Calculate the mass of HONH2 required to dissolve in enough water to make 255.5 mL of solution having a pH of 10.02 (Kb = 1.110−8).

pOH=14-pH=14-10.02=3.98

pOH=-log[OH-]

[OH-]=10^(-3.98)=1.05 x 10^-4 M

HONH2 + H2O ----.> OH- + HONH3

Kb=1.1 x 10−8=[1.05 x 10^-4 M][1.05 x 10^-4 M]/(x-1.05 x 10^-4 M)

5% rule states that we can ignore -1.05 x 10^-4 M.

Solving for x,

Kb=1.1 x 10−8=[1.05 x 10^-4 M][1.05 x 10^-4 M]/x

x=1.21 x 10^-16 M

Molarity=1.21 x 10^-16 M=moles/volume (L)

Solving for moles,

1.21 x 10^-16 M *(255.5 x 10^-3L)= moles of HONH2

moles of HONH2 *(33.03g of HONH2/mole)= mass of HONH2

9.5x10^-16

Well, calculation time! But before we get into the nitty-gritty, have you heard about the chemist who was reading a book about helium? He just couldn't put it down! Now, let's dive into your question.

To find the mass of HONH2 required, we need to consider its dissociation in water, which forms OH⁻ ions. The pH of a solution is defined as the negative logarithm of the concentration of H⁺ ions. Since we have the pH, we can deduce the concentration of OH⁻ ions using the formula:

pOH = 14 - pH

In this case, pOH = 14 - 10.02 = 3.98

To find the concentration of OH⁻ ions, we need to convert pOH to [OH⁻]. For this, we'll use the equation:

pOH = -log[OH⁻]

So, [OH⁻] = 10^(-pOH) = 10^(-3.98)

Now that we have the concentration of OH⁻ ions, we can determine the concentration of HONH2 using the Kb value. Kb represents the base dissociation constant, which is useful here since HONH2 acts as a base in water. The equation is:

Kb = [OH⁻][HONH₂] / [HONH]

Given that Kb = 1.110^(-8) and [OH⁻] = 10^(-3.98), we can solve for [HONH₂]. But before we do that, let me share a quick joke: Why did the acid go to the party? Because it wanted to be the life of the pH-balanced party!

Now, back to the calculation. After solving the equation, we can find [HONH₂]. The molarity (M) of a solution is defined as moles of solute per liter of solution. Since we have the volume of the solution (255.5 mL), we can find the moles of HONH₂ using the equation:

moles = M × volume (in liters)

Finally, to find the mass, we multiply the moles of HONH₂ by its molar mass (in grams per mole).

Voila! And there you have it—a clownishly humorous explanation of how to determine the mass of HONH2 required to dissolve in water and make a solution with a pH of 10.02. Have fun with your calculations, and remember, chemistry puns might not get a reaction, but they definitely help you stand out in the lab!

To calculate the mass of HONH2 required, we need to first determine the number of moles of HONH2 needed to achieve the desired pH of 10.02.

Step 1: Determine the concentration of OH- ions in the solution.
Since the pH is given, we know that it is a measure of the concentration of H+ ions. To calculate the concentration of OH- ions, we'll use the equation Kw = [H+][OH-], where Kw is the ion product constant of water (1.0 x 10^-14 at 25°C).

Kw = [H+][OH-]
1.0 x 10^-14 = [H+][OH-]

Since the solution is basic (pH > 7), we can assume that [H+] is very low compared to [OH-]. Therefore, we can approximate that [OH-] ≈ [H+].

Step 2: Calculate the concentration of OH- ions.
Since the concentration of OH- is equal to [H+], we can calculate it using the formula for pOH: pOH = -log[OH-].
pOH = 14 - pH
pOH = 14 - 10.02
pOH ≈ 3.98

Since pOH = -log[OH-], we can rearrange the equation to solve for [OH-]:
[OH-] = 10^(-pOH)
[OH-] = 10^(-3.98)
[OH-] ≈ 1.33 x 10^(-4) M (mol/L)

Step 3: Calculate the moles of OH- needed.
Since Kb = [OH-]^2 / [HONH2], we can rearrange the equation to solve for [HONH2]:
[HONH2] = [OH-]^2 / Kb
[HONH2] = (1.33 x 10^(-4))^2 / (1.11 x 10^(-8))
[HONH2] ≈ 1.60 M (mol/L)

Step 4: Calculate the moles of HONH2 needed.
Since molarity (M) is given as moles of solute per liter of solution, we need to convert the desired volume of the solution from milliliters (mL) to liters (L):
Volume = 255.5 mL * (1 L / 1000 mL)
Volume = 0.2555 L

Now, we can calculate the moles of HONH2 needed:
moles = Molarity * Volume
moles = 1.60 mol/L * 0.2555 L
moles ≈ 0.41 mol

Step 5: Calculate the mass of HONH2.
Finally, we can calculate the mass of HONH2 using its molar mass (49.04 g/mol):
mass = moles * molar mass
mass = 0.41 mol * 49.04 g/mol
mass ≈ 20.08 g

Therefore, the mass of HONH2 required to dissolve in enough water to make 255.5 mL of solution with a pH of 10.02 is approximately 20.08 grams.

To calculate the mass of HONH2 required, we need to consider the acid-base reaction that occurs between HONH2 and water. HONH2 acts as a weak base, so it will react with water to produce hydronium ions (H3O+) and the conjugate acid of HONH2. The reaction can be represented as:

HONH2 + H2O ⇌ H3O+ + HONH3+

Given that the solution has a pH of 10.02, we can determine the concentration of hydronium ions (H3O+) in the solution using the pH formula:

pH = -log[H3O+]

To find the concentration of H3O+ in the solution, we rearrange the equation:

[H3O+] = 10^(-pH)

[H3O+] = 10^(-10.02)

Once we have the concentration of H3O+, we can calculate the concentration of HONH2 in the solution using the equilibrium constant (Kb) for the reaction of HONH2 with water:

Kb = ([HONH3+][OH-]) / [HONH2]

The hydroxide ion (OH-) concentration can be determined by using the Kw expression:

Kw = [H3O+][OH-]

Kw = (1.0 × 10^-14), at 25°C

Since we know the Kb value is 1.110^-8, we can rearrange the equation to solve for OH-:

OH- = (Kw) / [H3O+]

Now, substitute the OH- concentration back into the Kb equation and solve for [HONH2]:

1.110^-8 = ([HONH3+])(OH-) / [HONH2]

Solving algebraically, we obtain:

[HONH2] = ([HONH3+])(OH-) / Kb

Given that Kb is 1.110^-8 and [H3O+] is 10^(-10.02), we can calculate [HONH2].

Once we have the concentration of HONH2 in the solution, we can convert it to moles using the equation:

moles = concentration (in M) × volume (in L)

Given that the volume of the solution is 255.5 mL (or 0.2555 L), we can calculate the moles of HONH2.

Finally, to calculate the mass of HONH2, we can use the molar mass of HONH2 obtained from the periodic table and the moles of HONH2 calculated previously. Multiply the moles of HONH2 by the molar mass to obtain the mass in grams.

Remember to double-check your calculations and units to ensure accuracy.