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

Calculate the molality of each of the following solutions: (a) $0.710 \mathrm{kg}$ 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 (d) $0.372 \mathrm{g}$ of tetrahydropyridine, $\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{N},$ in $125 \mathrm{g}$ of chloroform, $\mathrm{CHCl}_{3}$

Calculate the molality of each of the following solutions:
(a) $0.710 \mathrm{kg}$ 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
(d) $0.372 \mathrm{g}$ of tetrahydropyridine, $\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{N},$ in $125 \mathrm{g}$ of chloroform, $\mathrm{CHCl}_{3}$

Key Concepts

Molality

Molality is a measure of concentration defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality does not change with temperature because it is based on mass rather than volume, making it particularly useful in situations involving temperature fluctuations.

Mole

The mole is a fundamental unit in chemistry that quantifies the amount of substance. It represents 6.022 × 10^23 elementary entities (atoms, molecules, ions, etc.) and serves as a bridge between the mass of a substance and the number of particles within it.

Molar Mass

Molar mass is the mass of one mole of a substance, commonly expressed in grams per mole (g/mol). It is essential for converting a given mass of a substance to the number of moles, which is a critical step in concentration calculations such as molality.

Unit Conversion

Unit conversion involves converting measurements from one unit to another. In the context of molality, it is vital to convert the mass of the solvent to kilograms and the mass of the solute to moles using the molar mass, ensuring that the concentration is calculated correctly.

Transcript

00:01 Okay, so we have to calculate molality, which is equal to number of moles of the solute divided by mass of the solvent.

00:16 Okay, so this is going to be the general formula that we'll use for all the cases, and let's call this as equation number one.

00:24 Okay, so for first part, you are given mass of n .e .2, co3.

00:37 As 0 .710 kgs and then mass of water which is equal to 10 kg.

00:49 So first what we'll do is we'll find molecular mass of n .a .2.

01:01 Co3.

01:02 Okay.

01:03 And this is calculated from the number of atoms.

01:09 So you have two sodium so this is 22 .99 mass then you have one carbon and then you have three oxygen so this is equal to 105 .9 grams per mole so according to this formula enumerated it's number of moles of salute which is actually given mass divided by molar mass so given mass is 710 grams and molar mass is 105 .99 grams per mole so this is equal to 6 .69 moles now using equation 1 this will be equal to 6 .69 moles divided by 10 kg's so this is equal to 0 .67 moles per kg okay so this is molality answer moving on to the next part you are given mass of nh4 no 3 which is equal to 125 grams and then mass of water is 275 grams so what you'll do is first we'll find out, sorry, number of moles of nh4n03 is given mass over molecular mass, right? so molecular mass is equal to 14 .01 for nitrogen multiplied by 4 into 1 for hydrogen plus again nitrogen plus 3 into 1 for hydrogen plus 3 into 1.

03:36 16.

03:37 So this is equal to 80 .06 grams per mole...

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