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Questions and Answers
The cylinder will leak if the pressure exceeds 1.0 x 10^6 Pa.
True
The internal energy of an isolated system is variable.
False
Heat absorbed by the system is quantified by the symbol w.
False
The First Law of Thermodynamics states that energy can neither be created nor destroyed.
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For an ideal gas, the change in internal energy can occur through phase changes.
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Work done on the system is represented by a negative value in the context of the First Law of Thermodynamics.
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The mass of oxygen in 1.0 L of air at 20 °C and 1.0 atm pressure can be calculated using the ideal gas law.
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The molecular mass of O2 is 32 g/mol, which is necessary for calculations involving the gas.
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The formula for activity quantifies deviations from ideality using only the ionic concentration.
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The Debye Huckel Limiting Law expresses the relationship between the activity coefficient and ionic strength using the charges of the ions involved.
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In a fully dissociated solution of Na3PO4, the mean ionic concentration [±] is calculated based on the sum of the concentrations of all ions involved.
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The constant A in the Debye Huckel equation has a value of approximately 0.509 for water at 100 °C.
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Ionic strength I is directly proportional to the square of the concentration of the ions present in a solution.
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The change in enthalpy equals the heat transferred at constant volume.
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Enthalpy is defined as H = U + PV.
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Work done by the system during gas expansion is positive.
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At constant volume, the change in internal energy is equal to the heat added to the system.
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Thermodynamic state functions depend on the history of the system.
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Extensive properties are independent of the size of the system.
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The enthalpy of formation ($, ext{ΔH}_f$) is the heat absorbed when a mole of compound is formed from its elements at standard conditions.
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The thermodynamic change in enthalpy ($, ext{ΔH}$) is always positive for exothermic reactions.
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Pressure is an example of an extensive property.
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The equation $, ext{ΔU} = ext{q} - P ext{ΔV}$ represents the change in internal energy at constant pressure.
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The compound H3PO4 is dominated by its second dissociation.
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At 37 °C, the autoprotolysis constant Kw is equal to 10^-14.
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The pH of a neutral solution at 25 °C is 7.
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PKa plus pKb equals pKw for a given acid-base pair.
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Buffer solutions can consist of a strong acid and its conjugate base.
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The addition of H3O+ to a buffer solution significantly changes its pH.
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At a pH of 8.0, the ratio of TRIS to TRIS-H+ is calculated using the pKa of TRIS-H+, which is 8.08.
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Common buffer solutions like NaH2PO4 / Na2HPO4 have a pH range of 4-6.
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The buffering capacity breaks down when equal or greater concentrations of added acid are introduced.
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The addition of 1.0 × 10^-4 mol HNO3 to a buffer with concentrations of AcOH and AcONa at 2.25 × 10^-3 mol causes a large reduction in pH.
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The melting of ice at 0 ◦C absorbs heat amounting to $6.01$ kJ/mol.
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The change in entropy for melting ice while in equilibrium with water is approximately $22.0$ J/mol·K.
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Heat gained by the ice is always greater than the heat lost by the surrounding water during melting.
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The second law of thermodynamics states that the entropy of the universe decreases in a spontaneous process.
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For irreversible processes, the change in entropy (∆S) is always less than the heat transfer divided by temperature (q/T).
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A process is spontaneous if the Gibbs Free Energy (ΔG) is greater than or equal to zero.
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The heat lost by a hot object is denoted as a negative value (−q).
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In the irreversible transfer of heat, the total change in entropy of the universe can be negative.
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For a spontaneous process, the enthalpy change (ΔH) must be greater than the temperature times the change in entropy (TΔS).
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Equilibrium between ice and water occurs at a temperature of $273.15$ K.
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Study Notes
Cylinder Leakage
- A cylinder will leak a gas if the pressure inside exceeds 1.0 x 10^6 Pa.
Oxygen in Air
- The mole fraction of oxygen (O2) in air is 0.22.
- The mass of oxygen (O2) in 1.0 L of air at 20 °C and 1.0 atm pressure can be calculated using the ideal gas law (PV = nRT).
- To calculate the mass of oxygen, you need to convert °C to K and use the molecular mass of O2 (32 g mol−1).
First Law of Thermodynamics
- Energy can neither be created nor destroyed.
- Internal energy (U) is the total energy of a system, including translational, rotational, and vibrational motion of molecules and the energy stored in electrons.
- For an ideal gas, there is no energy due to interactions between molecules.
- The internal energy of an isolated system is constant.
Changes to Internal Energy
- The change in internal energy (U) is the difference between the internal energy after a change and before the change.
- The sum of the changes in internal energy of a system and its surroundings is zero (Usystem + Usurroundings = 0).
- The change in internal energy of a system is equal to the negative of the change in internal energy of the surroundings (Usystem = −Usurroundings).
Changing Internal Energy
- The internal energy of a system can be changed by heat transfer or work done on/by the system.
- Heat (q) is energy transferred between a system and its surroundings due to temperature differences.
- Work (w) is energy transferred between a system and its surroundings that can, in principle, lift a weight.
