8 g of Na and 48 g of Cl2 react according to 2Na + Cl2 → 2NaCl. What mass m of NaCl can form?
M(Na) = 22.99M(Cl2) = 70.9M(NaCl) = 58.44 g/mol
m = g
2.StoichiometryHard
In the reaction Fe2O3 + 3CO → 2Fe + 3CO2, 8 g of Fe2O3 reacts completely (the other reactants are in excess) and 4.1 g of CO2 is collected. Find the percent yield Y.
M(Fe2O3) = 159.69 g/molM(CO2) = 44.01 g/molactual: 4.1 g
Y = %
3.Molarity & dilutionMedium
You need 250 mL of 0.3 mol/L solution and have a 5 mol/L stock solution. What volume V1 of stock solution do you need?
c1 = 5 mol/Lc2 = 0.3 mol/LV2 = 250 mL
V1 = mL
4.Molarity & dilutionHard
250 mL of a 1 mol/L solution is mixed with 50 mL of a 2.5 mol/L solution of the same substance. Find the concentration c of the mixture (volumes are additive).
c1 = 1 mol/LV1 = 250 mLc2 = 2.5 mol/LV2 = 50 mL
c = mol/L
5.Ideal gas lawMedium
What volume V does 80 g of He occupy at 450 kPa and 25 °C? Treat it as an ideal gas.
A 200 g block of copper (c = 0.385 J/(g·°C)) at 170 °C is dropped into 200 g of water (c = 4.18 J/(g·°C)) at 25 °C in an insulated cup. Find the final temperature Tf.
0.5 mol/L of H₂ and 0.5 mol/L of I₂ are put in a container and react: H₂ + I₂ ⇌ 2HI, with Kc = 4. Find the equilibrium concentration [HI].
[H₂]₀ = [I₂]₀ = 0.5 mol/LKc = 4
[HI] = mol/L
10.Chemical equilibriumHard
PCl₅ decomposes: PCl₅ ⇌ PCl₃ + Cl₂, with Kc = 0.1 at the reaction temperature. A container starts with 0.25 mol/L of PCl₅ only. Find the equilibrium concentration [PCl5].
[PCl₅]₀ = 0.25 mol/LKc = 0.1
[PCl5] = mol/L
11.pH & buffersMedium
Find the pH pH of a 0.5 mol/L solution of lactic acid (Ka = 0.00014).
c = 0.5 mol/LKa = 0.00014
pH =
12.pH & buffersHard
A buffer contains 0.2 mol/L hydrofluoric acid and 0.1 mol/L of its sodium salt. Ka = 0.00068. Find the pH pH of the buffer.
[HA] = 0.2[A⁻] = 0.1Ka = 0.00068
pH =
13.Reaction kineticsMedium
A second-order reaction (−rA = k·CA²) in a batch reactor has k = 0.8 L/(mol·min) and starts at 2 mol/L. How long does it take to reach 50% conversion? Find t.
k = 0.8 L/(mol·min)CA0 = 2 mol/LX = 50 %
t = min
14.Reaction kineticsHard
A first-order reaction has k = 0.005 min⁻¹ at 25 °C and an activation energy of 80 kJ/mol. The batch reactor is now run at 45 °C for 45 min. Find the conversion X reached.
Stoichiometry: a balanced equation counts particles, not grams. Convert mass to moles with n = m/M, use the coefficients of the equation as the mole ratio, then convert back with m = n·M. With two reactants, the limiting reactant is the one that runs out first and fixes how much product forms.
Moles of each reactant
n(Na) = 8/22.99 = 0.348 mol
n(Cl2) = 48/70.9 = 0.677 mol
Limiting reactant
0.348/2 = 0.174, 0.677/1 = 0.677 → Na
Mass of product
n(NaCl) = 0.174·2 = 0.348 mol
m = 0.348·58.44 = 20.34 g
Answer
m = 20.34 g
2.Stoichiometry
Answer: Y = 61.99 %
Stoichiometry: a balanced equation counts particles, not grams. Convert mass to moles with n = m/M, use the coefficients of the equation as the mole ratio, then convert back with m = n·M. With two reactants, the limiting reactant is the one that runs out first and fixes how much product forms.
Theoretical yield
n(Fe2O3) = 8/159.69 = 0.0501 mol
m = 0.0501·3/1·44.01 = 6.614 g
Percent yield
Y = 4.1/6.614·100 = 61.99%
Answer
Y = 61.99%
3.Molarity & dilution
Answer: V1 = 15 mL
Molarity: concentration c = n/V in mol/L, with n = m/M. Diluting adds solvent but not solute, so the number of moles stays the same: c₁·V₁ = c₂·V₂. When two solutions of the same solute are mixed, the moles add up and so do the volumes.
Volume of stock solution
V1 = c2·V2/c1 = 0.3·250/5 = 15 mL
Answer
V1 = 15 mL
4.Molarity & dilution
Answer: c = 1.25 mol/L
Molarity: concentration c = n/V in mol/L, with n = m/M. Diluting adds solvent but not solute, so the number of moles stays the same: c₁·V₁ = c₂·V₂. When two solutions of the same solute are mixed, the moles add up and so do the volumes.
Total amount
n = 1·250 + 2.5·50 = 375 mmol
Concentration of the mixture
c = 375/300 = 1.25 mol/L
Answer
c = 1.25 mol/L
5.Ideal gas law
Answer: V = 110.1 L
Ideal gas law: PV = nRT, with n = m/M.
