Respuesta :
Answer: The vapor pressure of solution is 459.17 mmHg
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
- For testosterone:
Given mass of testosterone = 7.752 g
Molar mass of testosterone = 288.4 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of testosterone}=\frac{7.752g}{288.4g/mol}=0.027mol[/tex]
- For diethyl ether:
Given mass of diethyl ether = 208.0 g
Molar mass of diethyl ether = 74.12 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of diethyl ether}=\frac{208.0g}{74.12g/mol}=2.81mol[/tex]
Mole fraction of a substance is calculated by using the equation:
[tex]\chi_A=\frac{n_A}{n_A+n_B}[/tex]
[tex]\chi_{\text{testosterone}}=\frac{n_{\text{testosterone}}}{n_{\text{testosterone}}+n_{\text{diethyl ether}}}[/tex]
[tex]\chi_{\text{testosterone}}=\frac{0.027}{0.027+2.81}\\\\\chi_{\text{testosterone}}=0.0095[/tex]
The formula for relative lowering of vapor pressure will be:
[tex]\frac{p^o-p_s}{p^o}=i\times \chi_{\text{solute}}[/tex]
where,
[tex]p^o[/tex] = vapor pressure of solvent (diethyl ether) = 463.57 mmHg
[tex]p^s[/tex] = vapor pressure of the solution = ?
i = Van't Hoff factor = 1 (for non electrolytes)
[tex]\chi_{\text{solute}}[/tex] = mole fraction of solute (testosterone) = 0.0095
Putting values in above equation, we get:
[tex]\frac{463.57-p^s}{463.57}=1\times 0.0095\\\\p^s=459.17mmHg[/tex]
Hence, the vapor pressure of solution is 459.17 mmHg
