Final answer:
To calculate the mole ratio of C₂H₅OH and CH₃OH in aqueous solution, find the number of moles of each substance in the solution and divide the number of moles of C₂H₅OH by the number of moles of CH₃OH. Given the molality of C₂H₅OH and the mole fraction of CH₃OH, use the formulas to compute the moles of each substance and then calculate the mole ratio.
Step-by-step explanation:
To calculate the mole ratio of C₂H₅OH and CH₃OH in aqueous solution, we need to determine the number of moles of each substance in the solution. The mole ratio is then calculated by dividing the number of moles of C₂H₅OH by the number of moles of CH₃OH.
Given that the molality of C₂H₅OH is 40/9 (which is approximately 4.44) and the mole fraction of CH₃OH is 0.1, we can use these values to find the number of moles. The molality of C₂H₅OH tells us that there are 4.44 moles of C₂H₅OH per kilogram of water. The mole fraction of CH₃OH tells us that the proportion of CH₃OH in the solution is 0.1.
To find the number of moles of C₂H₅OH, we can use the formula:
moles of C₂H₅OH = (molality of C₂H₅OH) x (mass of water in kg).
To find the number of moles of CH₃OH, we can use the formula:
moles of CH₃OH = (mole fraction of CH₃OH) x (total moles of substances in solution).
Dividing the two values, we get the mole ratio of C₂H₅OH to CH₃OH.