Moles
n = 80/4.003 = 19.99 mol
T = 25 + 273.15 = 298.1 K
Volume
V = nRT/P = 19.99·8.314·298.1/450 = 110.1 L
Answer
V = 110.1 L
6.Ideal gas law
Answer: V2 = 22.96 L
Combined gas law: for a fixed amount of ideal gas, P1V1/T1 = P2V2/T2.
Absolute temperatures
T1 = 288.1 K, T2 = 463.1 K
Combined gas law
V2 = V1·(P1/P2)·(T2/T1) = 20·(250/350)·(463.1/288.1) = 22.96 L
Answer
V2 = 22.96 L
7.Calorimetry & enthalpy
Answer: Tf = 37.23 °C
Heat and enthalpy: heating a substance takes q = m·c·ΔT. In a calorimeter the heat lost by the hot object equals the heat gained by the cold one. The enthalpy change of a reaction follows from enthalpies of formation: ΔH° = ΣΔH°f(products) − ΣΔH°f(reactants), each multiplied by its coefficient.
Heat balance
200·0.385·(170 − Tf) = 200·4.18·(Tf − 25)
Solve for the final temperature
Tf = (77·170 + 836·25)/(77 + 836) = 37.23 °C
Answer
Tf = 37.23 °C
8.Calorimetry & enthalpy
Answer: ΔH° = −2802 kJ
Heat and enthalpy: heating a substance takes q = m·c·ΔT. In a calorimeter the heat lost by the hot object equals the heat gained by the cold one. The enthalpy change of a reaction follows from enthalpies of formation: ΔH° = ΣΔH°f(products) − ΣΔH°f(reactants), each multiplied by its coefficient.
Negative: the reaction gives off heat (exothermic).
9.Chemical equilibrium
Answer: [HI] = 0.5 mol/L
Chemical equilibrium: for aA + bB ⇌ cC + dD, the equilibrium constant is Kc = [C]c[D]d/([A]a[B]b), using concentrations at equilibrium. An ICE table (Initial, Change, Equilibrium) links the starting amounts to the equilibrium amounts through one unknown x, scaled by the coefficients.
Equilibrium expression
4 = (2x)²/(0.5 − x)²
Take the square root
2 = 2x/(0.5 − x) → x = 0.5·2/(2 + 2) = 0.25 mol/L
Equilibrium concentration
[HI] = 2x = 0.5 mol/L
Answer
[HI] = 0.5 mol/L
10.Chemical equilibrium
Answer: [PCl5] = 0.1342 mol/L
Chemical equilibrium: for aA + bB ⇌ cC + dD, the equilibrium constant is Kc = [C]c[D]d/([A]a[B]b), using concentrations at equilibrium. An ICE table (Initial, Change, Equilibrium) links the starting amounts to the equilibrium amounts through one unknown x, scaled by the coefficients.
Equilibrium expression
0.1 = x²/(0.25 − x) → x² + 0.1·x − 0.025 = 0
Solve the quadratic
x = (−0.1 + √(0.1² + 4·0.025))/2 = 0.1158 mol/L
Equilibrium concentration
[PCl₅] = 0.25 − 0.1158 = 0.1342 mol/L
Answer
[PCl5] = 0.1342 mol/L
11.pH & buffers
Answer: pH = 2.081
pH: pH = −log₁₀[H₃O⁺] and pOH = −log₁₀[OH⁻], with pH + pOH = 14 at 25 °C. Strong acids and bases ionise completely. A weak acid only partly: Ka = x²/(c − x), where x = [H₃O⁺]. A buffer of a weak acid and its conjugate base follows Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]).
Equilibrium
HA ⇌ H⁺ + A⁻: x mol/L of acid ionises.
Ka = x²/(0.5 − x) → x = 0.008297 mol/L
pH
pH = −log(0.008297) = 2.081
Answer
pH = 2.081
12.pH & buffers
Answer: pH = 2.866
pH: pH = −log₁₀[H₃O⁺] and pOH = −log₁₀[OH⁻], with pH + pOH = 14 at 25 °C. Strong acids and bases ionise completely. A weak acid only partly: Ka = x²/(c − x), where x = [H₃O⁺]. A buffer of a weak acid and its conjugate base follows Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]).
pKa
pKa = 3.167
Henderson–Hasselbalch
pH = 3.167 + log(0.1/0.2) = 2.866
Answer
pH = 2.866
13.Reaction kinetics
Answer: t = 0.625 min
Integrated rate laws: zero order: C = C₀ − kt (straight line, t½ = C₀/(2k)); first order: ln(C₀/C) = kt (t½ = ln 2/k); second order: 1/C − 1/C₀ = kt (t½ = 1/(kC₀)). Conversion X means C = C₀(1 − X).
Concentration at the end
CA = 2·(1 − 0.5) = 1 mol/L
Integrated second-order law
t = (1/CA − 1/CA0)/k = (1 − 0.5)/0.8 = 0.625 min
Answer
t = 0.625 min
14.Reaction kinetics
Answer: X = 81.93 %
Reaction rates: for a first-order reaction −dC/dt = kC, so C = C₀·e−kt and the half-life ln 2/k does not depend on concentration. For a second-order reaction 1/C = 1/C₀ + kt. The rate constant rises with temperature following Arrhenius: k = A·e−Ea/(RT).