A manometer attached to a flask contains NH3 gas have no difference in mercury level initially as shown in diagram. After the sparking into the flask, it have difference of 19 cm in mercury level in two columns. Calculate % dissociation of ammonia.
(1) 21% (2) 22% (3) 24% (4) 25%
25%
25%
To calculate the percent dissociation of ammonia, we need to determine the change in the pressure of ammonia before and after dissociation.
Since the mercury levels in the two columns of the manometer have a difference of 19 cm, we can use this information to find the pressure difference.
The pressure difference is directly proportional to the difference in height of the mercury columns. In this case, the pressure difference is equivalent to the difference in height between the two mercury columns, which is 19 cm.
Now, we need to convert the pressure difference to a pressure in atm. We know that the pressure due to a column of liquid is given by the equation:
Pressure = Density x Gravity x Height
Since we are using mercury in the manometer, the density of mercury is 13.6 g/cm^3 and the acceleration due to gravity is 9.8 m/s^2.
Converting the height difference from cm to meters:
Height difference = 19 cm = 19/100 m = 0.19 m
Calculating the pressure difference:
Pressure difference = Density x Gravity x Height difference
Pressure difference = (13.6 g/cm^3) x (9.8 m/s^2) x (0.19 m) = 24.3616 g/m^2/s^2
Now, we can calculate the percent dissociation of ammonia using the given equation:
Percent Dissociation = (Pressure difference / Initial pressure of ammonia) x 100
To find the initial pressure of ammonia, we can assume that the initial pressure is equal to the atmospheric pressure, which is approximately 1 atm.
Percent Dissociation = (24.3616 g/m^2/s^2 / 1 atm) x 100 = 24.3616%
Therefore, the percentage dissociation of ammonia is approximately 24%. Option (3) is the correct answer.
To calculate the percent dissociation of ammonia, we need to determine the change in the number of moles of ammonia in the flask.
First, let's understand the setup described in the question. A manometer is attached to a flask containing NH3 gas. Initially, there is no difference in the mercury levels between the two columns of the manometer. However, after sparking into the flask, there is a difference of 19 cm in the mercury levels.
The change in mercury level in the manometer is due to the change in pressure inside the flask. This change in pressure is caused by the dissociation of NH3 gas into its constituent gases, nitrogen (N2) and hydrogen (H2), when sparked.
To calculate the percent dissociation of NH3, we can use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas
Since the volume (V), temperature (T), and the gas constant (R) are constant in this case, we can simplify the equation to:
P = constant * n
Considering the two columns of mercury in the manometer, the pressure in the flask is equal to the difference in the heights of the mercury columns:
P = constant * (h1 - h2)
Where:
h1 is the height of the mercury column on one side of the manometer
h2 is the height of the mercury column on the other side of the manometer
In this case, the difference in the mercury levels is given as 19 cm, so:
P = constant * 19 cm
Now, to determine the percent dissociation of NH3, we need to find the change in the number of moles of NH3. From the balanced chemical equation for the dissociation of NH3:
2NH3 ⇌ N2 + 3H2
We can see that for every 2 moles of NH3, we get 1 mole of N2 and 3 moles of H2. Therefore, the change in the number of moles of NH3 is given by:
Δn(NH3) = -2 * x
Where:
x is the extent of dissociation of NH3
Now, we can substitute this into the equation relating pressure and moles:
P = constant * (-2 * x)
The initial pressure (P₀) is equal to the pressure before the sparking occurred, which is the pressure when there was no difference in the mercury levels. In this case, that is:
P₀ = constant * 0 cm = 0
So, after the sparking, the pressure is given by:
P = constant * (19 cm)
Therefore, we can rewrite the equation as:
19 cm = constant * (-2 * x)
Now, we know that the percent dissociation (α) is given by:
α = (Δn(NH3) / initial moles of NH3) * 100
Since we don't have the initial moles of NH3, we can express the percent dissociation in terms of the change in pressure:
α = (Δn(NH3) / initial moles of NH3) * 100
α = (2 * x / initial moles of NH3) * 100
Substituting into the equation relating pressure and moles:
α = (2 * x / initial moles of NH3) * 100
α = (2 * x / (constant * P₀)) * 100
Since P₀ is equal to 0 in this case, the equation simplifies to:
α = (2 * x / 0) * 100
α = ∞
Therefore, the percent dissociation of ammonia is infinite.