IB Chemistry Standard Level Paper 1 May 2023 Study Notes

Stoichiometric Relationships and the Gas Laws

Molar mass is a fundamental physical property of a substance, defined as the mass of one mole of that substance. The standard units for molar mass are $g\,mol^{-1}$. This must be distinguished from the atomic mass unit (amu), which describes the mass of a single atom, or the gram (g), which is a unit of absolute mass. The molecular formula of a compound provides the actual numbers of atoms of each element present in a single molecule. In contrast, the empirical formula represents the simplest whole-number ratio of atoms in a substance. For example, in an experimental setup where zinc powder is heated in an open crucible to form zinc oxide, recording the initial mass of zinc and the final mass of the oxide allows a student to determine both the percentage composition of the product and its empirical formula. However, one cannot derive the molecular formula from this data alone, especially for ionic compounds like zinc oxide which exist in lattice structures rather than discrete molecules.

To calculate the molar mass ($M$) of a gas using experimental data, one must apply the ideal gas law equation, $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal gas constant ($8.31\,J\,K^{-1}\,mol^{-1}$), and $T$ is the absolute temperature in Kelvin. Since $n = \frac{\text{mass (m)}}{\text{molar mass (M)}}$, the formula can be rearranged to $M = \frac{mRT}{PV}$. When processing data such as a gas mass of $40.0\,g$, a volume of $220\,cm^3$, a temperature of $17\,^{\circ}C$, and a pressure of $98\,kPa$, several unit conversions are necessary. Temperature must be converted to Kelvin ($17 + 273 = 290\,K$) and volume must be converted from $cm^3$ to $dm^3$ or $m^3$ depending on the units of $R$ and $P$. Using standard SI units where pressure is in $kPa$ and volume is in $dm^3$, the setup to find the molar mass is $M = \frac{40.0 \times 8.31 \times 290}{98 \times 0.220}$.

Atomic Structure and the Periodic Table

In the Bohr model of the atom, the maximum number of electrons that can occupy a specific principal energy level ($n$) is determined by the formula $2n^2$. For the fourth energy level ($n = 4$), the maximum capacity is $2 \times (4)^2 = 32$ electrons. This accommodates the $s$, $p$, $d$, and $f$ sub-levels. The periodic table is organized into blocks based on these sub-levels: the s-block (Groups 1 and 2), the p-block (Groups 13 to 18), the d-block (transition metals), and the f-block (lanthanides and actinides). The period number of an element is a direct indicator of its highest occupied energy level. For instance, an element in Period 3 has its valence electrons in the third principal energy shell.

Subatomic particles can be determined from isotopic notation. For the ion $^{32}_{16}S^{2-}$, the atomic number (16) indicates there are 16 protons. The mass number (32) allows for the calculation of neutrons by subtracting the atomic number from the mass number ($32 - 16 = 16$ neutrons). Because it is a $2-$ ion, it has gained two electrons relative to its neutral state, resulting in $16 + 2 = 18$ electrons. Elements with specific electron configurations, such as $1s^2 2s^2 2p^3$, have five valence electrons. To reach a stable octet, these elements typically gain three electrons to form a $3-$ ion, characteristic of group 15 elements like nitrogen.

Chemical Bonding and Structure

Ionic substances are characterized by high melting points and specific electrical conductivity properties; they do not conduct electricity in a solid state but do so when molten (liquid) or dissolved in water, due to the mobility of ions. This is typical of an ionic lattice structure at standard conditions ($298\,K$ and $100\,kPa$). In group 1 of the periodic table, the melting points of the alkali metals decrease as one moves down the group. This trend occurs because the radius of the metal ion increases, which weakens the metallic bond between the delocalized electrons and the increasingly distant positive nuclei.

While many atoms follow the octet rule, some molecules contain central atoms with an incomplete octet. A primary example is Boron trifluoride ($BF_3$), where the central boron atom is stable with only six valence electrons. In terms of atmospheric chemistry, oxygen ($O_2$) and ozone ($O_3$) exhibit different bonding strengths. Oxygen ($O = O$) contains a double bond, which is stronger than the resonance-stabilized bonds in ozone (bond order of 1.5). Because the bond in oxygen is stronger, it requires more energy to break, thus oxygen absorbs higher frequency (shorter wavelength) ultraviolet (UV) radiation compared to ozone.

