Calculate the [H3O+] concentration (in M) in a 0.1 M aqueous solution of NH3

In summary, the problem asks to calculate the concentration of [H3O+] in a 0.1 M aqueous solution of NH3 with a given Kb value. The answer is found to be 7.5 x 10–12 M. The given Kb value is not the ebullioscopic constant, but rather the dissociation constant for ammonia. Additional resources, such as an ICE table or pH calculator, can be used to solve the problem.
  • #1
sayeo87
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Homework Statement


Calculate the [H3O+] concentration (in M) in a 0.1 M aqueous solution of NH3.
[Kb = 1.8 x 10–5 ]
(a) 7.5 x 10–12 M (c) 1.8 x 10–6 M
(b) 3.0 x 10–10 M (d) 1.3 x 10–3 M


Homework Equations


ΔTb = Kb x m


The Attempt at a Solution


So... I'm kind of at a loss here. First of all to do anything useful with the ΔTb = Kb x m equation, they would have to give ΔTb right? And also, because its an aqueous solution, I assume we are dissolving NH3 into water. The Kb of water is 0.512... why then do they give a Kb value of 1.8 x 10–5?

Thanks in advance :smile: The answer is a, btw, but why!?
 
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  • #3


I would first clarify with the person who gave this question whether they meant to provide the Kb value for NH3 instead of water. The Kb value for NH3 is 1.8 x 10–5, which is much closer to the given answer of 7.5 x 10–12 M.

Assuming that was the intended Kb value, we can use the formula for calculating the [H3O+] concentration in a basic solution:

Kb = [OH-][H3O+] / [NH3]

Since we are given a 0.1 M solution of NH3, we can assume that the [NH3] is also 0.1 M. Plugging in the values, we get:

1.8 x 10–5 = [OH-][H3O+] / 0.1

Rearranging the equation, we get:

[H3O+] = (1.8 x 10–5)(0.1) / [OH-]

Now, we know that in a basic solution, the [OH-] concentration is equal to the [NH3] concentration (since NH3 is a weak base). So, we can substitute 0.1 M for [OH-], giving us:

[H3O+] = (1.8 x 10–5)(0.1) / 0.1

Simplifying, we get:

[H3O+] = 1.8 x 10–5 M

This is the [H3O+] concentration in the solution. However, the question asks for the [H3O+] concentration in M, so we need to convert this to scientific notation:

[H3O+] = 1.8 x 10–5 M = 1.8 x 10–12 M

Therefore, the answer is (a) 7.5 x 10–12 M.
 

1. What is the equation for calculating [H3O+] concentration in a solution of NH3?

The equation for calculating [H3O+] concentration in a solution of NH3 is:
[H3O+] = Kw / [NH3]

2. How do you determine the value of Kw in this equation?

Kw, also known as the autoionization constant, is a constant value equal to 1.0 x 10^-14 in water at 25°C. This value can be found in a chemistry reference book or online.

3. Can the [H3O+] concentration ever be greater than 0.1 M in this solution?

No, the [H3O+] concentration can never be greater than the initial concentration of the solution (0.1 M) because NH3 is a weak base and will not completely dissociate in water.

4. How does the [H3O+] concentration change if the initial concentration of NH3 is doubled?

If the initial concentration of NH3 is doubled to 0.2 M, then the [H3O+] concentration will decrease by half to 0.05 M. This is because the equilibrium constant for the dissociation of NH3 is a constant value, so increasing the concentration of NH3 will result in a decrease in [H3O+].

5. What is the significance of [H3O+] concentration in a solution of NH3?

The [H3O+] concentration is important in determining the pH of a solution. In the case of NH3, it is a weak base and will result in a basic solution. Therefore, the higher the [H3O+] concentration, the lower the pH will be.

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