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The vapor pressure of diethyl ether (ether) is 463.57 mm Hg at 25 °C. A nonvolatile, nonelectrolyte that dissolves in diethyl ether is testosterone. Calculate the vapor pressure of the solution at 25 °C when 7.752 grams of testosterone, C19H28O2 (288.4 g/mol), are dissolved in 208.0 grams of diethyl ether. diethyl ether = CH3CH2OCH2CH3 = 74.12 g/mol.

User Omar
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1 Answer

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Answer: The vapor pressure of solution is 459.17 mmHg

Step-by-step explanation:

To calculate the number of moles, we use the equation:


\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}} .....(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:


\text{Moles of testosterone}=(7.752g)/(288.4g/mol)=0.027mol

  • 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:


\text{Moles of diethyl ether}=(208.0g)/(74.12g/mol)=2.81mol

Mole fraction of a substance is calculated by using the equation:


\chi_A=(n_A)/(n_A+n_B)


\chi_{\text{testosterone}}=\frac{n_{\text{testosterone}}}{n_{\text{testosterone}}+n_{\text{diethyl ether}}}


\chi_{\text{testosterone}}=(0.027)/(0.027+2.81)\\\\\chi_{\text{testosterone}}=0.0095

The formula for relative lowering of vapor pressure will be:


(p^o-p_s)/(p^o)=i* \chi_{\text{solute}}

where,


p^o = vapor pressure of solvent (diethyl ether) = 463.57 mmHg


p^s = vapor pressure of the solution = ?

i = Van't Hoff factor = 1 (for non electrolytes)


\chi_{\text{solute}} = mole fraction of solute (testosterone) = 0.0095

Putting values in above equation, we get:


(463.57-p^s)/(463.57)=1* 0.0095\\\\p^s=459.17mmHg

Hence, the vapor pressure of solution is 459.17 mmHg

User Paddu
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