what mass of ammonium chloride is dissolved in 100 grams water in each of the following solutions in 1.10 molal NH4Cl solution, in a solution which is 75% water by mass in solution with a mole fraction of 0.15 NH4Cl?

please help me solve this problem. thank you!

To solve this problem, we need to know the definition of molality and mole fraction.

1. Molality (m) is defined as the number of moles of solute per kilogram of solvent. It is calculated using the formula:

Molality (m) = Moles of solute / Mass of solvent (in kg)

2. Mole fraction (X) is the ratio of the number of moles of a component to the total number of moles in the mixture. It is calculated using the formula:

Mole fraction (X) = Moles of component / Total moles in mixture

Now, let's solve each part of the problem:

1. In a 1.10 molal NH4Cl solution:
We are given that the solution is 1.10 molal, which means it contains 1.10 moles of NH4Cl per kilogram of water.
To find the mass of ammonium chloride, we need to convert the mass of water to kilograms and then use the molality equation.

Mass of NH4Cl = Molality x Mass of water (in kg)
Mass of water = 100 grams = 0.1 kg

Mass of NH4Cl = 1.10 molal x 0.1 kg = 0.11 kg

Therefore, there are 0.11 kilograms (or 110 grams) of ammonium chloride dissolved in 100 grams of water in a 1.10 molal NH4Cl solution.

2. In a solution which is 75% water by mass with a mole fraction of 0.15 NH4Cl:
We are given that the solution is 75% water by mass, which means it contains 75 grams of water and 25 grams of NH4Cl.
We are also given the mole fraction of NH4Cl, which is 0.15.

To find the mass of ammonium chloride, we can use the mole fraction equation to calculate the moles of NH4Cl, and then convert it to mass.

Moles of NH4Cl = Mole fraction x Total moles in mixture
Moles of water = 1 - Mole fraction

Mass of NH4Cl = Moles of NH4Cl x Molar mass of NH4Cl
Mass of water = Mass of mixture - Mass of NH4Cl

Mass of mixture = Mass of water + Mass of NH4Cl = 75 grams + 25 grams = 100 grams

Moles of NH4Cl = 0.15 x (25 grams / Molar mass of NH4Cl)
Moles of water = 1 - 0.15 = 0.85

Mass of NH4Cl = Moles of NH4Cl x Molar mass of NH4Cl
Mass of water = Moles of water x Molar mass of water = 0.85 x 18 g/mol = 15.3 grams

Mass of NH4Cl = 0.15 x (25 grams / Molar mass of NH4Cl) x Molar mass of NH4Cl
= 0.15 x 25 grams
= 3.75 grams

Therefore, there are 3.75 grams of ammonium chloride dissolved in 75 grams of water in a solution which is 75% water by mass with a mole fraction of 0.15 NH4Cl.

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