If the same volume (130-mL) of the buffer were 0.265 M in NH3 and 0.400 M in NH4Br, what mass of HCl could be handled before the pH fell below 9.00?
I used the henderson-hasselbalch equation to solve this. i set it up as 9=9.24551+log((0.03445-x)/(0.052+x))
0.03445= moles of NH3
0.052= moles of NH4Br
I calculated the grams to be .11 g but it was wrong. Did i set up my H-H equation wrong?
Assistance needed.
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See above for my response.
The x is small approximation doesn't work for this problem, so you have to set up an ICE table to solve for the amount of HCl, you can't use the H-H
Based on the information provided, it seems like you have set up the Henderson-Hasselbalch equation correctly. However, the mass of HCl that you calculated may be incorrect. Let's go through the problem step by step to determine where the mistake might be.
To solve this problem, we can use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the ratio of its conjugate acid and base concentrations:
pH = pKa + log([A-]/[HA])
Where:
pH is the desired pH (in this case, 9.00)
pKa is the negative logarithm of the acid dissociation constant (for NH3/NH4+ system, pKa = 9.24551)
[A-] is the concentration of the conjugate base (NH4+) in the buffer solution
[HA] is the concentration of the acid (NH3) in the buffer solution
You correctly identified [A-] as the concentration of NH4Br, which is 0.052 M, and [HA] as the concentration of NH3, which is 0.03445 M. The Henderson-Hasselbalch equation should be:
9.00 = 9.24551 + log((0.03445 - x) / (0.052 + x))
However, to solve for x (the change in concentration), you will need to rearrange the equation. After rearranging, you will get an equation that is not directly solvable analytically. Therefore, you should solve it numerically using trial and error or a computer program.
Here's an example of how you can solve it numerically using iteration:
1. Start with an initial guess for x, let's say x = 0.
2. Plug this value of x into the equation and calculate the left-hand side (LHS) and right-hand side (RHS) separately.
3. If LHS > RHS, increase the value of x; if LHS < RHS, decrease the value of x.
4. Repeat steps 2 and 3 until LHS is very close to RHS (e.g., within a small tolerance value like 0.001).
5. Once you have found the value of x, you can calculate the mass of HCl using the formula: mass = molar mass of HCl * moles of HCl.
By following this procedure, you should be able to find the correct value for x, which will allow you to calculate the mass of HCl accurately.