3.E: The First Law of Thermodynamics (Exercises)

Gas Law Practice problems with answers: 

Exercise \(\PageIndex{1}\)

An ideal gas originally at 0.85 atm and 66ºC was allowed to expand until its final volume, pressure, and temperature were 94 mL, 0.60 atm, and 45ºC, respectively. What was its initial volume?

Answer

71 mL

 

Exercise \(\PageIndex{2}\)

When you drink something from a straw, how does the liquid get from the glass up through the straw into your mouth?

Answer

When you close your mouth around the straw, you close off the atmosphere from outside to inside. During suction, you increase the volume inside your mouth, thus lowering the internal pressure and the atmospheric pressure exerted onto the liquid over comes the internal pressure and so the liquid flows into your mouth.

 

First Law of Thermodynamics Practice problems with answers:

Exercise \(\PageIndex{3}\)

A sports bottle containing Gatorade is held in a man's hand while running on a treadmill. Suppose the Gatorade is the system in question. Answer the subsequent questions.

1. Will the temperature rise due to the movement caused by the man's running?
2. Was any heat actually added to the system? If so, what was the source?
3. Was work done onto the system?
4. In what ways has the internal energy of the system been affected, if affected at all?

Answer

1. The man's running motion causes the Gatorade to be shaken. The shaking motion adds energy to the system and increases the random motion of the molecules. Since the motion of the molecules rises, so does the temperature of the system.

2. Yes, heat exchange did occur between the system and its surroundings (the heat given off from the man's hand).

3. Yes, work was done onto the system via the shaking motion.

4. The internal energy has been increased

 

Exercise \(\PageIndex{4}\)

For a constant-pressure process, the heat capacity per mole is given by the expression:

C_p per mole = (16.0 + 4.35 x 10^-3 T + 1.15 T²) J K^-1 mol^-1

Find the molar enthalpy  of oxygen gas from 38°C to 115^oC

Answer

Exercise \(\PageIndex{5}\)

You notice your system changes volume from 10 L to 30 L with a constant pressure at 770 torr. Then, there is a decrease in pressure to 740 torr with the volume staying constant at 30 L. Calculate the total amount of work done.

Answer

We split up the solution into two parts.

Work done during the volume change and the work done during the pressure change.

First part:

Second part:

Convert pressure to atm:

=107.4 J

Then add up the two works

w_tot= -2046.3+107.4=-1938.9 J

 

Exercise \(\PageIndex{6}\)

Determine the  at 343.15 K for . (Note: The heat of vaporization for water is known to be 40.79 kJ mol^-1 at 273.15 K, the  of  was determined to be 85.6 J K^-1 mol^-1 and the  of  was determined to be 54.35 J K^-1 mol^-1). Use the reaction below and give your final answer in kJ mol^-1.

Answer

 

 

 

 

Additional Practice problems

1.  1.00 mol of an ideal gas, initially occupying 12.2 L at 298 K, expands isothermally against a constant external pressure of 1.00 atm until the pressure of the gas is equal to the external pressure. Calculate Δp, q, w, ΔU, and ΔH for the expansion.
2. Some ice cubes are placed inside a sealed plastic bag on a hot day, what is the sign of w, q, ΔH, ΔU? What does this mean about the system?
3. Consider 1.00 mol of an ideal gas expanding isothermally at 298 K from an initial volume of 12.2 L to a final volume of 22.4 L. Calculate Δp, q, w, ΔU, and ΔH for the expansion.
4.  Use the following data [Huff, Squitieri, and Snyder, J. Am. Chem. Soc., 70, 3380 (1948)] to calculate the standard enthalpy of formation of tungsten carbide, WC(s).

   Reaction	ΔH^o (kJ)
   C(gr)+O2(g)→CO2(g)	-393.51
   WC(s)+5/2O^2(g)→WO3(s)+CO2(g)	-1195.79
   W(s)+3/2O2(g)→WO3(s)	-837.42

5. You are given a gas at 750 torr with a volume of 0.62 Liters at 25°C. A while later, you measure the temperature and notice a 5°C temperature increase in the system. Assuming there is no pressure change and that this is an ideal gas, what is the new volume?

6. Consider an ice cube melting.

a. Is the change of enthalpy positive or negative for this process?

b. Is the change of entropy positive or negative for this process?

 

7. 2.5 moles of CO₂ expands against an external pressure of 1.5 atm. It was initially at 9.0 atm and 30^ºC. The final volume is 35.0 L.

1. What is the final temperature?
2. Calculate q, w, and ΔU for the process

 

8. A 10.0 g sheet of gold with a temperature of 18.0°C is laid flat on a sheet of iron that weights 20.0 g and has a temperature of 55.6°C. Given that the specific heats of Au and Fe are 0.129 J g^_-1 °C^-1 and 0.444 J g^_-1 °C^-1, respectively, what is the final temperature of the combined metals? (Hint: The heat gained by the gold must be equal to the heat lost by the iron.)

 

9. What is ΔH if of 3.00 moles of O₂(g) are cooled from 175^ºC to 35.0^ºC and

Cp¯=(7.50×10⁻³T−2.30×10⁻⁶ T²  Jmol⁻¹K⁻¹

 

10.0 1.52 g of toluene (C₇H₈) is combusted in a constant volume bomb calorimeter at 25°C. Calculate the ΔrU¯ and ΔrH¯ for this reaction given that 39.183 kJ of heat was released.

 

 

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