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Wize High School Grade 12 Chemistry Textbook > Energy Changes

Calorimetry

First Law of ThermodynamicsPrevious Section
Introduction to Enthalpy (Heat Content of a System)Next Section
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Heat Capacity and Calorimetry

  • The relationship between heat entering or leaving a system and the resulting change in temperature is the heat capacity, C
  • This can be presented as C (heat capacity, units of J/K, describes the amout of heat needed to heat the substance/object by one degree) or c (specific heat capacity, units of J/gK or J/goC , amount of heat required to heat up 1 g of a substance by one degree).
  • Note that C=mc

q=C(ΔT) or q=mc(ΔT) q=C\left(\Delta T\right)\ or\ q=mc\left(\Delta T\right)\


Wize Tip
You should memorize water's specific heat value: c=4.18J/goC. This means that you would need to add 4.18J of energy in order to heat 1 g of water up by 1oC.

  • Calorimeters come in two general varieties: simple "coffee cup" calorimeters and bomb calorimeters
  • What is a calorimeter?
  • A calorimeter is just a container that is insulated. It holds a liquid that is usually water inside of it and you can have reactions happening inside of it as well.
  • A thermometer will be able to read the temperature changes of the water.
  • If the thermometer measures an increase in temperature, that means the water went up in temperature.
  • For a calorimeter, the water is the surroundings and the reaction is the system.
  • Therefore, if the water went up in temperature then that means it gained all of the heat from the system (or the reaction taking place inside the calorimeter). It didn't gain the heat from anywhere else because the calorimeter is insulated!
  • This means the system/reaction lost heat and is endothermic/exothermic:
    exothermic
    .
  • qwater=-qrxn where q=mcΔT

Wize Concept
For exothermic reactions, q < 0 (heat is being released by the system)
For endothermic reactions, q > 0 (heat is being gained by the system)

Coffee cup calorimeters

  • Essentially an open styrofoam cup with a thermometer, and are most frequently used to measure the temperature change of an aqueous reaction under constant
    pressure
    conditions
In general:
qsystem(sample) = -qsurroundings(H2O)
using q=mcΔT
(mass of sample)(c of sample)(ΔT of sample) = -(mass of H2O)(c of H2O)(ΔT of water)

Bomb calorimeters

  • Typically consist of a sealed reaction vessel loaded with a combustible material and filled with oxygen placed in a surrounding water bath. A combustion reaction is performed under constant
    volume
    conditions and the resulting change in temperature of the water bath is measured
In general:
qrxn = -qcalorimater
(mass of sample)(c of sample)(ΔT of sample) = -(C of calorimeter)(ΔT of calorimeter)
(using q=CΔT!)


Which kind of a substance needs more energy to undergo an increase in temperature of 5oC, something with a high or low specific heat?
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How many joules are needed to increase the temperature of 15.0g of Fe from 20.0oC to 40.0oC?
(cFe=0.4998 J/goC)

First, it is always helpful to write out the variables that we have:
m=15g
T1=20oC
T2=40oC
cFe=0.4998 J/goC
q=mcΔTq=mc\Delta T
q=? (Ans in joules!)

Now plug in the variables into the equation and solve!
q=mcΔTq=mc\Delta T
Can solve for ΔT first: ΔT=T2-T1=40 - 20= 20oC

q=(15g)(0.4998 J/goC)(20oC)
q=149.94 J
q=150J
If 500 mL of olive oil, initially at 25oC, received 1.25 kJ of energy, what is its final temperature?
(colive oil= 2.0J/goC, density=0.91 g/mL)
A 5.00 g mass of metal was heated to 100.0 oC and then placed into 100.0 g of water at 24oC. The temperature of the resulting mixture became 28oC.
How many joules did the water absorb?
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Example: Calorimetry

A block of 20 g20\ g lead cube (cp=0.128 J g−1K−1c_p=0.128\ J\ g^{-1}K^{-1}) is heated to 145° C145\degree\ C. The cube is then submerged into a Styrofoam cup containing 500 g500\ g of water at room temperature (cp=4.18 J g−1K−1c_p=4.18\ J\ g^{-1}K^{-1}). After the water and the lead cube come to thermal equilibrium, what is the final temperature of the water?

