<u>Answer:</u> The total pressure above the solution at 30°C is 45.29 mmHg
<u>Explanation:</u>
We are given:
Molality of methanol = 6.0 m
This means that 6.0 moles of methanol present in 1 kg or 1000 g of pure water
To calculate the number of moles, we use the equation:
![\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20moles%7D%3D%5Cfrac%7B%5Ctext%7BGiven%20mass%7D%7D%7B%5Ctext%7BMolar%20mass%7D%7D)
Given mass of water = 1000 g
Molar mass of water = 18 g/mol
Putting values in above equation, we get:
![\text{Moles of water}=\frac{1000g}{18g/mol}=55.56mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20water%7D%3D%5Cfrac%7B1000g%7D%7B18g%2Fmol%7D%3D55.56mol)
Mole fraction of a substance is given by:
![\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_{CH_3OH}=\frac{n_{CH_3OH}}{n_{CH_3OH}+n_{water}}\\\\\chi_{CH_3OH}=\frac{6}{6+55.56}=0.0975](https://tex.z-dn.net/?f=%5Cchi_%7BCH_3OH%7D%3D%5Cfrac%7Bn_%7BCH_3OH%7D%7D%7Bn_%7BCH_3OH%7D%2Bn_%7Bwater%7D%7D%5C%5C%5C%5C%5Cchi_%7BCH_3OH%7D%3D%5Cfrac%7B6%7D%7B6%2B55.56%7D%3D0.0975)
![\chi_{water}=\frac{n_{water}}{n_{CH_3OH}+n_{water}}\\\\\chi_{water}=\frac{55.56}{6+55.56}=0.9025](https://tex.z-dn.net/?f=%5Cchi_%7Bwater%7D%3D%5Cfrac%7Bn_%7Bwater%7D%7D%7Bn_%7BCH_3OH%7D%2Bn_%7Bwater%7D%7D%5C%5C%5C%5C%5Cchi_%7Bwater%7D%3D%5Cfrac%7B55.56%7D%7B6%2B55.56%7D%3D0.9025)
To calculate the total pressure, we use the equation given by Dalton and Raoults, which is:
![p_T=(p_A\times \chi_A)+(p_B\times \chi_B)](https://tex.z-dn.net/?f=p_T%3D%28p_A%5Ctimes%20%5Cchi_A%29%2B%28p_B%5Ctimes%20%5Cchi_B%29)
where,
= total vapor pressure = ?
We are given:
Mole fraction of methanol = 0.0975
Mole fraction of water = 0.9025
Vapor pressure of methanol = 170.0 mmHg
Vapor pressure of water = 31.82 mmHg
Putting values in above equation, we get:
![p_T=(170\times 0.0975)+(31.82\times 0.9025)\\\\p_T=45.29mmHg](https://tex.z-dn.net/?f=p_T%3D%28170%5Ctimes%200.0975%29%2B%2831.82%5Ctimes%200.9025%29%5C%5C%5C%5Cp_T%3D45.29mmHg)
Hence, the total pressure above the solution at 30°C is 45.29 mmHg