 2NH3(g) + CO2(g)
Since NH2COONH4 is a solid, it does not contribute to the equilibrium pressure. We only need to consider the partial pressures of NH3 and CO2.
Given that the equilibrium pressure for the sample is 3 atm, we can assume that this is the sum of the partial pressures of NH3 and CO2. Let's assume that the partial pressure of NH3 is x atm and the partial pressure of CO2 is y atm.
According to the balanced equation, we know that 2 moles of NH3 and 1 mole of CO2 are produced for every mole of NH2COONH4 that reacts.
Using the ideal gas law, we can write the equation for NH3:
PV = nRT
Where:
P = partial pressure of NH3 (in atm)
V = volume of the gas (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Since we are assuming x atm for the partial pressure of NH3, we can rewrite the equation as:
xV = 2nRT
Similarly, for CO2:
yV = nRT
Now, let's substitute the given equation for NH3 and CO2 into the equation for the total pressure:
x + y = 3
Dividing both sides of the equation by V, we have:
x/V + y/V = 3/V
Substituting the equations for x and y:
2nRT/V + nRT/V = 3/V
Factoring out nRT/V:
3nRT/V = 3/V
Canceling out the V terms:
3nRT = 3
Simplifying, we find:
nRT = 1
Since the temperature (T), gas constant (R), and volume (V) are constant, we can say that the number of moles (n) is also constant.
So, n = 1/mol
Now, we can define the equilibrium constant (K) in terms of the partial pressures:
K = (P(NH3)2 * P(CO2)) / (P(NH2COONH4))
Substituting the partial pressures with the given values, we have:
K = (x2 * y) / (1)
Since n = 1/mol, we have:
K = (x2 * y) / (1)
From the equation x + y = 3, we can solve for y:
y = 3 - x
Substituting this back into the equation for K, we have:
K = (x2 * (3 - x)) / (1)
Now, we need to find the value of x that satisfies this equation. Let's solve for x:
K = (x2 * (3 - x)) / (1)
To facilitate calculations, let's multiply both sides of the equation by 1:
K = (x2 * (3 - x)) / 1
Rearranging the equation:
K = (3x2 - x3) / 1
Since the options for Keq are given as whole numbers, you can try plugging in each of the answer choices for x to see if any of them result in an equilibrium constant (K) value of 3. However, it is important to note that this may be a time-consuming process.
Alternatively, you can use a graphing calculator or software to plot the equation K = (3x2 - x3) / 1 and find the value(s) of x that satisfy the equation. The corresponding values for K can then be calculated, and if one of the calculated K values matches the given equilibrium pressure of 3 atm, you have found the answer.
I understand that this process may seem complex, so please let me know if you would like further clarification or assistance with any specific step.
To calculate the equilibrium constant (K) for a reaction, you typically need the concentrations (or activities) of all the substances involved. However, in this case, you have been given the equilibrium pressure for the sample instead.
Firstly, you need to consider the stoichiometry of the reaction. From the balanced equation provided, you can see that 1 mole of NH2COONH4 produces 2 moles of NH3 and 1 mole of CO2.
To calculate the equilibrium constant (K), you can use the equation:
K = (P(NH3)^2 * P(CO2)) / P(NH2COONH4)
Here, P(NH3) represents the partial pressure of NH3, P(CO2) represents the partial pressure of CO2, and P(NH2COONH4) represents the equilibrium pressure of NH2COONH4.
In this case, you have been given the equilibrium pressure of the sample, which is 3 atm. Since NH2COONH4(s) is a solid, its concentration does not affect the equilibrium constant, so you can assume its partial pressure to be 1 atm.
Let's substitute the given values into the equation:
K = (P(NH3)^2 * P(CO2)) / P(NH2COONH4)
K = (P(NH3)^2 * P(CO2)) / 1 atm
Since you have not been given the partial pressures of NH3 and CO2 explicitly, you need to make an assumption to proceed. Let's assume that the volume of the container remains constant and that the reaction is ideal. In such cases, the partial pressures can be directly proportional to the moles of the respective substances.
From the stoichiometry of the reaction, we know that 1 mole of NH2COONH4 produces 2 moles of NH3. Therefore, we can assume that P(NH3) is equal to 2 times the equilibrium pressure of NH2COONH4, which is 2 * 3 atm = 6 atm.
Similarly, since 1 mole of NH2COONH4 produces 1 mole of CO2, we can assume that P(CO2) is equal to the equilibrium pressure of NH2COONH4, which is 3 atm.
Now, substituting these assumed values into the equation for K:
K = (P(NH3)^2 * P(CO2)) / 1 atm
K = (6 atm)^2 * (3 atm) / 1 atm
K = 108 atm^3 / 1 atm
K = 108
Therefore, the equilibrium constant (K) for the given reaction, when the equilibrium pressure of the sample is 3 atm, is 108.
None of the provided answer choices match the calculated value of 108, so none of the given choices are correct.