5.2 Calorimetry
The density of water is 1.0 g/mL, so 425 mL of water = _______ g.
425
Why is styrofoam a good insulator?
Air is a poor heat conductor and styrofoam is full of air pockets with no air movement.
What kind of calorimeter that operates at constant volume and is used to measure the energy produced by reactions that yield large amounts of heat and gaseous products, such as combustion reactions?
Bomb calorimeter
One _____ is equal to 1000 calories (1 kcal), the amount of energy needed to heat 1 kg of water by 1 °C.
Calorie
In humans, metabolism is typically measured in ______ per day.
Calories
5.33 The amount of fat recommended for someone with a daily diet of 2000 Calories is 65 g. What percent of calories in this diet would be supplied by this amount of fat if the average number of Calories for fat is 9.1 Calories/g?
Calories = g x Calories/g Calories = 65 g x 9.1 Calories/g Calories = 591.5 Calories Percent Calories of Fat = (Calories of Fat/Total Calories) x 100% Percent Calories of Fat = (591.5 Calories/2000 Calories) x 100% Percent Calories of Fat = 30%
5.37 A serving of breakfast cereal contains 3 g of protein, 18 g of carbohydrates, and 6 g of fat. What is the Calorie content of a serving of this cereal if the average number of Calories for fat is 9.1 Calories/g, for carbohydrates is 4.1 Calories/g, and for protein is 4.1 Calories/g?
Calories per serving of cereal = (g protein x 4.1 Calories/g protein) + (g carbohydrate x 4.1 Calories/g carbohydrate) + (g fat x 9.1 Calories/g fat) Calories per serving of cereal = (3 g x 4.1 Calories/g) + (18 g x 4.1 Calories/g) + (6 g x 9.1 Calories/g) Calories per serving of cereal = 140.7 Calories
What device is used to measure the amount of heat involved in a chemical or physical process?
Calorimeter
When an endothermic reaction occurs within a _______, the heat required is absorbed from the thermal energy of the solution, which decreases its temperature.
Calorimeter
When an exothermic reaction occurs in solution in a __________, the heat produced by the reaction absorbed by the solution, which increases its temperature.
Calorimeter
One technique used to measure the amount of heat involved in a chemical or physical process is known as:
Calorimetry
The measurement of heat transfer using ______ requires the definition of a system and its surroundings.
Calorimetry
What kind of calorimeters do most General chemistry students use?
Coffee-cup calorimeters
If the heat produced or consumed in the reaction (the "system"), qreaction, plus the heat absorbed by the solution (the "surroundings"), qsolution, must add up to zero, then the amount of heat produced or consumed in the reaction _______ the amount of heat absorbed or lost by the solution.
Equals
Putting your hand over hot water and feeling the warmth is due to heat loss. In calorimetry, heat loss is:
Error
Calorimetry is one technique used the measure the amount of _____ in a chemical or physical process.
Heat
Knowledge of the heat capacity of the surroundings, and careful measurements of the masses of the system and surroundings and their temperatures before and after the process allows one to calculate the:
Heat transferred
The best insulator is a vacuum because there is no _____ transfer between molecules.
Kinetic energy
Whole-body calorimeters are used to measure the ______ of individuals under different environmental conditions, different dietary regimes, and with different health conditions, such as diabetes.
Metabolisms
A ______ is the energy unit used to quantify the amount of energy derived from the metabolism of food.
Nutritional calorie (Calorie)
Coffee-cup calorimeters are constructed from two ______ cups. A thermometer and stirrer extend through the cover into the reaction mixture.
Polystyrene
Simple calorimeters are designed to operate at constant (atmospheric) _______ and are convenient to measure heat flow accompanying processes that occur in solution.
Pressure
In calorimetry, all matter other than the system being studied is known as the:
Surroundings
The other components of the calorimeter that serve to either provide heat to the system or absorb heat from the system are known as the:
Surroundings
In a calorimetric determination, an endothermic process occurs and heat, q, is positive, indicating that thermal energy is transferred from the ____ to the_____.
