Reactions & Rates
If a reaction has a rate constant (k) of 0.05 s⁻¹ and an initial concentration of reactant A of 0.2 M, what will be the concentration of A after 10 seconds?
Use the first-order reaction equation:
[A] = [A]₀ * e^(-kt)
[A] = 0.121
Define Le Chatelier's principle and give an example.
Le Chatelier's principle states that if a system in equilibrium is disturbed, it will shift to counteract the disturbance. An example is adding more reactants to a reaction, causing the equilibrium to shift towards the products.
Define pH and pKa in terms of acid-base chemistry. Also, calculate the pH of a 0.1 M hydrochloric acid (HCl) solution.
- pH is a measure of hydrogen ion concentration in a solution, while pKa is the negative logarithm of the acid dissociation constant (Ka), representing acid strength.
- pH = -log[H⁺] = 1
Explain the concept of Gibbs free energy (ΔG) and its relationship with spontaneity.
ΔG represents the energy available to do work in a system at constant temperature and pressure. A negative ΔG indicates a spontaneous process.
Define oxidation and reduction in terms of electron transfer.
Oxidation is the loss of electrons, while reduction is the gain of electrons.
OIL RIG
A reaction follows the rate law:
rate = k[A]²[B]
If the initial concentrations of A and B are both 0.1 M, calculate the rate constant (k) if the reaction rate is 0.02 M/s. Also, determine the order of this reaction.
Solve for k:
0.02 M/s = k(0.1 M)(2)(0.1 M)
k = 20 M2- s-1
Look at exponents and add to find the order of the reaction, which is 3.
Calculate the equilibrium constant (Kc) for the reaction: A + B ⟶ 3C, given that [A] = 0.1 M, [B] = 0.2 M, and [C] = 0.05 M at equilibrium.
Kc = [C]3 / [A][B]
Kc = 6.25×10−3M
Explain how a buffer solution resists changes in pH.
A buffer solution contains a weak acid and its conjugate base (or a weak base and its conjugate acid), which can neutralize added acids or bases, maintaining a relatively constant pH.
Calculate the change in Gibbs free energy (ΔG) for a reaction at 25°C with ΔH = -50 kJ/mol and ΔS = 100 J/mol∙K.
ΔG=ΔH−T⋅ΔS
ΔG=−79.8kJ/mol
Calculate the standard cell potential (E°cell) for the reaction:
Zn(s) + Cu²⁺(aq) ⟶ Zn²⁺(aq) + Cu(s)
Given:
E°(Zn²⁺/Zn) = -0.76 V
E°(Cu²⁺/Cu) = +0.34 V.
E°cell = E°(cathode) - E°(anode). Identify which half-reaction is the cathode and which is the anode based on standard reduction potentials. Larger reduction potential means more likely to be reduced.
E°cell = 0.34 V - (-0.76 V) = 1.10 V
Explain how temperature affects reaction rates using concepts of kinetics and activation energy.
By increasing temperature, more molecules have sufficient energy to overcome the activation energy (Ea). This leads to an increase in the rate of the reaction.
A solution at equilibrium with solid AgCl(s) has [Ag⁺] = 1 x 10⁻⁶ M and [Cl⁻] = 1.5 x 10⁻³ M. Calculate the Ksp for AgCl.
AgCl(s) ⇌ Ag+(aq) + Cl−(aq)
Ksp = [Ag+]×[Cl−] = 1.5×10−9 M2
Calculate the pH of a buffer solution containing 0.1 M acetic acid (CH₃COOH) and 0.05 M sodium acetate (CH₃COONa). Given: pKa of acetic acid = 4.76.
Use the Henderson-Hasselbalch equation:
pH = pKa + log([A⁻]/[HA])
pH = 4.76 + log(0.05/0.1)
pH = 4.46
A reaction has ΔH = -200 kJ/mol and ΔS = 150 J/mol∙K. Determine the temperature at which the reaction becomes spontaneous.
Use ΔG = ΔH - TΔS and set ΔG to zero to find the temperature where the reaction becomes spontaneous. WATCH UNITS!!
0 = -200000 J/mol - T(150 J/mol-K)
T = 1333 K
Calculate the equilibrium constant (K) for the reaction:
2Fe³⁺(aq) + 3Zn(s) ⟶ 2Fe(s) + 3Zn²⁺(aq) at 25°C
Given:
E°(Fe³⁺/Fe²⁺) = +0.77 V, E°(Zn²⁺/Zn) = -0.76 V.
Balanced Reaction:
2Fe3+(aq) + 3Zn(s) ⇌ 2Fe(s) + 3Zn2+(aq)
E°cell = E°(cathode) - E°(anode)
E°cell = 0.77 V - (-0.76 V) = 1.53 V
E°cell = (RT/nF) ln(K)
1.53 V = ( (8.314*298) / (2*96485) )ln(K)
K =
A solution contains 0.2 M HCOOH (formic acid) and 0.1 M NaHCOO (sodium formate). Calculate the pH before and after adding 0.01 moles of HCl to 1 liter of this solution. Given: pKa of formic acid = 3.75.
HCOOH + HCl ⇌ HCOO− + H3O+
First, calculate the pH of the buffer solution before the addition of HCl using the Henderson-Hasselbalch equation:
pH = pKa + log([A−]/[HA]) = 3.449
To calculate the pH after adding HCl, consider the change in concentration of formate ions ([HCOO-]) due to the reaction with HCl
[HCOO−]final= 0.1M − (0.01 mol HCl /1 L) = 0.09M
pHfinal = 3.75 + log(0.09/0.2) = 3.531
Balance the following redox reaction in acidic solution using the half-reaction method:
Cr2O72−+Fe2+→Cr3++Fe3+
6Fe2++Cr2O72−+14H+→2Cr3++7H2O+6Fe3+
The following reactions are coupled to produce a single of molecule A:
A ⟶ 2B + 3C K1 = 5.3 x 10-3
D ⟶ C K2 = 4.1 x 10-8
What is the Kc of the coupled reaction?
Finding the coupled reaction:
3D ⟶ 3C (K1)3 = 1.489 x 10-7
3C + 2B ⟶ A (K2)-1 = 2.439 x 107
3D + 2B ⟶ A
Kc = (1.489 x 10-7)(2.439 x 107) = 3.631
The reaction 2A + B <-> C was run with initial concentrations of [A]=0.275 M, [B]=0.525 M, and [C]=0 M. If [C] = 2.6 x 10-3 M at equilibrium, determine Gibbs free energy for the reaction at 298K.
deltaG=6.65 kJ/mol
Steps:
1. Fill out an ICE table
-From the table, you will find that [C] at equilibrium is x (x=2.6x10-3 M)
2. Find equilibrium concentrations from the ICE table and calculate K
3. Use deltaG=-RTlnK
A voltaic cell operates at 298 K with [Fe³⁺] = 0.1 M, [Fe²⁺] = 0.5 M, [Zn²⁺] = 1.0 M, and [Zn] = 0.1 M.
Calculate the cell potential (Ecell) using the standard reduction potentials:
E°(Fe³⁺/Fe²⁺) = +0.77 V, E°(Zn²⁺/Zn) = -0.76 V.
Use the Nernst equation with the given concentrations and standard reduction potentials to calculate Ecell under non-standard conditions.