qp,lead=−qp,watermCpΔT=−mcpΔT(20cg)(0.128 J g−1𝐾−1)(T2−418 K)=−(500 g)(4.18 J g−1K−1)(T2−298 K)(2.56 J K−1)T2−1070.08 J=(−2090 J K−1)T2+622820 J(2.56 J K−1)T2+(2090 J K−1)T2=622820 J+1070.08 JT2(2.56J K−1+2090 J K−1)=622820 J+1070.08 JT2=1070.88 J+622820 J(2.56 J K−1+2090 𝐽 K−1)=298.15 K\begin{array}{c} q_{p,lead}=-q_{p,water}\\[10pt] mC_p\Delta T=-mc_p\Delta T\\[10pt] (20cg)(0.128\ J\ g^{-1}𝐾^{-1})(T_2 - 418\ K) = -(500\ g)(4.18\ J\ g^{-1}K^{-1})(T_2 - 298\ K)\\[10pt] (2.56\ J\ K^{-1})T_2 - 1070.08\ J = (-2090\ J\ K^{-1} )T_2 + 622820\ J\\[10pt] (2.56\ J\ K^{-1})T_2+(2090\ J\ K^{-1} )T_2= 622820\ J + 1070.08\ J \\ \\ T_2(2.56 J\ K^{-1}+2090\ J\ K^{-1})=622820\ J + 1070.08\ J\\ \\ T_2=\dfrac{1070.88\ J + 622820\ J}{(2.56\ J\ K^{-1} + 2090\ 𝐽\ K^{-1})}=298.15\ K \end{array}
Wow! Water is a pretty good insulator
Extra Practice
Heat of Vaporization for Hexane
Hexane is heated from 0oC to 50oC and the equilibrium vapour pressure increases from 0.06 atm to 0.53 atm.
Calculate the ΔvapH for hexanes.
Thermochemistry: Melting ice
The standard enthalpy of fusion for water, ΔHfusiono=6.01 kJ/mol.\Delta H^o_{\textrm{fusion}}=6.01\ \textrm{kJ/mol}. Calculate the energy required (in KJ) to convert 26.0 g of ice at 0oC to liquid water at 20oC.
Calorimetry: Final temperature calculation
The ΔHsoln for the process when solid sodium hydroxide (NaOH) dissolves in water is 44 kJ/mol. When a 10.0 g sample of NaOH dissolves in 250.0 g of water in a coffee-cup calorimeter, the temperature increases from 23.0oC to _______oC. Assume that the solution has the same specific heat as liquid water, i.e. 4.18 J/gK.
Calorimetry: Heat of combustion
When 2g of rocket fuel, N2H4 is burned inside of a bomb-calorimeter, the temperature of the water rises from 22oC to 29oC. If there is 0.9kg of water and the heat capacity for the bomb is 822J/oC, what is the heat of the combustion for one mole of N2H4 in the bomb calorimeter?
Thermochemistry: Enthalpy change
The enthalpy of vaporization for water, ΔHovaporization = 40.7 kJ/mol. Determine the enthalpy change (in kJ) when 54.0 mL of water is condensed from steam at 100oC.
Thermochemistry: Melting ice
The standard enthalpy of fusion for water, ΔHfusiono=6.01 kJ/mol.\Delta H^o_{\textrm{fusion}}=6.01\ \textrm{kJ/mol}. Calculate the energy required (in KJ) to convert 26.0 g of ice at 0oC to liquid water at 20oC.
Calorimetry: Heat of combustion
When 2g of rocket fuel, N2H4 is burned inside of a bomb-calorimeter, the temperature of the water rises from 22oC to 29oC. If there is 0.9kg of water and the heat capacity for the bomb is 822J/oC, what is the heat of the combustion for one mole of N2H4 in the bomb calorimeter?
Calorimetry: Heat of combustion
When 2g of rocket fuel, N2H4 is burned inside of a bomb-calorimeter, the temperature of the water rises from 22oC to 29oC. If there is 0.9kg of water and the heat capacity for the bomb is 822J/oC, what is the heat of the combustion for one mole of N2H4 in the bomb calorimeter?
Enthalpy of Formation
What is the enthalpy of the following reaction when 0.35 g of Mg2+ is produced? Use the following information:
ΔH°f[Mg(OH)2(s)] = −924.5 kJ
ΔH°f[NH4+(aq)] = −132.5 kJ
Thermodynamics: Internal energy and Enthalpy
2.3 moles of an ideal gas initially at -12oC and 16 atm underwent a complete expansion against a constant external pressure of 1atm and did 1.1kJ of work. Calculate Δ𝑈, Δ𝐻, 𝑎𝑛𝑑 𝑞 for this process.
