0.100 M of NaNO2 and 0.050 HNO2.
what is the H3O of this solution? set up please.
Use the Henderson-Hasselbalch equation. NaNO2 is the base and HNO2 is the acid. You will need pKa for HNO2.
1 is not the answer
2.1x10^-5
i got 3.6x10^-6
i got 3.6x10^-4
To determine the H3O+ concentration of the solution, you need to consider the dissociation of both NaNO2 and HNO2 in water. Let's start by setting up the dissociation equations:
1. NaNO2 dissociates completely in water, giving Na+ ions and NO2- ions:
NaNO2 → Na+ + NO2-
2. HNO2 partially dissociates in water, leading to the formation of H3O+ ions and NO2- ions:
HNO2 + H2O ⇌ H3O+ + NO2-
Now, let's calculate the concentration of H3O+ ions in the solution step by step:
1. Calculate the initial concentrations of NaNO2 and HNO2:
- NaNO2 concentration = 0.100 M
- HNO2 concentration = 0.050 M
2. Since NaNO2 dissociates completely, the concentration of NO2- ions will also be 0.100 M.
3. For HNO2, we need to consider its dissociation constant (Ka), which is approximately 4.5 x 10^-4 at 25°C. The dissociation equation is:
HNO2 + H2O ⇌ H3O+ + NO2-
4. Let's assume x represents the concentration of HNO2 that dissociates. Initially, the concentration of H3O+ ions is 0 M, and the concentration of NO2- ions is 0.100 M.
5. At equilibrium, the concentrations of H3O+ and NO2- ions will be equal, so we can express them both as 0.100 M + x.
6. Apply the equilibrium expression to set up the equation:
Ka = [H3O+][NO2-] / [HNO2]
Remember, [NO2-] = 0.100 M + x, [HNO2] = 0.050 M, and [H3O+] = 0.100 M + x.
7. Plug in the values into the equilibrium expression:
4.5 x 10^-4 = (0.100 + x)(0.100 + x) / 0.050
8. Solve the equation for x. Rearrange the equation:
(0.100 + x)(0.100 + x) = 4.5 x 10^-4 * 0.050
Multiply:
0.01 + 0.200x + x^2 = 2.25 x 10^-5
Rearrange again:
x^2 + 0.2x - 2.25 x 10^-5 + 0.01 = 0
9. Solve the quadratic equation using the quadratic formula or factoring. In this case, the quadratic equation does not appear to factor nicely, so using the quadratic formula is more suitable.
10. Apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In the given equation, a = 1, b = 0.2, and c = - 2.25 x 10^-5 + 0.01. Substitute these values into the quadratic formula and solve for x.
Once you find the value of x, you can calculate the concentration of H3O+ ions, which is 0.100 M + x.