When 4.56 g of a solid mixture composed of NH4 Cl and CaCl2 was dissolved in 100.0 mL water, t

step 1 So let's say we have 100 milliliters of water. And to that, we add 4 .56 grams of a mixture of a

When 4.56 g of a solid mixture composed of NH4 Cl and CaCl2...

Key Concepts

Mixture Composition Analysis

Mixture composition analysis involves determining the relative amounts of components in a mixture through measurable physical quantities such as heat exchange. By linking the known heats of dissolution or reaction for each component with the overall observed energy change, one can deduce the composition of the mixture.

Enthalpy of Dissolution

The enthalpy of dissolution refers to the heat change when a substance dissolves in a solvent. It can be exothermic or endothermic; some salts release heat upon dissolving, while others absorb heat. This concept is used to understand and quantify the contribution of each component in a mixture to the overall heat energy change.

Systems of Linear Equations

Systems of linear equations are mathematical tools used to solve for multiple unknown variables simultaneously. In the context of mixture analysis, they are employed by setting up equations based on mass conservation and energy balance to determine the individual amounts of components in a mixture.

Calorimetry

Calorimetry is the measurement of heat exchanged in chemical reactions or physical changes. By monitoring temperature changes in a known mass of water or other medium, one can determine the energy released or absorbed during a process, applying the principle of conservation of energy.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. This property is essential in calorimetry since it allows the calculation of the energy change from the measured temperature change in the medium.

Transcript

00:01 So let's say we have 100 milliliters of water.

00:05 And to that, we add 4 .56 grams of a mixture of ammonium chloride and calcium chloride solids.

00:16 When that happens, the temperature of the water goes up by 5 .33 degrees celsius.

00:23 Let's figure out how many grams of each of our two substances we actually had in our 4 .56 grams.

00:31 That we poured in.

00:34 So to start, let's figure out the amount of heat that was actually absorbed by the water.

00:42 So the heat absorbed by the water, we know we can solve with ms -delta -t.

00:51 Now the water here, let's assume the density of the water is one, which means 100 milliliters is also equal to 100 grams and since we're doing we'll assume here like this is liquid water so the specific heat is going to be 4 .184 and we're told for the water that the change in temperature was 5 .33 degrees c so when we do the math on this we can find out that 2 ,230 joules of energy was absorbed by the water.

01:36 Now, law conservation of energy says, well, that heat had to have come from somewhere.

01:41 And so where to come from? well, it came from dissolving these two solids.

01:49 So the dissolution created, released the heat and the water absorbed it.

02:05 So that must mean that the dissolution itself released 2 ,230 joules.

02:21 Okay.

02:21 So now the issue becomes this amount of heat that was released was released by two different substances, and we don't know how much of each we have.

02:33 So what we can do to take a look at that is calculate the delta h required to dismal.

02:42 Each of these substances and then we can use in some sense almost like a ratio of those to figure out what the mass was for each of them.

02:51 So let's take a look at what happens in each of these reactions.

02:56 When we take solid ammonium chloride and dissolve it, all ammoniums are soluble.

03:05 So we're going to create the ammonium ion and the chloride ion, both aqueous, because we've dissolved them in the water.

03:19 And so we can do a delta h of reaction on this.

03:25 This is really more of dissolving, okay, but it's the same concept here.

03:31 We're gonna do some of the products minus the sum of the reactants.

03:36 And so we have one mole of nh4 plus, and the delta h of that is negative one 303.

03:52 We'll do the same thing with the chloride, 1 mole, negative 167 .2 kilojoules per mole.

04:08 That's the sum of our products.

04:10 Now we'll subtract our reactants.

04:13 One mole of nh4, cl, and its delta h is negative 315.

04:22 Kilojoules per mole.

04:28 So the delta h here is 15 .7 kilojoules per mole.

04:41 Now for reasons that you'll see in a couple minutes, what we're going to do right now is we're going to convert this into kilojoules per gram.

04:51 Mainly we want to know how many grams of each we're going to have, so we're going to need the unit of grams later.

04:55 So we'll go ahead and multiply or do dimensional analysis to find its molar mass.

05:04 Each mole of ammonium chloride is 53 .49 grams.

05:11 So the delta h of reaction here in kilojoules per gram is 0 .294 kilojoules per gram.

05:21 Now we'll do that same thing.

05:23 We did this process with the nh4 cl.

05:25 We'll do the same process with the calcium chloride.

05:30 Now for calcium chloride, just be careful in terms of how you break calcium chloride up.

05:39 We're going to have the calcium ion that's aqueous.

05:43 And remember, for ions, chloride is found as cl minus, not as cl2.

05:52 All right, so we have our reaction.

05:55 We'll find the delta h...

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