Calorimetry: Final temperature calculation
The ΔHsoln for the process when solid sodium hydroxide (NaOH) dissolves in water is 44 kJ/mol. When a 10.0 g sample of NaOH dissolves in 250.0 g of water in a coffee-cup calorimeter, the temperature increases from 23.0oC to _______oC. Assume that the solution has the same specific heat as liquid water, i.e. 4.18 J/gK.
Calorimetry: Heat of reaction
0.23 g of ethanol (C2H5OH) was burned in a bomb calorimeter (constant
volume
) leading to a temperature change from 22.50oC to 23.81oC. If the heat capacity of the calorimeter is 5.2 kJ/K, what would be the amount of heat generated by the combustion of exactly one mole of ethanol? ___________
Calorimetry: Temperature change
1. A 56.0 g block of iron heated to 90 °C is placed in a 4.8 kg water bath at 20 °C. What will be the final temperature of the iron? heat capacity of iron c = 0.450 J /gK, heat capacity of water is 4.185 J/gK
Calorimetry: Temperature change
How much heat energy is required to raise the temperature of 35.0 g of Al (c = 0.902 J/g K) from 18 °C to 65 °C? If this much energy were instead used to raise the temperature of 2.0 L of water, by how much would the temperature of the water change? Round to the nearest oC.
Calorimetry: Heat of reaction
4. A bomb calorimeter assembly has a heat capacity of 650 J/°C. The assembly is placed in a 3.0 L water bath and 2.5g of a fuel compound is burned in excess oxygen. If the temperature of the water bath increases by 4.8 °C, what is the value of qrxn?
What is the amount of heat released per gram of compound burned?
Calorimetry: Heat capacity
5. A fuel compound is burned in a bomb calorimeter, releasing 458 kJ of heat. The temperature of the calorimeter assembly and surrounding 2.5 L water bath increases from 23.5 °C to 28.6 °C. What is the heat capacity of the calorimeter assembly?
Calorimetry
When 1.00 kg of lead (specific heat =0.13 J g-1°C-1) at 125oC is added to a quantity of water at 18.0°C, the final temperature of the lead-water mixture is 32.0°C. What is the volume of water present?
Note: the density of H2O(l) is 1.00g mL-1 and the specific heat capacity is 4.18J g-1 oC-1
A 2.00 mole sample of a monoatomic ideal gas is initially at 1.00 L and 1.00 atm. Calculate the total q, w, ΔE{\small \Delta\text{E}}and ΔH{\small \Delta \text{H}}when the final conditions are 0.500 L and 5.00 atm along the pathway where the volume is compressed first.
[Do NOT include units in your answers]
Thermochemistry: Energy required to melt ice
You are lost on an expedition and you need some water to drink. There is ice around at an ambient temperature of -22oC. Using the thermodynamic information below, how much energy is required to take 1 kg of ice and warm it up to water at 12oC.
cp,s(ice)=2.01 JK−1mol−1ΔHfuso=6.01 kJmol−1cp,s(water)=4.18 JK−1mol−1ΔHfuso=44.00 kJmol−1\begin{array}{lr} c_{p,s}(ice) = 2.01\ J K^{-1} mol^{-1} & \Delta H^o_{fus} = 6.01\ kJ mol^{-1} \\ c_{p,s}(water) = 4.18\ J K^{-1} mol^{-1} & \Delta H^o_{fus} = 44.00\ kJ mol^{-1} \end{array}
Heat of Vaporization for Hexane
Hexane is heated from 0oC to 50oC and the equilibrium vapour pressure increases from 0.06 atm to 0.53 atm.
a) Calculate the ΔvapH for hexanes.
