If a buffer is composed of 23.34 mL of 0.147 M acetic acid and 33.66 mL of 0.185 M sodium acetate, how many mL of 0.100 M NaOH can be added before the buffer capacity is reached

25.5mL of 0.100M NaOH are needed to reach buffer capacity.

Explanation:

The buffer capacity is reached when the ratio between moles of conjugate base (Sodium acetate) and moles of weak acid (Acetic acid) is 10:

Moles sodium acetate / Moles Acetic acid = 10

The reaction of acetic acid, HA, with NaOH, to produce sodium acetate, NaA is:

HA + NaOH → H2O + NaA

That means the moles of NaOH added = Moles of HA that are being subtracted and moles of NaA that are been produced.

The initial moles of each species is:

Acetic acid:

23.34mL = 0.02334L * (0.147mol / L) = 0.00343 moles Acetic Acid

Sodium Acetate:

33.66mL = 0.03366L * (0.185mol / L) = 0.00623 moles Sodium Acetate

We can write the moles of each species when NaOH is added as:

Moles sodium acetate / Moles Acetic acid = 10

0.00623 moles + X / 0.00343 moles - X = 10

Where X are moles of NaOH added

Solving for X:

0.00623 moles + X = 0.0343 moles - 10X

11X = 0.0281

X = 0.00255 moles of NaOH are needed

In Liters:

0.0255mol NaOH * (1L / 0.100mol) = 0.0255L of 0.100M NaOH are needed =

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

answer: -

reaction:

na + cl ⇌ nacl

balanced chemical equation:

na + 2cl ⇌ nacl2

sodium + clorine goes to form sodium chloride (table salt).

the product is nacl2.

and the reactants are na and cl.

(note: if you don’t know what ⇌ means, read below: -

⇌(double head arrow) means reversible reaction).