Chapter 5 Key

5.1.  The temperature of 1 gram of burning wood is approximately the same for both a match and a bonfire. This is an intensive property and depends on the material (wood). However, the overall amount of produced heat depends on the amount of material; this is an extensive property. The amount of wood in a bonfire is much greater than that in a match; the total amount of produced heat is also much greater, which is why we can sit around a bonfire to stay warm, but a match would not provide enough heat to keep us from getting cold.

 

5.3.  Heat capacity refers to the heat required to raise the temperature of the mass of the substance 1 degree; specific heat refers to the heat required to raise the temperature of 1 gram of the substance 1 degree. Thus, heat capacity is an extensive property, and specific heat is an intensive one.

 

5.5.  (a)  47.6 J/°C;  11.38 cal/°C (b)  407 J/°C;  97.3 cal/°C

 

5.7.  1310 J;  313 cal

 

5.9.  7.15°C

 

5.11.  (a)  0.390 J/g·°C (b)  Copper is a likely candidate.

 

5.13.  We assume that the density of water is 1.0 g/cm³ (1 g/mL) and that it takes as much energy to keep the water at 85°F as to heat it from 72°F to 85°F. We also assume that only the water is going to be heated. Energy required = 7.47 kWh

 

5.15.  lesser; more heat would be lost to the coffee cup and the environment and so ΔT for the water would be lesser and the calculated q would be lesser

 

5.17.  greater, since taking the calorimeter’s heat capacity into account will compensate for the thermal energy transferred to the solution from the calorimeter; this approach includes the calorimeter itself, along with the solution, as “surroundings”: q_rxn = −(q_solution + q_calorimeter); since both q_solution and q_calorimeter are negative, including the latter term (q_rxn) will yield a greater value for the heat of the dissolution

 

5.19.  The temperature of the coffee will drop 1 degree.

 

5.21.  5.7 × 10² kJ

 

5.23.  38.5°C

 

5.25.  −2.2 kJ;  The heat produced shows that the reaction is exothermic.

 

5.27.  1.4 kJ

 

5.29.  22.6. Since the mass and the heat capacity of the solution is approximately equal to that of the water, the two-fold increase in the amount of water leads to a two-fold decrease of the temperature change.

 

5.31.  11.7 kJ

 

5.33.  30%

 

5.35.  0.24 g

 

5.37.  1.4 × 10² Calories

 

5.39.  The enthalpy change of the indicated reaction is for exactly 1 mol HCL and 1 mol NaOH; the heat in the example is produced by 0.0500 mol HCl and 0.0500 mol NaOH.

 

5.41.  25 kJ/mol

 

5.43.  81 kJ/mol

 

5.45.  5204.4 kJ

 

5.47.  1.83 × 10⁻² mol

 

5.49.  –802 kJ/mol

 

5.51.  15.5 kJ/ºC

 

5.53.  7.43 g

 

5.55.  Yes.

 

5.57.  459.6 kJ

 

5.59.  −494 kJ/mol

 

5.61.  44.01 kJ/mol

 

5.63.  −394 kJ

 

5.65.  265 kJ

 

5.67.  90.3 kJ/mol

 

5.69.  (a)  −1615.0 kJ/mol (b)  −484.3 kJ/mol (c)  164.2 kJ (d)  −232.1 kJ

 

5.71.  −54.04 kJ/mol

 

5.73.  −2660 kJ/mol

 

5.75.  –66.4 kJ

 

5.77.  −122.8 kJ

 

5.79.  3.7 kg

 

5.81.  On the assumption that the best rocket fuel is the one that gives off the most heat, B₂H₆ is the prime candidate.

 

5.83.  −88.2 kJ

 

5.85.

(a)  C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(l)

(b)  1.57 × 10³ L air

(c)  −104.6 kJ/mol

(d)  75.2°C

 

5.87.

(a) -802.5 kJ

(b) 4.6 × 10⁶ kJ

(c) $71

 

5.90.

(a)  First, this bottle is from Jamaica, so it does not need to follow the same food labeling rules, so it is not “illegal.” Secondly, in the United States all calorie content ends in “0” or “5” due to rounding up or down. Less than 5 calories can be listed as 0. Hank guesses that the 17 calories come from sugar, but to get to 17 calories would take over 4 grams of sugar, so it should be listed in the nutrition facts if this label was made in the United States. Other possibilies of achieving 17 are: the calories may not all be from sugar or the total calories may not actually be 17.

(b)  Using a bomb calorimeter where the dehydrated and crushed food item is combusted. The heat generated is measured by the rise in the temperature of the surronding water.

(c) To be clear, eating an extra 5 calories a day, every day, is definitly significant. But, the precision behind the listed calorie content is not significant down to the 5-calorie level. Since the precision available at the serving size level (how much you eat) has only 2 significant figures, then you only need 2 significant figures in the calorie content since the important number is multiplying (number of calories per serving) x (serving size) = number of calories consumed.

(d)  More precision would make consumers think that we know the number of calories consumed to a greater extent than we actually do. There are differences in each cracker, each piece of bread, etc. Rounding can make the consumer think they are being manipulated (since one slice of pizza can by 70 calories, but two is 150 calories!), but it saves us from companies trying to play games. If we were told that a food item was now only 298 calories when it once was 300 calories, it sounds like a savings, but we just don’t actually know these values to this level of precision. Thus, the FDA is saving us as consumers from false impressions of precison.