<u>Answer:</u> The vapor pressure of solution is 459.17 mmHg
<u>Explanation:</u>
To calculate the number of moles, we use the equation:
.....(1)
Given mass of testosterone = 7.752 g
Molar mass of testosterone = 288.4 g/mol
Putting values in equation 1, we get:
![\text{Moles of testosterone}=\frac{7.752g}{288.4g/mol}=0.027mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20testosterone%7D%3D%5Cfrac%7B7.752g%7D%7B288.4g%2Fmol%7D%3D0.027mol)
- <u>For diethyl ether:</u>
Given mass of diethyl ether = 208.0 g
Molar mass of diethyl ether = 74.12 g/mol
Putting values in equation 1, we get:
![\text{Moles of diethyl ether}=\frac{208.0g}{74.12g/mol}=2.81mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20diethyl%20ether%7D%3D%5Cfrac%7B208.0g%7D%7B74.12g%2Fmol%7D%3D2.81mol)
Mole fraction of a substance is calculated by using the equation:
![\chi_A=\frac{n_A}{n_A+n_B}](https://tex.z-dn.net/?f=%5Cchi_A%3D%5Cfrac%7Bn_A%7D%7Bn_A%2Bn_B%7D)
![\chi_{\text{testosterone}}=\frac{n_{\text{testosterone}}}{n_{\text{testosterone}}+n_{\text{diethyl ether}}}](https://tex.z-dn.net/?f=%5Cchi_%7B%5Ctext%7Btestosterone%7D%7D%3D%5Cfrac%7Bn_%7B%5Ctext%7Btestosterone%7D%7D%7D%7Bn_%7B%5Ctext%7Btestosterone%7D%7D%2Bn_%7B%5Ctext%7Bdiethyl%20ether%7D%7D%7D)
![\chi_{\text{testosterone}}=\frac{0.027}{0.027+2.81}\\\\\chi_{\text{testosterone}}=0.0095](https://tex.z-dn.net/?f=%5Cchi_%7B%5Ctext%7Btestosterone%7D%7D%3D%5Cfrac%7B0.027%7D%7B0.027%2B2.81%7D%5C%5C%5C%5C%5Cchi_%7B%5Ctext%7Btestosterone%7D%7D%3D0.0095)
The formula for relative lowering of vapor pressure will be:
![\frac{p^o-p_s}{p^o}=i\times \chi_{\text{solute}}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%5Eo-p_s%7D%7Bp%5Eo%7D%3Di%5Ctimes%20%5Cchi_%7B%5Ctext%7Bsolute%7D%7D)
where,
= vapor pressure of solvent (diethyl ether) = 463.57 mmHg
= vapor pressure of the solution = ?
i = Van't Hoff factor = 1 (for non electrolytes)
= mole fraction of solute (testosterone) = 0.0095
Putting values in above equation, we get:
![\frac{463.57-p^s}{463.57}=1\times 0.0095\\\\p^s=459.17mmHg](https://tex.z-dn.net/?f=%5Cfrac%7B463.57-p%5Es%7D%7B463.57%7D%3D1%5Ctimes%200.0095%5C%5C%5C%5Cp%5Es%3D459.17mmHg)
Hence, the vapor pressure of solution is 459.17 mmHg