Explanation:
1) Mass of carbon dioxide = 100 g
Molar mass of carbon dioxide = 44 g/mol
Moles of carbon dioxide =![\frac{100 g}{44 g/mol}=2.273 moles](https://tex.z-dn.net/?f=%5Cfrac%7B100%20g%7D%7B44%20g%2Fmol%7D%3D2.273%20moles)
1 mol = 0.001 kmol
2.273 moles= 2.273 × 0.001 kmol = ![2.273\times 10^{-3} kmol](https://tex.z-dn.net/?f=%202.273%5Ctimes%2010%5E%7B-3%7D%20kmol)
2) 1 liter of ethyl alcohol of density ![0.789 g/cm^3](https://tex.z-dn.net/?f=0.789%20g%2Fcm%5E3)
Volume of ethyl alcohol ,V= 1 L = 1000 mL
Density of ethyl alcohol =d = ![0.789 g/cm^3](https://tex.z-dn.net/?f=0.789%20g%2Fcm%5E3)
![1 cm^3=1 mL](https://tex.z-dn.net/?f=1%20cm%5E3%3D1%20mL)
Mass of ethyl alcohol = m
![m=d\times V=0.789 g/cm^3\times 1000 mL=789 g](https://tex.z-dn.net/?f=m%3Dd%5Ctimes%20V%3D0.789%20g%2Fcm%5E3%5Ctimes%201000%20mL%3D789%20g)
Molar mass of ethyl alcohol = 46 g/mol
Moles of ethyl alcohol = ![\frac{789 g}{46 g/mol}=17.152 mol](https://tex.z-dn.net/?f=%5Cfrac%7B789%20g%7D%7B46%20g%2Fmol%7D%3D17.152%20mol)
![17.152 mol=17.152\times 0.001 kmol=1.7152\times 10^{-4} kmol](https://tex.z-dn.net/?f=17.152%20mol%3D17.152%5Ctimes%200.001%20kmol%3D1.7152%5Ctimes%2010%5E%7B-4%7D%20kmol)
3) Volume of oxygen gas,V =
![1 m^3= 1000 L](https://tex.z-dn.net/?f=1%20m%5E3%3D%201000%20L)
Temperature of the gas = T= 25°C = 298.15 K
Pressure of the gas ,P= 1 atm
Moles of oxygen gas = n
![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
![n=\frac{RT}{PV}=\frac{0.0821 atm L/mol K\times 298.15 K}{1 atm\times 1500 L}=0.01632 mol](https://tex.z-dn.net/?f=n%3D%5Cfrac%7BRT%7D%7BPV%7D%3D%5Cfrac%7B0.0821%20atm%20L%2Fmol%20K%5Ctimes%20298.15%20K%7D%7B1%20atm%5Ctimes%201500%20L%7D%3D0.01632%20mol)
0.01632 mol = 0.01632 × 0.001 kmol=![1.632\times 10^{-5} kmol](https://tex.z-dn.net/?f=1.632%5Ctimes%2010%5E%7B-5%7D%20kmol)
4) Volume water in mixture = 1 L
Density of water = ![1000 kg/m^3=\frac{1,000,000 g}{1000 L}=1000 g/L](https://tex.z-dn.net/?f=1000%20kg%2Fm%5E3%3D%5Cfrac%7B1%2C000%2C000%20g%7D%7B1000%20L%7D%3D1000%20g%2FL)
Mass of water = ![1000 g/L\times 1 L = 1000 g](https://tex.z-dn.net/?f=1000%20g%2FL%5Ctimes%201%20L%20%3D%201000%20g)
Volume of alcohol = 2.5 L
Density of alcohol = ![789 kg/m^3=\frac{789000 g}{1000 L}=789 g/L](https://tex.z-dn.net/?f=789%20kg%2Fm%5E3%3D%5Cfrac%7B789000%20g%7D%7B1000%20L%7D%3D789%20g%2FL)
Mass of alcohol = ![789 g/L\times 2.5 L = 1972.5 g](https://tex.z-dn.net/?f=789%20g%2FL%5Ctimes%202.5%20L%20%3D%201972.5%20g)
Mass of mixture = 1000 g + 1972.5 g = 2972.5 g
Mass percentage of water :
![\frac{1000 g}{2972.5 g}\times 100=33.64\%](https://tex.z-dn.net/?f=%5Cfrac%7B1000%20g%7D%7B2972.5%20g%7D%5Ctimes%20100%3D33.64%5C%25)
Mass percentage of alcohol :
![\frac{1972.5 g}{2972.5 g}\times 100=66.36\%](https://tex.z-dn.net/?f=%5Cfrac%7B1972.5%20g%7D%7B2972.5%20g%7D%5Ctimes%20100%3D66.36%5C%25)
Moles of water :
![n_1=\frac{1000 g}{18 g/mol}=55.55 mol](https://tex.z-dn.net/?f=n_1%3D%5Cfrac%7B1000%20g%7D%7B18%20g%2Fmol%7D%3D55.55%20mol)
Moles of alcohol =
![n_2=\frac{1972.5 g}{46 g/mol}=42.88 mol](https://tex.z-dn.net/?f=n_2%3D%5Cfrac%7B1972.5%20g%7D%7B46%20g%2Fmol%7D%3D42.88%20mol)
Mole fraction of water :
![\chi_1=\frac{n_1}{n_1+n_2}=\frac{55.55 mol}{55.55 mol+42.88 mol}=0.5644](https://tex.z-dn.net/?f=%5Cchi_1%3D%5Cfrac%7Bn_1%7D%7Bn_1%2Bn_2%7D%3D%5Cfrac%7B55.55%20mol%7D%7B55.55%20mol%2B42.88%20mol%7D%3D0.5644)
Mole fraction of alcohol :
![\chi_2=\frac{n_2}{n_1+n_2}=\frac{42.88 mol}{55.55 mol+42.88 mol}=0.4356](https://tex.z-dn.net/?f=%5Cchi_2%3D%5Cfrac%7Bn_2%7D%7Bn_1%2Bn_2%7D%3D%5Cfrac%7B42.88%20mol%7D%7B55.55%20mol%2B42.88%20mol%7D%3D0.4356)