Surroundings, system
In calorimetry, the portion of matter undergoing a chemical or physical change being studied is called the:
System
In a calorimetric determination, an exothermic process occurs and heat, q, is negative, indicating that thermal energy is transferred from the _____ to its _______.
System, surroundings
In a simple calorimetry process, heat is transferred from a piece of hot metal to the cool water until both are the same:
Temperature
In a calorimeter, the ______ change, along with the specific heat and mass of the solution, can be used to calculate the amount of heat.
Temperature change
Calorimetry is used to measure amounts of heat transferred _______ a substance.
To or from
Food calories are measured from combustion to completion. True or False?
True
If the calorimeter is well insulated, we don't have to worry about time. True or False?
True
Polystyrene is a fantastic insulator. True or False.
True
We know the specific heat of water to 6 significant figures. True or False?
True
Since calorimeters are good at minimizing heat loss during reactions, we can say that the heat produced or consumed in the reaction (the "system"), qreaction, plus the heat absorbed by the solution (the "surroundings"), qsolution, must add up to:
Zero
One Calorie is equal to 1000 calories (1 kcal), the amount of energy needed to heat 1 ____ of water by 1 °C.
kg
A 248-g piece of copper at 314 °C is dropped into 390 mL of water initially at 22.6 °C. Assuming that all heat transfer occurs between the copper and the water, calculate the final temperature. (Hint: combine like term)
qcopper = -qwater (c x m x ∆T)copper = -(c x m x ∆T)water ccopperx mcopper x (Tf,rebar-Ti,rebar) = -cwater x mwater x (Tf,water - Ti,water) 0.385 J/g °C x 248 g x (Tf,copper - 314 °C) = -4.184 J/g °C x 390 g x (Tf,water - 22 °C) 95.48Tf,copper - 29980.72 = -1631.76Tf,water + 35898.72 95.48Tf,copper + 1631.76Tf,water = 29980.72 + 35898.72 1727.25Tf = 65878.72 Tf = 65878.72/1727.25 Tf = 38.1 °C
A 248-g piece of copper is dropped into 390 mL of water at 22.6 °C. The final temperature of the water was measured at 39.9 °C. Calculate the initial temperature of the piece of copper. Assume that all heat transfer occurs between the copper and the water.
qcopper = -qwater (c x m x ∆T)copper = -(c x m x ∆T)water ccopperx mcopper x (Tf,rebar-Ti,rebar) = -cwater x mwater x (Tf,water - Ti,water) Ti,copper = (cwater x mwater x (Tf,water-Ti,water)/ccopper x mcopper) +Tf,copper Ti,copper=(4.184 J/g °C)(390 g)(39.9 °C-22.6 °C)/(0.385 J/g °C)(248 g)) + 39.9 °C Ti,copper=335.6 °C
5.21 The temperature of the cooling water as it leaves a hot engine of an automobile is 240 °F. After it passes through the radiator is has a temperature of 175 °F. Calculate the amount of heat transferred from the engine to the surroundings by one gallon of water with a specific heat of 4.184 J/g °C.
qengine = -qwater qengine = -(cwater x mwater x (Tf,water - Ti,water)) qengine = -(4.184 J/g °C x 3785.4118 g x (79.444 - 115.556 °C) qengine = -5.72 x 10⁵ J = -572 kJ
5.19 How much will the temperature of a cup (180 g) of coffee at 95 °C to be reduced when a 45 g silver spoon (specific heat 0.24 J/g °C) at 25 °C is placed in the coffee and the two are allowed to reach the same temperature? Assume that coffee has the same density and specific heat as water.
