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ICE Princess25 [194]
3 years ago
14

Answer the following using the following information: ∆Hfus=6.02 kJ/mol; ∆Hvap= 40.7 kJ/mol; specific heat of water is 4.184 J/g

∙˚C; specific heat of ice is 2.06 J/g∙˚C; specific heat of water vapor is 2.03 J/g∙˚C.
A. How much heat is required to vaporize 25 g of water at 100˚C?

B. How much heat is required to convert 25 g of ice at -4.0 ˚C to water vapor at 105 ˚C (report your answer to three significant figures)?

C. An ice cube at 0.00 ˚C with a mass of 8.32 g is placed into 55 g of water, initially at 25 ˚C. If no heat is lost to the surroundings, what is the final temperature of the entire water sample after all the ice is melted (report your answer to three significant figures)?
Chemistry
1 answer:
OLga [1]3 years ago
8 0

Answer:

A. 56 kJ

B. 75.8 kJ

C. 11 ˚C

Explanation:

A. The heat of vaporization, ∆Hvap = 40.7 kJ/mol, gives the amount of energy per mole of water required to vaporize water to steam. The molar mass of water is 18.02 g/mol.

Q = M·∆Hvap = (25 g)(mol/18.02g)(40.7 kJ/mol) = 56 kJ

B. Five steps are necessary in this process. First, the ice will be warmed to 0 °C, then melted to water. The water will be heated to 100 °C, then vaporized. Finally, the vapor will be heated from 100 °C to 105 °C.

We calculate the heat required to warm the ice from -4.0 °C to 0 °C:

Q₁ = mcΔt = (25 g)(2.06 J∙g⁻¹˚C⁻¹)(0 °C - (-4.0 °C)) = 206 J

Then we calculate the heat required to melt the ice to water:

Q₂ = M∙∆Hfus = (25 g)(mol/18.02 g)(6.02 kJ/mol) = 8.35 kJ

Then, we calculate the heat required to warm the water from 0 °C to 100 °C.

Q₃ = mcΔt = (25 g)(4.184 J∙g⁻¹˚C⁻)(100 °C - 0 °C) = 10460 J

Then we calculate the heat required to vaporize the water:

Q₄ = M∙∆Hvap = (25 g)(mol/18.02 g)(40.7 kJ/mol)  = 56.5 kJ

Finally, the vapor is heated from 100 °C to 105 °C.

Q₅ = mcΔt = (25 g)(2.03 J∙g⁻¹˚C⁻)(105 °C - 100 °C) = 254 J

The total heat required is the sum of Q₁ through Q₅

Qtotal = Q₁ + Q₂ + Q₃ + Q₄ + Q₅

Qtotal = (206 J)(1 kJ/1000J) + 8.35 kJ + (10460 J)(1 kJ/1000J) + 56.5 kJ + (254 J)(1 kJ/1000J)

Qtotal = 75.8 kJ

C. The heat required to melt the ice is provided by the water as it decreases in temperature.  

First, we calculate the energy required to melt ice to water

Q = M∙∆Hfus = (8.32 g)(mol/18.02 g)(6.02 kJ/mol) = 2.779 kJ

There are at least two ways to solve this problem. Here, we will calculate the heat lost when all the water is brought to a temperature of 0 °C:

Q = mc∆t = (55 g)(4.184 J∙g⁻¹˚C⁻¹)(25 °C - 0°C) = 5753 J

We see that the water has enough energy to melt all of the ice. The residual heat energy of the water after melting all the ice is:

5753 J - (2.779 kJ)(1000J/kJ) = 2974 J

Now the problem becomes that we have (8.32 g + 55 g) = 63.32 g of water at 0 °C that will be raised to some final temperature by the residual heat of 2974 J:

Q = mcΔt ⇒ Δt = Q/(mc)

Δt = (2974 J) / (63.32 g)(4.184 J∙g⁻¹˚C⁻¹) = 11 ˚C

T(final) - T(inital) = 11 ˚C

T(final) = 11 ˚C + T(inital) = 11 ˚C + 0 ˚C  = 11 ˚C

Thus, the final temperature will be 11 ˚C.

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The Bible provides an answer. A great amount of energy had to be expended to produce such great organization. As one scientist states the problem, energy was not enough. If you are asked to "reduce the entropy" of your room (put it in order), you certainly need to put in some effort (energy). But just adding energy is not enough. You could let loose a bull in your room, and it would expend a great deal of energy; however, that energy would not decrease but would increase the disorder of the room. Therefore, scientists know that to produce order, energy must be intelligently directed. Evolution requires that atoms and molecules assemble themselves into increasing order, but the science of thermodynamics assures us that the entire universe, when left to itself, is converting to disorder. The Apostle Paul referred to this concept when he said through inspiration that the entire earth is "subject to the bondage of decay." The original state required an intelligence to organize the complexities of the universe.

Christians, of course, have an answer to these perplexing questions: God. God is the Creator of the universe, the ultimate source of its energy and order. He created it with no entropy (no disorder). When man sinned, the universe began to increase in entropy (become more and more disordered). For Christians a discussion of energy, thermodynamics, and entropy is inspiring. These subjects invariably point us to the One who created the universe and sustains it by His power. Christians also know that His power will one day totally renew the universe and entropy will have no part in it.

Christians need never be afraid of science. God is in control of the universe and all the laws of the universe operate according to His will and design. Christians should be confident that they have the answers to the perplexing questions of nature.

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The above attitude allows christians to ignore questions that are difficult and this leads to mental complacency.

"This is gods work. I must not question or touch this". Is their motto.

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Science in general, tries to explain and understand and make further progress and additions to human knowledge. Christians will only try to understand what they have been taught and integrate any new knowledge when the older beliefs become untenable.
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Explanation:

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