At 25 degrees Celsius, the base ionization constant for NH3 is 1.8 x ^-5. Determine the percentage ionization of a M solution of ammonia at 25 degree Celsius.
You need to insert the molarity.
Sorry, its 0.150 M solution of ammonia at 25 degrees celsius
...........NH3 + H2O ==> NH4^+ + OH^-
initial..0.150M...........0........0
change.....-x.............x........x
equil...0.150-x............x.......x
Kb = 1.8E-5 = (NH4^+)(OH^-)/(NH3)
Substitute into Kb expression and solve for x = (OH^-).
Then %ion = [(OH^-)/0.1]*100 = ?
Well, isn't ammonia quite the joker when it comes to ionization! Let's see if we can figure it out together.
The percentage ionization can be calculated using the formula:
% ionization = (concentration of ionized NH3 / initial concentration of NH3) x 100
But hold your laughter, we need to find the concentration of ionized NH3 first. Since the base ionization constant (Ka) for NH3 is given as 1.8 x 10^-5, we can use that to determine the concentration of ionized NH3.
NH3 + H2O ⇌ NH4+ + OH-
At equilibrium, we'll assume that x is the concentration of NH4+ (which is also the concentration of OH-). Because the initial concentration of NH3 is M, the change in concentration of NH3 will be -x and the change in concentration of NH4+ (and OH-) will be +x. The concentration of NH3 (undissociated) remaining at equilibrium will then be (M - x).
Using the base ionization equation, we can set up an equation:
(Ka) = ([NH4+][OH-]) / ([NH3])
(Ka) = (x)(x) / (M - x)
Now, we need to remember that the percentage ionization is equal to the concentration of ionized NH3 divided by the initial concentration of NH3, multiplied by 100.
So, putting everything together:
% ionization = (x / M) x 100
Finally, substitute the calculated value of x from the equation (Ka) = (x)(x) / (M - x), into the equation to find the percentage ionization at 25 degrees Celsius.
And voila! You'll have your answer. Just remember to keep your sense of humor intact throughout the whole process!
To determine the percentage ionization of a solution of ammonia (NH3) at 25 degrees Celsius, we need to know the value of the base ionization constant (also known as the base dissociation constant or Kb) for ammonia and the concentration of the ammonia solution.
The base ionization constant (Kb) for ammonia at 25 degrees Celsius is given as 1.8 x 10^-5. This value represents the equilibrium expression for the dissociation of ammonia in water, defined as:
NH3 + H2O ⇌ NH4+ + OH-
The concentration of the ammonia solution is given as "M" (which means the concentration is 1 M, or 1 mole per liter).
To determine the percentage ionization, we need to calculate the concentration of the hydroxide ion (OH-) formed (due to the ionization of ammonia) and then compare it to the initial concentration of ammonia.
Since ammonia is a weak base, we assume that the concentration of hydroxide ions is equal to the concentration of ammonia that has ionized.
Let's proceed with the calculation.
Step 1: Write the equilibrium expression for the ionization of NH3:
NH3 + H2O ⇌ NH4+ + OH-
Step 2: Assume that "x" is the degree of ionization of NH3, and based on the balanced equation, the concentration of NH4+ and OH- ions is also "x".
Step 3: Write the equilibrium expression using concentrations:
Kb = [NH4+][OH-] / [NH3]
From the equation, we can see that [NH3] = 1 M, and [NH4+] = [OH-] = x M. Plugging in these values:
Kb = (x)(x) / (1 - x)
Step 4: Substitute the value of Kb (1.8 x 10^-5) and solve for x:
1.8 x 10^-5 = x^2 / (1 - x)
Step 5: Rearrange the equation and solve for x:
1.8 x 10^-5 - 1.8 x 10^-5x = x^2
Rearranging again, we get:
0 = x^2 + 1.8 x 10^-5x - 1.8 x 10^-5
Now we can use the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / 2a
Using this formula, where a = 1, b = 1.8 x 10^-5, and c = -1.8 x 10^-5, we can solve for x.
Step 6: Calculate the percentage ionization:
Percentage ionization = (x / 1 M) * 100
By solving the quadratic equation, we find the value of x, which represents the degree of ionization of ammonia. Dividing x by the initial concentration of ammonia (1 M) and multiplying by 100 will give us the percentage ionization.
Please note that due to the quadratic equation calculation, the value of x might be very small. Hence, the percentage ionization of the solution will also be relatively small.