Nitrogen tetraoxide is known to dissociate accoding to the equation;N2O4(g)_2NO2(g).A250mlsample of the gas mixture weighs 0.257bar.Calculate the partial pressure of each gas.(Hint:obtain the pressure it had before dissociation ,and then use the idea of equilibrium constant to arrive at the desired answer).
To calculate the partial pressure of each gas, we need to use the equilibrium constant expression and the ideal gas law. Here are the steps to solve this problem:
Step 1: Calculate the number of moles of N2O4 and NO2 in the 250 mL sample.
Using the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature, we can rearrange the equation to solve for n.
n = PV / RT
Given:
P = 0.257 bar (pressure of the gas sample)
V = 250 mL (volume of the gas sample)
R = 0.0831 L·bar/(mol·K) (ideal gas constant)
T = Unknown
First, we need to convert the volume from mL to L:
V = 250 mL × (1 L / 1000 mL) = 0.25 L
We'll assume that the gas sample is at room temperature, around 298 K.
Now, we can calculate the number of moles for each gas:
For N2O4:
n(N2O4) = (0.257 bar) × (0.25 L) / (0.0831 L·bar/(mol·K) × 298 K)
For NO2:
n(NO2) = 2 × n(N2O4) (According to the balanced equation)
Step 2: Calculate the total pressure before dissociation.
Since the partial pressure of N2O4 is equal to its total pressure before dissociation, we calculate it using the ideal gas law:
P(N2O4) = n(N2O4) × (RT / V) = n(N2O4) × (0.0831 L·bar/(mol·K) × 298 K / 0.25 L)
Step 3: Calculate the equilibrium constant (K) using the balanced equation.
The molar concentration of each gas at equilibrium can be given as follows:
[N2O4] = n(N2O4) / V
[NO2] = n(NO2) / V
The equilibrium constant expression is given by:
K = ([NO2]^2) / [N2O4]
Substituting the values of [NO2], [N2O4], and K into the equation:
K = { (n(NO2) / V)^2 } / (n(N2O4) / V)
Step 4: Calculate the concentration of NO2 using the equilibrium constant and partial pressure of N2O4.
Rearranging the equation for K and substituting the partial pressure of N2O4:
K = (P(NO2)^2) / P(N2O4)
Solving for P(NO2):
P(NO2) = sqrt(K × P(N2O4))
Step 5: Calculate the partial pressure of each gas.
The partial pressure of N2O4 is equal to its total pressure before dissociation:
P(N2O4) = n(N2O4) × (RT / V)
Since the partial pressure of N2O4 dissociates into NO2, the partial pressure of NO2 is calculated as:
P(NO2) = sqrt(K × P(N2O4))
Plug in the calculated values to find the partial pressures of N2O4 and NO2.
I hope this explanation helps you understand how to calculate the partial pressures using the equilibrium constant and ideal gas law.