Suppose that 0.95 gof water condenses on a 75.0 g block of iron that is initially at 22^∘ C . If

Suppose that 0.95 gof water condenses on a 75.0 g block of...

Key Concepts

Latent Heat

Latent heat refers to the energy absorbed or released during a phase change of a substance, without a change in temperature. In processes like condensation or vaporization, the substance transitions between phases (liquid to gas or vice versa) by releasing or absorbing energy characterized by the latent heat value.

Specific Heat Capacity

Specific heat capacity is the property of a substance that indicates how much energy is needed to raise a unit mass of that substance by one degree in temperature. It plays a crucial role in calculating temperature changes in materials when heat is added or removed.

Conservation of Energy

The principle of conservation of energy in thermal processes states that energy cannot be created or destroyed; it can only be transferred. In heat transfer problems, the energy lost by one part of the system (e.g., released during condensation) must equal the energy gained by another part (e.g., absorbed by a block of metal).

Phase Change

Phase change is the transformation of a substance from one state of matter to another, such as from vapor to liquid. This process involves latent heat, where energy is exchanged without a change in temperature until the phase transition is complete.

Transcript

00:01 To answer this question to find the final temperature of the iron block after the condensation of water, we'll need to utilize the heat equation.

00:09 Here, as shown, the heat equation is written as the heat transferred in the process, is equal to the mass of the iron block times the heat capacity of the iron block, times the change in temperature.

00:23 Now, we're interested in finding what the final temperature is, so we're going to expand out this equation to show that the heat is, equal to the mass of the iron block times the heat capacity times the final temperature minus the initial temperature.

00:39 Now we want to solve for the final temperature.

00:42 So we're going to divide by the mass of the iron block times the heat capacity on both sides of our equation.

00:51 And this will leave us with the heat divided by the mass times the heat capacity of the iron block is equal to the change in temperature.

01:00 Now, since we're just looking for the final temperature, we're going to add the initial temperature to both sides of this equation.

01:08 That will cancel out this subtraction on the right -hand side, and we will be left with the heat transferred in this physical process divided by the mass of the iron block times the heat capacity of the iron block plus the initial temperature will be equal to the final temperature, which we're interested in finding.

01:30 Now, we know the mass of the iron block.

01:35 The heat capacity of the iron block is 0 .45 joules per gram celsius.

01:46 And our initial temperature is 22 degrees celsius.

01:53 And also the mass of the iron block is 75 grams.

01:58 Now, the only thing we don't have in this equation is the heat that's transferred.

02:03 But because this is the heat that's transferred is just from the condensation of water, we can utilize the enthalpy of vaporization to solve for this heat.

02:12 Now, we're told that the enthalpy of vaporization is equal to 44 .0 kilojoules per mole.

02:23 But we're having a condensation reaction here, but the condensation is just the reverse of vaporization.

02:31 So the amount of heat required to vaporize something, is the amount of heat that is removed during condensation just by getting the negative of this number.

02:44 So that would be minus 44 .0 kilojoules per mole for the enthalpy of condensation.

02:53 But we don't want the enthalpy of condensation.

02:55 We want the heat.

02:56 So to get the heat from the enthalpy, we just need to multiply the enthalpy of condensation by the amount of moles of water that are being condensed.

03:04 Now, we're only told the mass of h2o, which is given as 0 .95 grams.

03:13 But we can always find the moles of some mass of a molecule given its molar mass.

03:21 And here we have the molar mass of h2o.

03:25 And looking at the periodic table, you have about one dalton for hydrogen, each hydrogen, and then 16 dalton's for oxygen.

03:36 So we have two hydrogen, so 1 plus 1 plus 16 is 18.

03:40 Although if we use the periodic table, we find that the exact molar mass is a little different.

03:45 It's 18 .01528 grams per mole.

03:52 Now to get the moles, all we do, so the moles of h2o, all we do is we get the mass of h2o, and we divide by the molar mass of h2o.

04:06 So substituting our values, we have 0 .95 grams for the mass of water.

04:13 And we have 18 .1528 grams per mole.

04:21 Now, looking at our units, we see we have grams in the numerator, and then denominator we have grams per mole.

04:27 So the grams are going to cancel, and the moles are going to move to the numerator...

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