The question is: what is the ratio [NH3/[NH4+] in an ammonia/ammonium chloride buffer solution with pH= 10.00? (pKa for ammonia=9.25)
When working the problem, I tried to solve it a bit backwards, in that I plugged in each of the multiple choices I was given to see which would equal 10.
Such as:
pH=pKa +log(salt/base)
9.25 +log(5.62)=10 pH
So my ratio would be 5.62 since that number makes it equal 10, or am I just doing this completely wrong?
My calculator is broken so I can't check your number; however, there is nothing wrong with doing it the way you tried. You can do it straight, however, by
pH = pKa + log (base)/(acid)
10 = 9.25 + log (base)/(acid) and solve for (base)/(acid)
Well, let's analyze your approach. You're on the right track using the Henderson-Hasselbalch equation:
pH = pKa + log([salt]/[base])
However, the ratio you're looking for is actually [NH3]/[NH4+], not [salt]/[base]. In this case, the salt is ammonium chloride (NH4Cl) and the base is ammonia (NH3).
Using the Henderson-Hasselbalch equation, we can rearrange the equation to solve for the ratio:
pH = pKa + log([NH4+]/[NH3])
Since the pH is given as 10.00 and the pKa for ammonia is 9.25, we can substitute those values:
10.00 = 9.25 + log([NH4+]/[NH3])
Now let's solve for the ratio:
log([NH4+]/[NH3]) = 10.00 - 9.25
log([NH4+]/[NH3]) = 0.75
[NH4+]/[NH3] = 10^0.75
So the ratio [NH4+]/[NH3] is approximately 5.62.
It looks like you made a small error in your calculations, but you were on the right track! Just keep in mind that the ratio you're looking for is [NH3]/[NH4+] and not [salt]/[base]. Keep up the good work!
To determine the ratio of [NH3]/[NH4+] in the ammonia/ammonium chloride buffer solution with pH=10.00, you can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this case, ammonia (NH3) is the base (A-) and ammonium (NH4+) is the acid (HA). The pKa for ammonia is given as 9.25.
Using the given pH of 10.00, the equation becomes:
10.00 = 9.25 + log([NH3]/[NH4+])
Rearranging the equation, we have:
log([NH3]/[NH4+]) = 10.00 - 9.25
log([NH3]/[NH4+]) = 0.75
Now, we need to convert the logarithmic form to the exponential form to find the ratio:
[NH3]/[NH4+] = 10^(0.75)
Using a calculator, we find:
[NH3]/[NH4+] ≈ 5.62
Therefore, the ratio of [NH3]/[NH4+] in the ammonia/ammonium chloride buffer solution with pH=10.00 is approximately 5.62.
To determine the ratio of [NH3]/[NH4+] in an ammonia/ammonium chloride buffer solution with pH = 10.00, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this equation, [A-] represents the concentration of the conjugate base (NH3 in this case), and [HA] represents the concentration of the acidic form (NH4+). The pKa is given as 9.25.
First, let's rearrange the equation to solve for the ratio [A-]/[HA]:
pH - pKa = log([A-]/[HA])
Now, substitute the known values:
10.00 - 9.25 = log([A-]/[HA])
0.75 = log([A-]/[HA])
To find the ratio, we need to convert the logarithmic form to regular form. In other words, we need to find the antilog or inverse log. We can use base 10 since we are dealing with logarithms to the base 10.
10^0.75 = [A-]/[HA]
Now, calculate the value of 10^0.75:
10^0.75 ≈ 5.623
So, the ratio of [NH3]/[NH4+] in the ammonia/ammonium chloride buffer solution with pH = 10.00 is approximately 5.623.
To summarize, your approach of plugging in the options to find the one that makes the equation equal pH = 10.00 is not correct. Instead, you should use the Henderson-Hasselbalch equation and solve for the ratio by converting the logarithmic form to regular form using base 10.