How many grams of dry NH4Cl need to be added to 1.90 L of a 0.200 M solution of ammonia, NH3, to prepare a buffer solution that has a pH of 8.99? Kb for ammonia is1.8*10^-5.
Can anyone help me with this question? I have no idea how to solve it.
To solve this question, we need to use the Henderson-Hasselbalch equation for buffer solutions:
pH = pKa + log ([A-]/[HA])
In this case, NH3 is the base (A-) and NH4Cl is the corresponding acid (HA). We can assume that all of the NH3 will be converted to NH4+ and Cl- ions.
Step 1: Finding pKa
To find pKa, we can use the Kb value provided. The relationship between Kb and pKa is given by:
Kw = Ka * Kb
Since Kw = 1.0 x 10^-14 at 25°C and pKa + pKb = 14, we can rearrange the equation to solve for pKa:
1.0 x 10^-14 = Ka * 1.8 x 10^-5
pKa = -log(Ka) = -log(1.8 x 10^-5)
Now we have the value of pKa.
Step 2: Calculating the moles of NH3 needed
To calculate the moles of NH3 needed, we can use the formula:
Moles = volume (L) * concentration (M)
Moles of NH3 = 1.90 L * 0.200 M
Step 3: Determining the ratio of NH3 to NH4Cl needed
According to the Henderson-Hasselbalch equation, the ratio of NH3 to NH4Cl is determined by the logarithmic term:
log ([A-]/[HA])
Since we want the pH to be 8.99, we can plug in the values into the equation:
8.99 = pKa + log ([A-]/[HA])
Solving for logarithmic term,
log ([A-]/[HA]) = 8.99 - pKa
Step 4: Calculating the amount of NH4Cl needed
To calculate the moles of NH4Cl needed, we can rearrange the equation from Step 3 and substitute the moles of NH3:
log ([A-]/[HA]) = 8.99 - pKa
log ([A-]/[HA]) = 8.99 - (-log(1.8 x 10^-5))
Now, let's solve for [A-]/[HA]:
[A-]/[HA] = 10^(8.99 - (-log(1.8 x 10^-5)))
Since NH3 and NH4Cl react in a 1:1 ratio, the moles of NH4Cl needed will be the same as the moles of NH3. Therefore, the moles of NH4Cl needed is equal to the moles of NH3 calculated in step 2.
Step 5: Converting moles of NH4Cl to grams
To convert moles of NH4Cl to grams, we need to know the molar mass of NH4Cl, which is:
Molar mass = molar mass of N + 4 * molar mass of H + molar mass of Cl
Now, you can calculate the grams of NH4Cl needed by multiplying the moles calculated in step 4 by the molar mass of NH4Cl.
To summarize,
1. Calculate pKa using the relationship between Kb and pKa: pKa = -log(Ka)
2. Calculate the moles of NH3 using the formula: Moles = volume (L) * concentration (M)
3. Determine the ratio of NH3 to NH4Cl using the Henderson-Hasselbalch equation: log ([A-]/[HA]) = 8.99 - pKa
4. Calculate the moles of NH4Cl using the calculated ratio in step 3.
5. Convert moles of NH4Cl to grams using the molar mass of NH4Cl.
Now you have all the steps needed to solve the problem.