Calculate the osmotic pressure of each of the following aqueous solutions at 27^∘ C a. 10.0 g of

Calculate the osmotic pressure of each of the following...

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend only on the number of solute particles relative to solvent particles and not on the type of chemical species present. Osmotic pressure is one such property, and understanding it involves recognizing that the effects on the physical properties of the solution, such as boiling point elevation, freezing point depression, and vapor pressure lowering, are determined by solute concentration and dissociation.

Molarity and Concentration

Molarity is defined as the number of moles of solute per liter of solution. It is a crucial concept in solution chemistry because it provides a way to quantify how concentrated a solution is, which directly impacts properties such as osmotic pressure. Correct calculation of molarity is essential for accurately applying formulas in colligative property problems.

Temperature Conversion

Temperature plays an important role in calculating osmotic pressure since the temperature in the equation must be expressed in Kelvin. Converting temperature from degrees Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. This conversion is necessary for ensuring the use of absolute temperature in thermodynamic formulas.

Osmotic Pressure

Osmotic pressure is the pressure required to stop the flow of solvent across a semipermeable membrane that separates two solutions with different solute concentrations. It is a colligative property, meaning it depends on the number of solute particles in the solution rather than their identity. The osmotic pressure (?) is typically calculated using the formula ? = M R T, where M is the molarity of the solution, R is the universal gas constant, and T is the temperature in Kelvin.

van't Hoff Factor

The van't Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For electrolytes that dissociate into ions, this factor adjusts the concentration used in calculations of colligative properties like osmotic pressure. For non-electrolytes that do not dissociate, the van't Hoff factor is 1, whereas for strong electrolytes it generally equals the total number of ions produced per formula unit in solution.

Transcript

00:01 Okay, so this is problem 84 in chapter 11 of chemistry, the science, and context.

00:08 Okay.

00:09 And so it wants us to calculate our osmotic pressure, okay, at 27 degrees celsius for all of these solutions.

00:15 Okay.

00:16 And so remember the equation for osmotic pressure is that the osmotic pressure equals i times the molarity, times our our constant, times the temperature.

00:27 Okay.

00:27 And so the temperature, because of our constant, this is the gas constant, and its unit has kelvin in it.

00:36 So we have to convert this to kelvin first.

00:38 To convert to kelvin, you have to add 273.

00:42 And so we get 300 kelvin.

00:49 So we're going to use 300 kelvin for all of our calculations.

00:52 All right.

00:54 And so first we need to find our i and our molarity.

01:02 Nacli equals 2, because i know that this is an electrolyte.

01:05 It's going to dissociate into n -a ions, sodium ions, and chloride ions.

01:11 Okay? so we already know that i is equal to 2.

01:13 We now just need to find molarity.

01:15 And we have grams and liters.

01:18 So we just have to determine the number of moles and then divide that by liter.

01:25 And so first, we need to find the molecular weight.

01:28 So molecular weight of nacl is 22 .99.

01:33 That's from the periodic table plus 35 .45.

01:37 And this is all in grams per mole.

01:39 Okay.

01:39 And so this ends up being 58 .44 grams per mole.

01:45 Okay? so that is the molecular weight, and we can use that to find out the number of moles.

01:50 We just do 10 grams times.

01:54 I'm just omitting the 0.

01:57 So it's just 10 grams times 58 .44 grams over, under mole.

02:03 And that cancels out the grams, so we're left with moles.

02:08 And this calculates out to be 0 .17111 moles.

02:16 Okay? and the molarity is going to be moles over liter.

02:19 So if we can just divide this by 1 .5 liters to find our molarity.

02:27 And so this ends up being 0 .1141, okay, as the molarity, moles over a liter.

02:35 Okay.

02:36 And so now we can plug that into our equation for osmotic pressure.

02:42 So osmotic pressure will be, and our i is two, so that's where we get the two from.

02:48 Our molarity, we just got 0 .1141.

02:54 Our r constant, we're going to be using the 0 .0 821, 821, and that's liters per 8tm per mole kelvin, okay? and the temperature, again, is 300 kelvin, okay? and so to double check, the calvins cancel out.

03:18 Moles under liters is the inverse of molarity, so these can't.

03:22 And sold those out, and we're left with atm, which is perfect because it's supposed to be osmotic pressure.

03:27 And so all of this, if i were to multiply this out, this multiplied out to be 5 .621 atm.

03:37 Okay, so that is the osmotic pressure for our nacl, our sodium chloride solution.

03:45 Okay? let's do the same thing for b.

03:47 So for b, i first found the molecular weight...

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