Energetics and Thermochemistry

The enthalpy of combustion ($\Delta H_c$) can be calculated using calorimetry data with the formula $q = mc\Delta T$, where $m$ is the mass of the substance being heated (usually water), $c$ is the specific heat capacity ($4.2\,J\,g^{-1}\,K^{-1}$ for water), and $\Delta T$ is the temperature change. To find the molar enthalpy in $kJ\,mol^{-1}$, the total heat energy ($q$) is divided by the number of moles of fuel burned and then converted from Joules to Kilojoules. For a scenario involving $75\,g$ of water, a temperature rise of $24\,^{\circ}C$, and $0.015\,mol$ of propan-1-ol, the calculation is $\Delta H = -\frac{75 \times 4.2 \times 24}{0.015 \times 1000}$. The negative sign indicates that combustion is an exothermic process.

Dissolution processes can be endothermic or exothermic. If the temperature of a solution decreases when a solid dissolves, the process is endothermic. On an enthalpy profile diagram, this is represented by the enthalpy of the aqueous product ($X(aq)$) being higher than the enthalpy of the solid reactant ($X(s)$). Activation energy and reaction pathways can be modified by catalysts. On an enthalpy profile, a dotted line that follows a lower energy path from reactants to products represents the use of a catalyst, which provides an alternative reaction route with a lower activation energy ($E_a$).

Chemical Kinetics and Equilibrium

The average kinetic energy ($KE$) of particles in a gas is directly proportional to the absolute temperature in Kelvin. This relationship is defined by the formula $KE = \frac{1}{2}mv^2$. If the absolute temperature of a gas is doubled, the average kinetic energy of the particles also increases by a factor of 2. In the study of chemical equilibrium, the reaction quotient ($Q$) measures the relative amounts of products and reactants at any given time. A very low value of $Q$ (e.g., $4.9 \times 10^{-3}$) indicates that the system has a low relative amount of products compared to reactants at that specific moment.

Acids, Bases, and Redox Processes

Neutralization reactions between an acid and a base produce a salt and water. For example, the reaction between nitric acid ($HNO_3$) and calcium hydroxide ($Ca(OH)_2$) yields calcium nitrate ($Ca(NO_3)_2$) and water ($H_2O$). According to the Brønsted–Lowry theory, a strong acid is an efficient proton donor. When a strong acid loses a proton, it forms a weak conjugate base. Redox chemistry involves the transfer of electrons, identified by changes in oxidation states. Oxidation of nitrogen occurs when its oxidation state increases, such as the conversion of ammonia ($NH_3$, where N is $-3$) to nitrogen gas ($N_2$, where N is $0$). In contrast, the reduction of nitrogen can be seen in the conversion of $NO_2$ to $NO$.

Chemical nomenclature for ionic compounds requires identifying the oxidation state of the metal. Copper(I) sulfide indicates that the copper ion has a $1+$ charge ($Cu^+$), while the sulfide ion has a $2-$ charge ($S^{2-}$), resulting in the chemical formula $Cu_2S$. In electrochemistry, an electrolytic cell is a device that converts electrical energy into chemical energy. These cells facilitate non-spontaneous reactions, meaning the reaction would not occur without an external power source.

Organic Chemistry

Organic compounds are categorized by their functional groups. An ether is characterized by an oxygen atom connected to two alkyl or aryl groups ($R-O-R'$), such as dimethyl ether ($CH_3OCH_3$). Within a homologous series, such as primary alcohols, the boiling point increases as the carbon chain length increases. This is due to the increase in the strength of London dispersion forces between the molecules, as there are more electrons and a larger surface area for temporary dipoles.

Benzene is a unique aromatic hydrocarbon that undergoes substitution reactions more readily than addition reactions. This preference is due to the resonance stabilization of the benzene ring; addition reactions would disrupt the stable delocalized pi-electron system. For identification of unsaturation, bromine water is used as a reagent. In the presence of an alkene like ethene ($C_2H_4$), the orange color of bromine water disappears as the bromine adds across the double bond, even in the dark.

Measurement, Data Processing, and Analysis

Accuracy in experimental science is assessed through percentage error calculations. The formula is $\text{Percentage Error} = |\frac{\text{Literature Value} - \text{Experimental Value}}{\text{Literature Value}}| \times 100$. For instance, if the experimental enthalpy of combustion is $-2100\,kJ\,mol^{-1}$ and the literature value is $-3500\,kJ\,mol^{-1}$, the error is $\frac{1400}{3500} \times 100 = 40\%$. Accuracy can be improved by repeating measurements to reduce the impact of random errors, such as the difficulty in judging the exact end-point of a titration. Systematic errors, such as an unzeroed balance or a consistently misread thermometer, are not improved by simple repetition. Finally, various analytical techniques serve specific purposes: Infra-red (IR) spectroscopy is primarily used to identify functional groups by measuring the vibrations of specific chemical bonds, while mass spectroscopy is used to determine molecular mass and structural fragments.