Respuesta :
Answer: The molar mass of the unknown compound is 223.2 g/mol
Explanation:
To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
[tex]\pi=iMRT[/tex]
where,
[tex]\pi[/tex] = osmotic pressure of the solution = 8.44 torr
i = Van't hoff factor = 1 (for non-electrolytes)
M = molarity of solute = ?
R = Gas constant = [tex]62.3637\text{ L torr }mol^{-1}K^{-1}[/tex]
T = temperature of the solution = [tex]25^oC=[273+25]=298K[/tex]
Putting values in above equation, we get:
[tex]8.44torr=1\times M\times 62.3637\text{ L. torr }mol^{-1}K^{-1}\times 298K\\\\M=\frac{8.44}{1\times 62.3637\times 298}=4.54\times 10^{-4}M[/tex]
To calculate the molecular mass of solute, 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 = [tex]4.54\times 10^{-4}M[/tex]
Given mass of unknown compound = 15.2 mg = 0.0152 g (Conversion factor: 1 g = 1000 mg)
Volume of solution = 150.0 mL
Putting values in above equation, we get:
[tex]4.54\times 10^{-4}M=\frac{0.0152\times 1000}{\text{Molar mass of unknown compound}\times 150.0}\\\\\text{Molar mass of unknown compound}=\frac{0.0152\times 1000}{150.0\times 4.54\times 10^{-4}}=223.2g/mol[/tex]
Hence, the molar mass of the unknown compound is 223.2 g/mol
Answer:
The molecular mass of the unknown compound found in the aqueous solution was 223.2 g/mol.
Explanation:
To get molar mass of compound from the given weight, the concentration of compound is elucidated, thereby leading to the calculation of molar mass.
The concentration of solute in an aqueous solution can be derived from the osmotic pressure equation:
Osmotic pressure [tex]\rm \left ( \pi \right )[/tex] = Van't Hoff factor (i) [tex]\times[/tex] Molarity of solute (M) [tex]\times[/tex] Gas constant (R) [tex]\times[/tex] Temperature (T)
From the given values in the question and applying constant values:
8.44 torr = 1 (for non electrolytes) [tex]\times[/tex] M [tex]\times[/tex] [tex]\rm 62.3637\;L\;^-^1\;torr\;mol^-^1\;K^-^1[/tex] [tex]\times[/tex] 298 K
M = 4.54 [tex]\times 10^-^4[/tex] M
From the molarity of the given compound the molar mass can be calculated as:
Molarity = [tex]\rm \frac{weight}{molecular weight} \;\times\;\frac{1000}{volume (ml)}[/tex]
4.54 [tex]\times 10^-^4[/tex] = [tex]\rm \frac{0.0152\;g}{molecular weight} \;\times\;\frac{1000}{150ml}[/tex]
molecular weight = 223.2 g/mol.
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