b) The human nose can detect hexane at a partial pressure of 0.005 atm. Estimate the temperature at which we can no longer smell hexane.
Copper, Silver, water ,Gold, hydrogensulfide and have specific heats of 0.385, 0.235, 4.18, 0.129, and 1.342 Jg-1oC-1 respectively. Which of the following would need smallest quantity of heat to change the temperature of 5400kg by 65oC
An alkane’s vapour pressure at 25.00 °C is 6.00 kPa. What is its vapour pressure at 80.00 °C if the enthalpy of vaporization is 43.0 kJ/mol? (Give your answer in kPa)
Sucrose, C12H22O11, can be metabolized for energy in the body according to the reaction: C12H22O11 (s) + 12 O2 (g) →\rightarrow 12 CO2 (g) + 11 H2O (l) ΔHo = -5.65x103 kJ
How many grams of sucrose must be burned to raise the temperature of 50.0 kg of water by 1.00oC? The specific heat capacity of water is 4.184 J g-1 K-1.
Calorimetry: Heat of reaction
The temperature of a 12.58 g sample of calcium carbonate (CaCO3(s)) increases from 23.6oC to 38.2oC. If the specific heat capacity of calcium carbonate is 0.82 J/g K. How many joules of heat are absorbed?
Calorimetry: Energy of vaporization of water
How much energy is required to bring 1.00 g of liquid water from 35 °C to 165 °C water vapour? The enthalpy of vaporization of water is +40.7 kJ/mol, the specific heat capacity of liquid water is 4.18 J / g °C, and the specific heat capacity of water vapour is 1.87 J/g °C.
From the following reaction:
2C6H12O6(s)+2O2(g)→12CO2(g)+4H2O(l)ΔHrxn=−1680kJ2C_6H_{12} O_{6(s)}+2O_{2(g)} \to 12CO_{2(g)}+4H_2O_{(l)} \hspace{20pt} \Delta H_{rxn}=-1680 kJ
When an unknown quantity of sugar (C6H12O6) is burned, it was determined that the internal energy of the system decreased by 960 kJ and that 15.7 kJ of work was done on the system. How many grams of sugar were present at the beginning of this specific reaction?
A chemical compound has a molecular weight of 89.05 g/mol. 1.400 grams of this compound underwent complete combustion under constant pressure conditions in a calorimeter with a heat capacity of 2.980 × 103 J/ °C. The temperature went up by 11.95 °C. Calculate the standard heat of combustion of the compound.
Calorimetry: Heat capacity of calorimeter
The combustion of 1.00 mol of glucose (C6H12O6) gives off 2.82x103 kJ of heat (i.e. ΔHcomb = 2.82x103 kJ mol-1). If 1.80 g glucose (molar mass is 180) is burned in a bomb calorimeter and the temperature of the calorimeter increases from 19.00oC to 23.50oC, what is the heat capacity of the calorimeter (kJ/oC)?
Calorimetry: Heat requirement
How much heat is required to convert a 15.5 g ice cube at -5.00oC to liquid water at 0oC? (The specific heat of ice is 2.09 J/g K, the specific heat of water is 4.18 J/g K, and the ΔHfus for water=334 J/g).
Thermochemistry: Melting ice
The standard enthalpy of fusion for water, ΔHfusiono=6.01 kJ/mol.\Delta H^o_{\textrm{fusion}}=6.01\ \textrm{kJ/mol}. Calculate the energy required (in KJ) to convert 26.0 g of ice at 0oC to liquid water at 20oC.
Enthalpy: Heat of vaporization
The enthalpy of vaporization for water, ΔHovaporization = 40.7 kJ/mol. Determine the enthalpy change (in kJ) when 54.0 mL of water is condensed from steam at 100oC.
Calorimetry: Using Heat Qualitatively
Consider the following four samples, all initially at room temperature:
The glass cubes are cooled to the same low temperature, and each is placed into one of the containers of room temperature gas.
