Question

You are given a 1.00 g sample of an unknown tri-protic acid, which you dissolve in 50.0 mL of water containing phenolphthalein indicator. You titrate the acid solution with standardized 0.400 M KOH(aq). It requires 39.06 mL of the KOH solution to produce a light pink indicator color. What is the molecular weight of the unknown acid?

Answer 1

Answer:

21.33 g/mol

Explanation:

Considering:-

$Normality=Molarity\times {n-factor}$

So, Given that:-

Let Molarity of tri-protic acid = x M

n-factor of tri-protic acid = 3 (3 dissociable H)

So,  

Normality of tri-protic acid = x/3 N

So, Given that:-

Let Molarity of KOH = 0.400 M

n-factor of KOH = 1 (1 dissociable OH)

So,  

Normality of KOH = 0.400 N

Considering:-

At equivalence point

Gram equivalents of acid = Gram equivalents of base

So,

$Normality_{acid}\times Volume_{acid}=Normality_{base}\times Volume_{base}$

Given  that:  

$Normality_{base}=0.400\ N$  

$Volume_{base}=39.06\ mL$  

$Volume_{acid}=50.0\ mL$  

$Normality_{acid}=x/3\ N$  

So,    

$\frac{x}{3}\times 50=0.400\times 39.06$

x = 0.93744 M

Also,

Considering:

$Molarity=\frac{Moles\ of\ solute}{Volume\ of\ the\ solution}$

Or,

$Moles =Molarity \times {Volume\ of\ the\ solution}$

Given :

For tri-protic acid :

Molarity = 0.93744 M

Volume = 50.0 mL

The conversion of mL to L is shown below:

1 mL = 10⁻³ L

Thus, volume = 50.0×10⁻³ L

Thus, moles of tri-protic acid :

$Moles=0.93744 \times {50.0\times 10^{-3}}\ moles$

Moles of tri-protic acid  = 0.046872 moles

Also, Given mass = 1.00 g

So,

Molar mass = Mass/Moles = 1.00g / 0.046872 moles = 21.33 g/mol

21.33 g/mol is the molecular weight of the unknown acid.