Properties of Substances and Mixtures
According to kinetic molecular theory, when you increase the temperature of a gas at constant volume, this property of the gas increases because particles move faster and collide with the walls more forcefully.
What is pressure?
In the reaction 2NO₂ → 2NO + O₂, the rate of disappearance of NO₂ is measured at 0.040 mol/L·s. This is the rate of appearance of O₂ at that same moment.
What is 0.020 mol/L·s? (O₂ is produced at half the rate NO₂ is consumed, based on stoichiometric coefficients)
A 100.0 g sample of an unknown metal at 80.0°C is placed into a coffee-cup calorimeter containing 100.0 g of water initially at 20.0°C. The system reaches thermal equilibrium at 28.0°C. This is the specific heat capacity of the unknown metal. (c of water = 4.18 J/g·°C)
What is approximately 0.642 J/g·°C?
(Heat lost by metal = heat gained by water) m_metal × c_metal × ΔT_metal = m_water × c_water × ΔT_water 100.0 × c × (80.0 − 28.0) = 100.0 × 4.18 × (28.0 − 20.0) 100.0 × c × 52.0 = 100.0 × 4.18 × 8.0 5,200c = 3,344 c ≈ 0.643 J/g·°C
For the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), this is the correctly written equilibrium expression Kc.
What is Kc = [NH₃]² / [N₂][H₂]³? (Products over reactants, each raised to the power of its stoichiometric coefficient. Pure solids and liquids are excluded.)
A solution has a hydroxide ion concentration of 1.0 × 10⁻³ M at 25°C. Identify whether it is acidic, basic, or neutral, and calculate its pH.
What is basic, pH = 11? pOH = −log(1.0×10⁻³) = 3. pH = 14 − 3 = 11. Since pH > 7, the solution is basic.
A 2.0 mol sample of gas is held at 300 K in a 5.0 L container. Using PV = nRT, this is the approximate pressure in atm. (R = 0.0821 L·atm/mol·K)
What is approximately 9.85 atm? (P = nRT/V = (2.0)(0.0821)(300)/5.0)
Two reactions have the same activation energy, but Reaction A is significantly faster at the same temperature. Rather than temperature or concentration, this is the factor — rooted in the collision model — that explains the rate difference.
What is the orientation (geometry) of collisions / the frequency factor (A) in the Arrhenius equation? (Not all collisions with sufficient energy lead to reaction — molecules must collide with the correct spatial orientation. Reaction A has a higher frequency of properly oriented collisions.)
Given: (1) C + O₂ → CO₂, ΔH = −394 kJ and (2) 2CO + O₂ → 2CO₂, ΔH = −566 kJ, this is the ΔH for the reaction 2C + O₂ → 2CO.
What is −222 kJ? (Multiply rxn 1 by 2: ΔH = −788 kJ. Reverse rxn 2: ΔH = +566 kJ. Sum: −788 + 566 = −222 kJ)
For the endothermic reaction: N₂(g) + O₂(g) ⇌ 2NO(g), a student increases the temperature AND decreases the volume of the container. This is the direction the equilibrium shifts and the reasoning for each stress applied.
What is a shift to the right for both stresses? (Increasing temperature favors the endothermic forward direction. Decreasing volume increases pressure, but since both sides have 2 moles of gas, there is no net shift from pressure — only temperature drives the shift right.)
HCl acts as an acid with water, donating a proton to form H₃O⁺ and Cl⁻. Identify the two conjugate acid-base pairs in this reaction and name the theory that defines them.
What is the Brønsted-Lowry theory? Pair 1: HCl (acid) / Cl⁻ (conjugate base). Pair 2: H₂O (base) / H₃O⁺ (conjugate acid). Each pair differs by exactly one proton.
At high pressure and low temperature, real gases deviate from ideal behavior because the ideal gas law ignores these two factors accounted for in the van der Waals equation.
What are the volume of gas molecules and intermolecular attractive forces?
For a first-order reaction with a rate constant k = 0.0250 min⁻¹, this is the half-life of the reaction in minutes.
What is approximately 27.7 minutes? (t₁/₂ = ln2 / k = 0.693 / 0.0250)
For a reaction with ΔH = +45 kJ/mol and ΔS = +150 J/mol·K, this is the minimum temperature in Kelvin above which the reaction becomes thermodynamically favorable.
What is 300 K? (Set ΔG = 0: T = ΔH/ΔS = 45,000 J / 150 J/K = 300 K. Above this T, ΔG becomes negative.)
For the reaction H₂(g) + I₂(g) ⇌ 2HI(g), Kc = 50.0 at a given temperature. At a particular moment, [H₂] = 0.20 M, [I₂] = 0.20 M, and [HI] = 0.80 M. This is the value of Q, and this is the direction the reaction must proceed to reach equilibrium.
What is Q = 16.0, and the reaction shifts to the right (forward)? (Q = (0.80)² / (0.20)(0.20) = 0.64/0.04 = 16.0. Since Q < K, the reaction proceeds forward to produce more HI.)
For a weak acid HA with Ka = 1.8 × 10⁻⁵, this is the approximate pH of a 0.10 M solution. (Hint: use the approximation [H⁺] ≈ √(Ka × C).)
What is pH ≈ 2.87? [H⁺] = √(1.8×10⁻⁵ × 0.10) = √(1.8×10⁻⁶) ≈ 1.34×10⁻³ M → pH = −log(1.34×10⁻³) ≈ 2.87
A solution measured in a 1.0 cm cuvette has an absorbance of 0.75. If the molar absorptivity (ε) is 150 L·mol⁻¹·cm⁻¹, this is the molar concentration of the solution, calculated using A = εbc.
