Calculate the molality of each of the following solutions:...

Calculate the molality of each of the following solutions: (a) 0.710 kg of sodium carbonate (washing soda), Na_ $\mathrm{CO}_{3},$ in 10.0 $\mathrm{kg}$ of waturated 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, $C_{5} \mathrm{H}_{9} \mathrm{N},$ in 125 $\mathrm{g}$ of chloroform, CHCl_{3}

Calculate the molality of each of the following solutions:
(a) 0.710 kg of sodium carbonate (washing soda), Na_ $\mathrm{CO}_{3},$ in 10.0 $\mathrm{kg}$ of waturated 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, $C_{5} \mathrm{H}_{9} \mathrm{N},$ in 125 $\mathrm{g}$ of chloroform, CHCl_{3}

Key Concepts

Molality

Molality is a concentration unit defined as the number of moles of a solute per kilogram of solvent. It is particularly useful in scenarios where temperature changes may affect volume, as it is based solely on mass, making it ideal for analyzing colligative properties.

Conversion of Mass to Moles

To determine the number of moles present in a given mass of a substance, the mass is divided by the molar mass of that substance. This conversion is essential for concentration calculations, including those involving molality.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole. It is a key factor in converting a substance’s mass to its mole equivalent, thereby linking the measurable mass to the number of particles involved in a chemical process.

Mass of Solvent

In molality calculations, only the mass of the solvent is used, typically expressed in kilograms. Determining the accurate mass of the solvent is crucial since molality reflects the number of moles of solute per kilogram of solvent, not the total solution mass.

Transcript

00:01 To calculate molality, we simply need to know the moles of the solute, and we need to know the kilograms of the solvent.

00:10 So for the following solutions, we need to convert the mass of the solute into moles solute, and then we need to convert the mass, if not in kilograms, of the solvent, into kilograms of solvent.

00:24 The first solution is a .710 kilogram sodium carbonate solution in 10 .0 kilograms of water.

00:35 So we'll convert the 0 .710 kilograms of the solute sodium carbonate into gram's sodium carbonate by multiplying by 1 ,000.

00:49 We'll then convert the grams sodium carbonate into moles sodium carbonate by dividing by its molar mass, 106 grams.

00:57 Per mole and we'll get point six, i'm sorry, 6 .698 moles of sodium carbonate.

01:06 To calculate molality, we'll take the moles of sodium carbonate, 6 .698, then divide by the kilograms of the solvent water, which was provided at 12 kilograms.

01:20 This gives us a molality of 0 .6698.

01:24 Or to just three significant figures, 0 .670.

01:33 Part b, we have 125 grams of ammonium nitrate.

01:39 We'll convert the moles of ammonium nitrate.

01:41 I'm sorry, we'll convert the grams ammonium nitrate, this being the solute into moles of ammonium nitrate.

01:50 To do that, we simply divide by the molar mass of ammonium nitrate.

01:55 82 .04 grams per mole.

02:01 I'm sorry, just 80 .04 grams per mole.

02:04 This gives us 1 .5662 .2.

02:07 This gives us 1 .562.

02:07 Moles of ammonium nitrate...