qmetal = -qwater (mmetal x cmetal x (Tf,metal - Ti,metal)) = -(mwater x cwater x (Tf,water - Ti,water)) (45 g x 0.24 J/g °C x (Tf,metal - 25 °C)) = - (180 g x 4.184 J/g °C x (Tf, water - 95 °C) 10.8Tf - 270 = -(753.12Tf - 71546.4) 10.8Tf + 753.12Tf = -270 + 71546.4 763.92Tf = 71276.4 Tf = 93.3 °C
A 59.7 g piece of metal that had been submerged in boiling water was quickly transferred into 60.0 mL of water initially at 22.0 °C. The final temperature is 28.5 °C. Use these data to determine the specific heat of the metal. Use this result to identify the metal. (hint: since the metal was in boiling water, we can assume its initial temperature is 100 °C)
qmetal = -qwater cmetal x mmetal x (Tf,metal-Ti,metal) = -cwater x mwater x (Tf,water-Ti,water) cmetal = -(cwater x mwater x (Tf,water-Ti,water)/(mmetal x (Tf,metal-Ti,metal) cmetal = -(4.184 J/g °C x 60.0 g x (28.5 °C - 22.0 °C)/(59.7 g x (28.5 °C - 100 °C) cmetal = 0.382 J/g °C Metal is most likely copper
A 92.9-g piece of a silver/gray metal is heated to 178.0 °C, and then quickly transferred into 75.0 mL of water initially at 24.0 °C. After 5 minutes, both the metal and the water have reached the same temperature: 29.7 °C. Determine the specific heat and the identity of the metal.
qmetal = -qwater cmetal x mmetal x (Tf,metal-Ti,metal) = -cwater x mwater x (Tf,water-Ti,water) cmetal = -(cwater x mwater x (Tf,water-Ti,water)/(mmetal x (Tf,metal-Ti,metal) cmetal = -(4.184 J/g °C x 75.0 g x (29.7 °C - 24.0 °C)/(92.9 g x (29.7 °C - 178.0 °C) cmetal = 0.1298 J/g °C Since the metal is silver/gray is color, it is most likely lead (0.130 J/g °C) and not gold (0.129 J/g °C)
Write the formula for the following: The heat produced or consumed in the reaction (the "system"), qreaction, plus the heat absorbed by the solution (the "surroundings"), qsolution, must add up to zero.
qreaction + qsolution = 0
What concept (in formula form) lies at the heart of all calorimetry problems and calculations?
qreaction = -qsolution
Write the formula for the following: The amount of heat produced or consumed in the reaction equals the amount of heat absorbed or lost by the solution.
qreaction = -qsolution
5.25 Dissolving 3.0 g of CaCl₂(s) in 150.0 g of water in a calorimeter at 22.4 °C causes the temperature to rise to 25.8 °C. What is the approximate amount of heat involved in the dissolution, assuming the heat capacity of the resulting solution is 4.18 J/g °C? Is the reaction exothermic or endothermic?
qreaction = -qsolution qreaction = -(csolution x msolution x (Tf,solution - Ti,solution)) qreaction = -(4.184 J/g °C x 153.0 g x (25.8 - 22.4 °C) qreaction = -2176 J = -2.2 kJ The reaction is exothermic.
A 360-g piece of rebar (a steel rod used for reinforcing concrete) is dropped into 425 mL of water at 24.0 °C. The final temperature of the water was measured as 42.7 °C. Calculate the initial temperature of the piece of rebar. Assume the specific heat of steel is approximately the same as that for iron, and that all heat transfer occurs between the iron and water (there is no heat exchange with the surroundings).
qrebar = -qwater (c x m x ∆T)rebar = -(c x m x ∆T)water crebar x mrebar x (Tf,rebar-Ti,rebar) = -cwater x mwater x (Tf,water - Ti,water) Ti,rebar = (cwater x mwater x (Tf,water-Ti,water)/crebar x mrebar) + Tf,rebar Ti,rebar = ((4.184 J/g °C)(425 g)(42.7 °C-24.0 °C)/(0.449 J/g °C)(360 g)) + 42.7 °C Ti,rebar = 248 °C
5.31 When a 0.740-g sample of trinitrotoluene (TNT), C₇H₅N₂O₆, is burned in a bomb calorimeter, the temperature increases from 23.4 °C to 26.9 C. The heat capacity of the calorimeter is 534 J/g °C, and it contains 675 mL of water. How much heat was produced by the combustion of the TNT sample?
