Respuesta :
Answer: The molar mass of the saccharin is 181 g/mol
Explanation:
We are given:
pH of the solution = 12.190
To calculate pOH of the solution, we use the equation:
[tex]pH+pOH=14\\pOH=14-12.190=1.81[/tex]
To calculate the [tex]OH^-[/tex] concentration, we use the equation:
[tex]pOH=-\log[OH^-]\\\\1.81=-\log [OH^-][/tex]
[tex][OH^-]=0.0155M[/tex]
As, saccharin is a weak base. Let us consider be as BOH
The equation for the reaction of BOH with water follows:
[tex]BOH+H_2O\rightleftharpoons BH^++OH^-[/tex]
Initial: c
At eqllm: c-x x x
Value of x = [tex][OH^-]=0.0155M[/tex]
The expression of [tex]K_b[/tex] for above equation follows:
[tex]K_b=\frac{[BH^+]\times [OH^-]}{[BOH]}[/tex]
We are given:
[tex]K_b=4.80\times 10^{-3}[/tex]
[tex][BH^+]=0.0155M[/tex]
[tex][OH^-]=0.0155M[/tex]
[tex][BOH]=c-0.0155[/tex]
Putting values in above expression, we get:
[tex]4.80\times 10^{-3}=\frac{0.0155\times 0.0155}{c-0.0155}\\\\c=0.0655M[/tex]
Concentration of saccharin = 0.0655 M
To calculate the molecular mass of saccharin, we use the equation used to calculate the molarity of solution:
[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}[/tex]
We are given:
Molarity of solution = 0.0655 M
Given mass of saccharin = 0.297 g
Volume of solution = 25.0 mL
Putting values in above equation, we get:
[tex]0.0655M=\frac{0.297\times 1000}{\text{Molar mass of saccharin}\times 25.0}\\\\\text{Molar mass of saccharin}=\frac{0.297\times 1000}{0.0655\times 25}=181g/mol[/tex]
Hence, the molar mass of the saccharin is 181 g/mol
