Respuesta :
Answer: The vapor pressure of solution is 23.1 torr
Explanation:
To calculate the mass of water, we use the equation:
[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex]
Density of water = 1 g/mL
Volume of water = 250.0 mL
Putting values in above equation, we get:
[tex]1g/mL=\frac{\text{Mass of water}}{250.0mL}\\\\\text{Mass of water}=(1g/mL\times 250.0mL)=250g[/tex]
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 glucose:
Given mass of glucose = 76.6 g
Molar mass of glucose = 180.2 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of glucose}=\frac{76.6g}{180.2g/mol}=0.425mol[/tex]
- For water:
Given mass of water = 250 g
Molar mass of water = 18 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of water}=\frac{250g}{18g/mol}=13.9mol[/tex]
Mole fraction of a substance is given by:
[tex]\chi_A=\frac{n_A}{n_A+n_B}[/tex]
Mole fraction of glucose, [tex]\chi_{(glucose)}=\frac{0.425}{0.425+13.9}=0.030[/tex]
As, the relative lowering of vapor pressure is directly proportional to the amount of dissolved solute.
The equation used to calculate relative lowering of vapor pressure follows:
[tex]\frac{p^o-p_s}{p^o}=i\times \chi_{solute}[/tex]
where,
[tex]\frac{p^o-p_s}{p^o}[/tex] = relative lowering in vapor pressure
i = Van't Hoff factor = 1 (for non electrolytes)
[tex]\chi_{solute}[/tex] = mole fraction of solute = 0.030
[tex]p^o[/tex] = vapor pressure of pure water = 23.8 torr
[tex]p_s[/tex] = vapor pressure of solution = ?
Putting values in above equation, we get:
[tex]\frac{23.8-p_s}{23.8}=1\times 0.030\\\\p_s=23.1torr[/tex]
Hence, the vapor pressure of solution is 23.1 torr
