Answer:
The value is [tex]Z = 311.33 \ g/mol[/tex]
Explanation:
From the question we are told that
The mass of saxitoxin is [tex]m = 12.5 mg = 12.5 * 10^{-6} g[/tex]
The volume of water is [tex]V = 3.10 mL = 3.10 *10^{-3} L[/tex]
The osmotic pressure is [tex]P = 0.236 = \frac{0.236}{760} = 3.105 * 10^{-4} atm[/tex]
The temperature is [tex]T = 19^oC = 19 + 273 = 292 \ K[/tex]
Generally the osmotic pressure is mathematically represented as
[tex]P = C * T * R[/tex]
Here R is the gas constant with value
[tex]R = 0.0821 ( L .atm /mol. K)[/tex]
and C is the concentration of saxitoxin
So
[tex]3.105 * 10^{-4} = C * 0.0821 * 292 [/tex]
[tex] C = 1.295 *10^{-5} mol/L [/tex]
Generally the number of moles of saxitoxin is mathematically represented as
[tex]n = C * V[/tex]
=> [tex]n = 1.295 *10^{-5} *3.10 *10^{-3}[/tex]
=> [tex]n = 4.015 *10^{-8} \ mol[/tex]
Generally the molar mass of saxitoxin is mathematically represented as
[tex]Z = \frac{m}{n}[/tex]
=> [tex]Z = \frac{12.5 * 10^{-6}}{ 4.015 *10^{-8}}[/tex]
=> [tex]Z = 311.33 \ g/mol[/tex]
