Calculate the ratio of [NH3]/[NH4+] that gives a solution of pH = 10.60.
Well, you know what they say - pH is like a rollercoaster ride for protons! So, let's buckle up and take a wild ride through this problem.
To calculate the ratio of [NH3]/[NH4+], we need to understand the relationship between the pKa of a weak acid such as NH4+ (ammonium) and the pH of the solution.
The Henderson-Hasselbalch equation is the key to this rollercoaster ride: pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base (NH3) and [HA] is the concentration of the acid (NH4+).
For NH4+/NH3, the pKa value is approximately 9.25. So, to reach a pH of 10.60, we need to set up our equation like this:
10.60 = 9.25 + log([NH3]/[NH4+])
By rearranging the equation, we get:
log([NH3]/[NH4+]) = 10.60 - 9.25
log([NH3]/[NH4+]) = 1.35
To get rid of logarithms, we can convert it into an exponential equation:
[NH3]/[NH4+] = 10^(1.35)
Calculating that exponential value, we get approximately 20.56.
So, the ratio of [NH3]/[NH4+] that gives a solution with pH = 10.60 is approximately 20.56:1.
And there you have it! Just don't forget to enjoy the proton-coaster ride along the way.
To calculate the ratio of [NH3] to [NH4+] that gives a solution of pH = 10.60, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this case, NH3 (ammonia) acts as a weak base (A-) and NH4+ (ammonium) acts as its conjugate acid (HA).
The pKa of the NH4+/NH3 system is approximately 9.24 (taken from literature values).
Let's plug in the values into the equation:
10.60 = 9.24 + log([NH3]/[NH4+])
Rearranging the equation, we get:
log([NH3]/[NH4+]) = 10.60 - 9.24
log([NH3]/[NH4+]) = 1.36
Now, we need to convert the logarithmic expression into its exponential form:
[NH3]/[NH4+] = 10^(1.36)
Using a calculator, we get:
[NH3]/[NH4+] ≈ 22.38
Therefore, the ratio of [NH3]/[NH4+] that gives a solution of pH = 10.60 is approximately 22.38.
To calculate the ratio of [NH3]/[NH4+] for a solution with a given pH, we need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is:
pH = pKa + log10 ([A-]/[HA])
In this equation, pH is the given pH of the solution, pKa is the dissociation constant of the weak acid (NH4+), and [A-] and [HA] are the concentrations of the base (NH3) and acid (NH4+), respectively.
First, we need to find the pKa of NH4+. The pKa value can be found in a chemistry reference book or online. For NH4+, the pKa value is 9.25.
Next, we need to rearrange the Henderson-Hasselbalch equation to solve for the ratio [A-]/[HA]. The equation becomes:
[A-]/[HA] = 10^(pH - pKa)
Now we can substitute the given pH value (pH = 10.60) and the pKa value (pKa = 9.25) into the equation:
[A-]/[HA] = 10^(10.60 - 9.25)
[A-]/[HA] = 10^1.35
Using the logarithmic property of exponents, we can rewrite this equation:
[A-]/[HA] = 25.12
Therefore, the ratio of [NH3]/[NH4+] that gives a solution with a pH of 10.60 is approximately 25.12.