What is 0.005 mol/L (5.0 × 10⁻³ M)? (c = A/εb = 0.75 / (150 × 1.0))
For a two-step reaction mechanism where step 1 is fast and reversible (A ⇌ B) and step 2 is slow (B + C → D), this is the overall rate law, expressed in terms of reactants only — not intermediates.
What is rate = k[A][C]? (B is an intermediate; substituting the equilibrium from step 1 gives rate = k[A][C])
In a galvanic cell, the standard reduction potential of Cu²⁺/Cu is +0.34 V and that of Zn²⁺/Zn is −0.76 V. Zinc serves as the anode. This is the standard cell potential E°cell, and this is the sign of ΔG°, confirming the reaction is spontaneous.
What is E°cell = +1.10 V, and ΔG° is negative? (E°cell = E°cathode − E°anode = 0.34 − (−0.76) = +1.10 V. A positive E°cell means ΔG° = −nFE° < 0, confirming spontaneity.)
The Ksp of silver chloride (AgCl) is 1.8 × 10⁻¹⁰. A solution already contains 0.10 M Cl⁻ ions from dissolved NaCl. Using an ICE table, this is the molar solubility of AgCl in this solution — and this is the name of the phenomenon responsible for the dramatic decrease compared to pure water.
What is 1.8 × 10⁻⁹ M, and the common ion effect? (AgCl ⇌ Ag⁺ + Cl⁻. Ksp = [Ag⁺][Cl⁻] = (x)(0.10 + x) ≈ (x)(0.10) = 1.8 × 10⁻¹⁰ → x = 1.8 × 10⁻⁹ M. Compare to pure water solubility of √(1.8 × 10⁻¹⁰) ≈ 1.3 × 10⁻⁵ M — a ~7,000× reduction!)
A buffer is prepared by mixing 0.20 mol of acetic acid (pKa = 4.74) and 0.10 mol of sodium acetate in 1.0 L of solution. Calculate the pH, and predict whether adding a small amount of strong acid will increase or decrease the pH.
What is pH ≈ 4.44, and the pH decreases? Using Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA]) = 4.74 + log(0.10/0.20) = 4.74 + log(0.5) = 4.74 − 0.30 ≈ 4.44. Adding strong acid consumes acetate (A⁻), shifting the ratio down and decreasing pH.
Although SO₂ and CO₂ have similar molar masses, SO₂ has a significantly higher boiling point of –10°C compared to CO₂'s –78.5°C. This specific difference in molecular geometry — and the type of intermolecular force it creates — is responsible for the disparity.
What is the fact that SO₂ is a bent molecule with a net dipole moment, giving it dipole-dipole forces, while CO₂ is linear and nonpolar, leaving it with only London dispersion forces?
For the reaction A + B → products, the following initial rate data is collected at constant temperature: Trial 1: [A] = 0.10 M, [B] = 0.10 M, rate = 2.0 × 10⁻³ M/s. Trial 2: [A] = 0.20 M, [B] = 0.10 M, rate = 8.0 × 10⁻³ M/s. Trial 3: [A] = 0.10 M, [B] = 0.20 M, rate = 4.0 × 10⁻³ M/s. This is the full rate law and the numerical value of the rate constant k with units.
What is rate = k[A]²[B], where k = 2.0 M⁻²s⁻¹? (Comparing trials 1 & 2: rate quadruples when [A] doubles → second order in A. Comparing trials 1 & 3: rate doubles when [B] doubles → first order in B. k = 2.0×10⁻³ / (0.10)²(0.10) = 2.0 M⁻²s⁻¹)
A nonspontaneous reaction has ΔG° = +38 kJ/mol at 298 K. It is coupled to ATP hydrolysis, which has ΔG° = −30 kJ/mol. This is the ΔG° of the coupled system, this is whether it is now spontaneous, and, using ΔG° = −RT ln K, this is the approximate equilibrium constant K for the coupled reaction. (R = 8.314 J/mol·K)
What is ΔG° = +8 kJ/mol, still nonspontaneous, and K ≈ 0.040? (ΔG°coupled = +38 + (−30) = +8 kJ/mol. Still > 0, so nonspontaneous. ln K = −ΔG°/RT = −8000/(8.314 × 298) ≈ −3.23 → K = e^−3.23 ≈ 0.040)
For the reaction: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), Kc = 280 at a certain temperature. If 0.40 mol of SO₂ and 0.30 mol of O₂ are placed in a 1.0 L container with no SO₃ initially present, this is the setup of the ICE table and the approximate equilibrium concentration of SO₃, using the small-x approximation.
The approximate equilibrium concentration of SO3 is 0.40 mol/L. Because the equilibrium constant K is very large, the reaction proceeds almost to completion.
To use the "small-x" approximation for a large K, assume the reaction goes to completion and then calculate the back-reaction (whatever tiny amount reforms)
If SO2 is fully consumed: 0.40 - 2x = 0; x = 0.20
If O2 is fully consumed: 0.30 - x = ); x = 0.30
This makes SO2 the limiting reactant so [SO2] = 2(0.20) = 0.40 M
A 50.0 mL sample of 0.100 M acetic acid (Ka = 1.8 × 10⁻⁵) is titrated with 0.100 M NaOH. At the equivalence point, only sodium acetate remains. Calculate the pH at this equivalence point.
What is pH ≈ 8.72? At equivalence: [CH₃COO⁻] = 0.0500 M. Kb = Kw/Ka = 1×10⁻¹⁴/1.8×10⁻⁵ ≈ 5.56×10⁻¹⁰. [OH⁻] = √(Kb × C) = √(5.56×10⁻¹⁰ × 0.0500) ≈ 5.27×10⁻⁶ M. pOH ≈ 5.28 → pH ≈ 8.72 (≈8.7–8.9 accepted).