Relating Work to Pressure and Volume
- Work done on the system (+ve): Pressure (P) x Volume change (dV)
- Expansion; work done by the system (-ve); Pressure (P) x Volume change (dV).
Change in Internal Energy (U)
- U = q + w
- At constant volume, V = 0, so U = qv (subscript ‘v’ implies constant volume).
- Most pharmaceutical processes occur at constant pressure.
- U = qp − PV (subscript ‘p’ implies constant pressure).
Enthalpy (H)
- H = U + PV.
- For a process at constant pressure, H = U + PV.
- The change in enthalpy equals the heat transferred at constant pressure (H = qp).
Thermochemistry
- Thermochemistry examines heat transfers (enthalpy changes) during important processes, such as melting, binding, dilution, and reactions.
- Enthalpy of formation (Hf) is the heat absorbed at constant pressure when 1 mole of a compound is formed from its elements in their most stable forms.
- Hf⁰ is the value of Hf at 25 ⁰C and 1 atmosphere pressure.
- Exothermic processes release heat (H -ve).
- Endothermic processes absorb heat (H +ve).
Thermodynamic State Functions
- The value of a state function depends only on the present condition (state) of the system, not its history.
- U and H are state functions.
- w and q are not state functions (they are pathway-dependent).
Intensive vs. Extensive Properties
- Intensive properties are independent of the size of the system (e.g., pressure, temperature).
- Extensive properties depend on the size of the system (e.g., internal energy, enthalpy).
Entropy
- Entropy (S) measures the disorder or randomness of a system.
- The change in entropy (S) for a reversible process is equal to the heat transferred (qrev) divided by the temperature (T).
- S = qrev/T
Irreversible Transfer of Heat
- The transfer of heat from a hot object to a cold object is an irreversible process.
- The entropy of the universe increases during an irreversible process.
Second Law of Thermodynamics
- In a spontaneous process, the entropy of the universe increases.
- This can be expressed as: S ≥ q/T.
Gibbs Free Energy
- Gibbs Free Energy (G) combines enthalpy and entropy changes to predict the spontaneity of a process.
- G = H − TS.
- A process is spontaneous if G < 0.
Bases in Water
- Bases react with water to form hydroxide ions (OH-).
- The strength of a base is measured by its base dissociation constant (Kb).
- pKb = −log10Kb.
pKa of Conjugate Acid
- The pKa of the conjugate acid can be used as a measure of the basicity of a base.
- If a base is strong, its conjugate acid is weak, and vice versa.
Dissociation of Water
- Water can undergo autoprotolysis, where it reacts with itself to form hydronium ions (H3O+) and hydroxide ions (OH-).
- The autoprotolysis constant of water (Kw) is the product of the hydronium and hydroxide ion concentrations: Kw = [H3O+][HO−] = 10−14 at 25 °C.
- pH + pOH = 14.
- Neutrality is at pH 7 (at 25 °C).
Ka, Kb, and Kw
- Ka and Kb are the acid and base dissociation constants, respectively.
- Kw is the autoprotolysis constant of water.
- pKa + pKb = pKw.
Henderson-Hasselbalch Equations
- The Henderson-Hasselbalch equations relate the pH, pKa, and the concentrations of an acidic or basic solution.
- For acids: pH = pKa + log10([A-]/[HA])
- For bases: pOH = pKb + log10([BH+]/[B])
Buffer Solutions
- A buffer solution resists changes in pH upon the addition of small amounts of acid or base.
- A buffer solution contains a weak acid and its conjugate base, or a weak base and its conjugate acid.
Buffering Effect
- The buffering effect occurs because the conjugate base of a weak acid can neutralize added acid, and the weak acid can neutralize added base.
Common Buffers
- NaH2PO4 / Na2HPO4 pH range 6-8
- KH2PO4 / K2HPO4 pH range 6-8
- TRIS (Tris(hydroxymethyl)aminomethane) pH range 7-9
- HEPES pH range 6.8 – 8.2
TRIS/TRIS-H+ Buffer
- The TRIS/TRIS-H+ buffer is a common buffer used in biological applications.
- The pKa of TRIS-H+ is 8.08.
Activity of Ions in Solution
- The activity (ai) of an ion in solution is a measure of its effective concentration, taking into account interactions with other ions.
- ai = i[i], where i is the activity coefficient of the ion.
- The activity coefficient quantifies deviations from ideality.
Ionic Strength
- Ionic strength (I) is a measure of the concentration of ions in a solution.
- I = ½ ∑i zi² ci, where zi is the charge of the ion and ci is its concentration.
Mean Activity Coefficient
- The mean activity coefficient (±) is a measure of the average activity of the ions in a solution.
Worked Examples
- The text includes several worked examples to illustrate concepts such as calculating ionic strength, mean activity coefficient, and mean activity.
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Description
Test your understanding of cylinder leakage, the composition of oxygen in air, and the First Law of Thermodynamics. This quiz covers essential concepts related to internal energy changes and ideal gas behavior. Enhance your knowledge of gas laws and thermodynamic principles.