qrxd = -(qwater + qbomb) qrxd = -((cwater x mwater x (Tf,water - Ti,water) + (cbomb x (Tf,bomb - Ti,bomb) qrxd = -((4.184 J/g °C x 675 g x (26.9 - 23.4 °C)) + (534 J/g °C x (26.9 - 23.4 °C) qrxd = 11753.7 J = 11.8 kJ This reaction released 11.8 kJ of heat when 0.740 g of TNT was burned
When 3.12 g of glucose, C₆H₁₂O₆, is burned in a bomb calorimeter, the temperature of the calorimeter increases from 23.8 °C to 35.6 C. The calorimeter contains 775 g of water, and the bomb itself has a capacity of 893 J/°C. How much heat was produced by the combustion of the glucose sample?
qrxn = -(qwater + qbomb) qrxn = -[(4.184 J/g °C x 775 g x (35.6 °C - 23.8 °C) + 893 J/°C x (35.6 °C - 23.8 °C)] qrxn = -(38,300 J + 10,500 J) qrxn = -48,000 J = -48 kJ
When 0.963 g of benzene, C₆H₆, is burned in a bomb calorimeter, the temperature of the calorimeter increases by 8.39 °C. The bomb has a heat capacity of 784 J/°C and is submerged in 925 mL of water. How much heat was produced by the combustion of the glucose sample?
qrxn = -(qwater + qbomb) qrxn = -[(4.184 J/g °C x 925 g x (8.39 °C) + 784 J/°C x (8.39 °C)] qrxn = -(32,470 J + 6577 J) qrxn = -39047 J = 39.0 kJ
When 50.0 mL of 0.10 M HCl(aq) and 50.0 mL of 0.10 M NaOH(aq), both at 22.0 °C, are added to a coffee cup calorimeter, the temperature of the mixture reaches a maximum of 28.9 °C. What is the approximate amount of heat produced by this reaction?
qsolution = (c x m x ∆T)solution qsolution = (4.184 J/g °C x 100 g x (28.9-22.0 °C) qsolution = 2886.96 J/g °C qreaction = -gsolution qreaction = 2886.96 J/g
When 100 mL of 0.200 M NaCl(aq) and 100 mL of 0.200 M AgNO₃(aq), both at 21.9 °C, are mixed in a coffee cup calorimeter, the temperature increases to 23.5 °C as solid AgCl forms. How much heat is produced by this precipitation reaction?
qsolution = (c x m x ∆T)solution qsolution = (4.184 J/g °C x 200 g x (23.5 - 21.9 °C) qsolution = 1338.88 J qreaction = -qsolution qreaction = -1338.88 J = 1.34 kJ
When a 3.00-g sample of KCl was added to 3.00 x 10² g of water in a coffee cup calorimeter, the temperature decreased by 1.05 °C. How much heat is involved in the dissolution of the KCl?
qsolution = c x m x ∆T qsolution = 4.184 J/g °C x 303 g x (-1.05 °C) qsolution = -1331 J = 1.33 kJ
When solid ammonium nitrate dissolves in water, the solution becomes cold. This is the basis for an "instant ice pack." When 3.21 g of solid NH₄NO₃ dissolves in 50.0 g of water at 24.9 °C in a calorimeter, the temperature decreases to 20.3 °C. Calculate the value of q for this reaction.
qsolution = c x m x ∆T qsolution = 4.184 J/g °C x 53.21 g x (20.3-24.9 °C) qsolution = -1024.1 J qreaction = -qsolution qreaction= 1024.1 J = 1.02 kJ
Most calorimetry measurements are done in solution. Water is most often used because water properties are well known and so are helpful in accurately measuring:
∆T
