You need to produce a buffer solution that has a pH of 4.87. You already have a solution that contains 10. mmol (millimoles) of acetic acid. How many millimoles of sodium acetate will you need to add to this solution? Ka for acetic acid is 1.8×10−5.

13.34 mmol NaOAc needed

Explanation:

Use the Henderson-Hasselbalch Equation to determine the [OAc⁻]:[HOAc] ratio that will give a pH = 4.87. Then use that ratio to calculate the amount of NaOAc needed to make the buffer solution. ([pKa(HOAc) = -log(Ka) = -log(1.8 x 10⁻⁵)  = 4.75)

pH = pKa + log([OAc⁻]/[HOAc])

4.87 = 4.75 + log([OAc⁻]/[HOAc])

log([OAc⁻]/[HOAc]) = 4.87 - 4.75 = 0.1253

[OAc⁻]/[HOAc] = 10⁰°¹²³⁵ = 1.334

That is, for a OAc⁻/HOAc buffer with a pH of 4.87 the [OAc⁻]:[HOAc] ratio must be 1.334:1.000.

Given that the system already contains 10 mmol HOAc one can determine the amount of OAc⁻ needed relative to the starting amount of HOAc as follows:

1.334/1.000 = (mmol NaOAc)/10mmol HOAc

=> mmol NaOAc = (10mmol HOAc)(1.334/1.000) = 13.34mmol NaOAc needed.

Test Calculation:

Assuming Molar concentrations, the following verifies the NaOAc quantity needed ...

               HOAc         =>           H⁺        +       OAc⁻

C(Bfr)    0.0100M                     [H⁺]              0.01334M

Ka(HOAc) = [H⁺][OAc⁻]/[HOAc] = [H⁺](0.01334)/(0.0100M) = 1.8 x 10⁻⁵

[H⁺] = [(1.8 x 10⁻⁵)(0.0100)/(0.01334)]M = 1.349 x 10⁻⁵M

pH = -log[H⁺] - -log(1.349 x 10⁻⁵) = -(-4.87) = 4.87                              =>  QED

u i forgot the answer?

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.