Calculate the mole fraction of each solute and solvent: (a)...

Calculate the mole fraction of each solute and solvent: (a) 0.710 kg of sodium carbonate (washing soda), $\mathrm{Na}_{2} \mathrm{CO}_{3},$ in 10.0 $\mathrm{kg}$ of water - a saturated solution at $0^{\circ} \mathrm{C}$ (b) 125 $\mathrm{g}$ of $\mathrm{NH}_{4} \mathrm{NO}_{3}$ in 275 $\mathrm{g}$ of water - a mixture used to make an instant ice pack (c) 25 $\mathrm{g}$ of $\mathrm{Cl}_{2}$ in 125 $\mathrm{g}$ of dichloromethane, $\mathrm{CH}_{2} \mathrm{Cl}_{2}$ (d) 0.372 g of tetrahydropyridine, $\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{N},$ in 125 $\mathrm{g}$ of chloroform, $\mathrm{CHCl}_{3}$

Calculate the mole fraction of each solute and solvent:
(a) 0.710 kg of sodium carbonate (washing soda), $\mathrm{Na}_{2} \mathrm{CO}_{3},$ in 10.0 $\mathrm{kg}$ of water - a saturated solution at $0^{\circ} \mathrm{C}$
(b) 125 $\mathrm{g}$ of $\mathrm{NH}_{4} \mathrm{NO}_{3}$ in 275 $\mathrm{g}$ of water - a mixture used to make an instant ice pack
(c) 25 $\mathrm{g}$ of $\mathrm{Cl}_{2}$ in 125 $\mathrm{g}$ of dichloromethane, $\mathrm{CH}_{2} \mathrm{Cl}_{2}$
(d) 0.372 g of tetrahydropyridine, $\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{N},$ in 125 $\mathrm{g}$ of chloroform, $\mathrm{CHCl}_{3}$

Key Concepts

Solution Composition

Solution composition refers to the makeup of a solution, which includes both the solute(s) and the solvent. Understanding the individual contributions of each component—in terms of moles—is key for calculating properties like mole fraction. This concept is foundational in solution chemistry, where the interactions and proportions of different substances affect the overall behavior and properties of the solution.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It serves as a conversion factor between the mass of a substance and the number of moles, enabling calculations that relate the mass of a chemical to the number of its constituent particles. Accurate molar mass values are essential for computations involving mole fractions, stoichiometry, and reaction yields.

Mole Fraction

Mole fraction is a way to express the concentration of a component in a mixture. It is defined as the ratio of the number of moles of the component to the total number of moles of all components present in the mixture. This dimensionless quantity is particularly useful in thermodynamic calculations and provides a way to compare the relative amounts of substances regardless of their molar masses.

Mass-to-Mole Conversion

Mass-to-mole conversion is the process of converting a given mass of a substance to the number of moles using its molar mass. This conversion is crucial in chemical calculations because reactions occur based on mole ratios rather than mass ratios. The conversion is performed by dividing the mass of the substance by its molar mass.

Transcript

00:01 To calculate the mole fraction of the salyut and the solvent in each of these solutions.

00:07 We first must calculate the moles of solute and solvent that are present.

00:13 We can do this by converting their masses into moles using their molar masses for part a we have .710 kg of sodium carbonate.

00:32 We can convert the kg sodium carbonate into g sodium carbonate by multiplying by 1000.

00:40 Then we will convert the grams sodium carbonate into molds sodium carbonate by dividing by the molar mass of sodium carbonate, 106.0 and we get 6.698 moles sodium carbonate.

00:59 Now we need to take the mass of the water, the solvent 10 kg and convert it into mel's.

01:08 We can convert the kg into g by multiplying by 1000.

01:12 We can then convert the grams into moles by divided by the molar mass of water and we get 555 2 moles of water.

01:25 Now to solve for the more fraction mole fraction of sodium carbonate will be the moles of sodium carbonate divided by the total moles which will be the some of the moles sodium carbonate and water.

01:38 And we get a mole fraction of .012 mole fraction, water will be the moles of water divided by the total moles, and we get .988 as the mole fraction for part b.

01:54 We have 100 and 25 g of ammonium nitrate will convert the grams of ammonium nitrate into moles ammonium nitrate by divided by the molar mass of ammonium nitrate.

02:05 And we get 1.562.

02:09 Next we'll take the mass of the solvent in this case water, 275g and converted into moles of water by dividing by the molar mass of water, and we'll get 15.27 moles of water.

02:31 To solve for the mole fraction of ammonium nitrate will take the moles ammonium nitrate divided by the total moles, the moles of ammonia nitrate plus those of water.

02:43 And we get .093...

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