To prepare a buffer solution with a specific pH using a weak base and its conjugate acid, we use the…

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To prepare a buffer solution with a specific pH using a weak base and its conjugate acid, we use the Henderson-Hasselbalch equation for bases. The buffer system consists of ammonia (NH3) as the wea

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To prepare a buffer solution with a specific pH using a weak base and its conjugate acid, we use the Henderson-Hasselbalch equation for bases. The buffer system consists of ammonia ( $NH_3$ ) as the weak base and ammonium ion ( $NH_4^+$ ) as its conjugate acid, which comes from ammonium sulfate ( $(NH_4)_2SO_4$ ).

Given:

Target pH = 9.45
Volume of $NH_3$ solution = 425 mL = 0.425 L
Concentration of $NH_3$ = 0.258 M
The base dissociation constant ( $K_b$ ) for $NH_3$ is $1.8 \times 10^{-5}$ .
Molar mass of $(NH_4)_2SO_4$ $(N H_{4})_{2} S O_{4}$ :
- N: $2 \times 14.01 = 28.02$ g/mol
- H: $8 \times 1.008 = 8.064$ g/mol
- S: $1 \times 32.07 = 32.07$ g/mol
- O: $4 \times 16.00 = 64.00$ g/mol
- Total molar mass = $28.02 + 8.064 + 32.07 + 64.00 = 132.154$ g/mol

Calculate the $pOH$ from the given $pH$ .
$pOH = 14 - pH$ $pOH = 14 - 9.45$ $pOH = 4.55$
Calculate the $pK_b$ for ammonia ( $NH_3$ ).
$pK_b = -\log(K_b)$ $pK_b = -\log(1.8 \times 10^{-5})$ $pK_b \approx 4.7447$
Use the Henderson-Hasselbalch equation to find the required concentration of the conjugate acid ( $[NH_4^+]$ ).
The Henderson-Hasselbalch equation for a basic buffer is:
$pOH = pK_b + \log\left(\frac{[\text{conjugate acid}]}{[\text{weak base}]}\right)$ $pOH = pK_b + \log\left(\frac{[NH_4^+]}{[NH_3]}\right)$
Substitute the known values:
$4.55 = 4.7447 + \log\left(\frac{[NH_4^+]}{0.258 \text{ M}}\right)$
Rearrange to solve for the logarithm term:
$\log\left(\frac{[NH_4^+]}{0.258 \text{ M}}\right) = 4.55 - 4.7447$ $\log\left(\frac{[NH_4^+]}{0.258 \text{ M}}\right) = -0.1947$
Take the antilog (10 to the power of both sides):
$\frac{[NH_4^+]}{0.258 \text{ M}} = 10^{-0.1947}$ $\frac{[NH_4^+]}{0.258 \text{ M}} \approx 0.6387$
Solve for $[NH_4^+]$ :
$[NH_4^+] = 0.6387 \times 0.258 \text{ M}$ $[NH_4^+] \approx 0.1648 \text{ M}$
Calculate the total moles of $NH_4^+$ needed.
$\text{Moles of } NH_4^+ = \text{Concentration} \times \text{Volume}$ $\text{Moles of } NH_4^+ = 0.1648 \text{ mol/L} \times 0.425 \text{ L}$ $\text{Moles of } NH_4^+ \approx 0.07004 \text{ mol}$
Determine the moles of $(NH_4)_2SO_4$ required.
Ammonium sulfate, $(NH_4)_2SO_4$ , dissociates to produce two $NH_4^+$ ions for every one formula unit:
$(NH_4)_2SO_4(s) \rightarrow 2NH_4^+(aq) + SO_4^{2-}(aq)$
Therefore, the moles of $(NH_4)_2SO_4$ needed are half the moles of $NH_4^+$ :
$\text{Moles of } (NH_4)_2SO_4 = \frac{\text{Moles of } NH_4^+}{2}$ $\text{Moles of } (NH_4)_2SO_4 = \frac{0.07004 \text{ mol}}{2}$ $\text{Moles of } (NH_4)_2SO_4 \approx 0.03502 \text{ mol}$
Calculate the mass of $(NH_4)_2SO_4$ needed.
$\text{Mass of } (NH_4)_2SO_4 = \text{Moles} \times \text{Molar Mass}$ $\text{Mass of } (NH_4)_2SO_4 = 0.03502 \text{ mol} \times 132.154 \text{ g/mol}$ $\text{Mass of } (NH_4)_2SO_4 \approx 4.628 \text{ g}$
Rounding to three significant figures (consistent with 0.258 M and 425 mL):
$\text{Mass of } (NH_4)_2SO_4 = \boxed{\text{4.63 g}}$

To prepare a buffer solution with a specific pH using a weak base and its conjugate acid, we use the Henderson-Hasselbalch equation for bases. The buffer system consists of ammonia (NH3) as the wea

Answer

Step-by-step solution

Calculate the $pOH$ from the given $pH$ .

Calculate the $pK_b$ for ammonia ( $NH_3$ ).

Use the Henderson-Hasselbalch equation to find the required concentration of the conjugate acid ( $[NH_4^+]$ ).

Calculate the total moles of $NH_4^+$ needed.

Determine the moles of $(NH_4)_2SO_4$ required.

Calculate the mass of $(NH_4)_2SO_4$ needed.

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To prepare a buffer solution with a specific pH using a weak base and its conjugate acid, we use the Henderson-Hasselbalch equation for bases. The buffer system consists of ammonia (NH3) as the wea

Answer

Step-by-step solution

Calculate the pOHpOHpOH from the given pHpHpH.

Calculate the pKbpK_bpKb​ for ammonia (NH3NH_3NH3​).

Use the Henderson-Hasselbalch equation to find the required concentration of the conjugate acid ([NH4+][NH_4^+][NH4+​]).

Calculate the total moles of NH4+NH_4^+NH4+​ needed.

Determine the moles of (NH4)2SO4(NH_4)_2SO_4(NH4​)2​SO4​ required.

Calculate the mass of (NH4)2SO4(NH_4)_2SO_4(NH4​)2​SO4​ needed.

Still stuck on this one?

More Languages Questions

Calculate the $pOH$ from the given $pH$ .

Calculate the $pK_b$ for ammonia ( $NH_3$ ).

Use the Henderson-Hasselbalch equation to find the required concentration of the conjugate acid ( $[NH_4^+]$ ).

Calculate the total moles of $NH_4^+$ needed.

Determine the moles of $(NH_4)_2SO_4$ required.

Calculate the mass of $(NH_4)_2SO_4$ needed.