(a) If Container A had a lower final temperature at thermal equilibrium than Container B, which gas has the lower specific heat capacity?
Calorimetry
From the following reaction:
2C6H12O6(s)+2O2(g)→12CO2(g)+4H2O(l)ΔHrxn=−1680kJ/mol⋅rxn2C_6H_{12}O_6(s)+2O_2(g)→12CO_2(g)+4H_2O(l)\qquad \qquad ΔH_{rxn}=-1680kJ/mol\cdot rxn
When an unknown quantity of sugar (C6H12O6) is burned, it was determined that the internal energy of the system decreased by 960 kJ and that 15.7 kJ of work was done on the system. How many grams of sugar were present at the beginning of this specific reaction?
Thermochemistry: Calorimetry
Consider the following balanced chemical equation:
2CℓF3(g)+2O2(g)→Cℓ2O(g)+3F2O(g)∆rH°=???2 CℓF_3(g) + 2 O_2(g) → Cℓ_2O (g) + 3 F_2O (g) \qquad ∆_rH° = ???
Substance△fH° @ 25°C (kJ/mol)CℓF3(g)??Cℓ2O(g)80.3F2O(g)–21.7F2(g)0\def\arraystretch{1.5} \begin{array}{|c|c|} \hline \rm Substance & △_fH° \ @ \ 25°C \ (kJ/mol) \\ \hline CℓF_3 (g) & ?? \\ \hline Cℓ_2O (g) & 80.3 \\ \hline F_2O (g) & – 21.7 \\ \hline F_2 (g) & 0 \\ \hline \end{array}
Thermochemistry: Calorimetry
Ethene gas (C2H4) reacts with fluorine gas according to the following balanced equation:
C2H4(g)+6F2(g)→2CF4(g)+4HF(g)ΔrH°=−3012 kJ/mol⋅rxn @ 25°CC_2H_4 (g) + 6 F_2 (g) → 2 CF_4 (g) + 4 HF (g) \qquadΔ_rH° = −3012\ kJ/mol·rxn\ @ \ 25°C
Substance△fH° @ 25°C(kJ/mol)C2H4(g)??F2(g)0CF4(g)–933HF(g)–273.3\def\arraystretch{1.5} \begin{array}{|c|c|} \hline \rm{Substance} & △_fH° \ @ \ 25°C(kJ/mol) \\ \hline C_2H_4 (g) & ?? \\ \hline F_2 (g) & 0 \\ \hline CF_4 (g) & – 933 \\ \hline HF (g) & – 273.3 \\ \hline \end{array}
Calculate ΔHof of SO2(g) given the following: (answer in kJ)
S(s)+1.5O2(g)→SO3(g),ΔH=−395.8kJS_{(s)}+1.5O_{2(g)}\to SO_{3(g)}, \Delta H=-395.8kJ
2SO2(g)+O2(g)→2SO3(g),ΔH=−198.2kJ2SO_{2(g)}+O_{2(g)}\to 2SO_{3(g)}, \Delta H=-198.2kJ
The standard enthalpy of formation for the amino acid glycine C2H5NO2(s) is –528 kJ/mol at 25°C. Which reaction below has an enthalpy change equal to this value?
Calorimetry
Equal masses of copper and iron are both heated to a temperature of 100°C. Each piece of hot metal is then placed into its own beaker containing 1 L of water. If both beakers start with the same initial temperature, which beaker of water will have the higher final temperature?
Additional information: Cu (specific heat = 0.377 J/g°C); Fe (specific heat = 0.450 J/g°C)
Calorimetry
The temperature of a 12.58 g sample of calcium carbonate (CaCO3 (s)) increases from 23.6oC to 38.2oC. If the specific heat of calcium carbonate is 0.82 J/g K, how many joules of heat are absorbed?
Thermochemistry Calculations
The standard enthalpy of fusion for water, ΔHofusion = 6.01 kJ/mol. Calculate the energy required (in kJ) to convert 26.0 g of ice at 0oC to liquid water at 20oC.
Thermochemistry: Enthalpy change
The enthalpy of vaporization for water, ΔHovaporization = 40.7 kJ/mol. Determine the enthalpy change (in kJ) when 54.0 mL of water is condensed from steam at 100oC.
Bomb Calorimetry
A fuel compound was burned in oxygen in a bomb calorimeter with a combined heat capacity of 56.5 k] / K (Bomb assembly and water). The temperature of the surrounding water bath increased from 23.5 to 34.6 °C as a result. Calculate ΔEsys\Delta E_{sys}for this process? Consider any change in pressure due to gaseous products to be negligible.