Physical chemistry

State the relative charge and relative mass of an electron.

A particle contains 15 protons, 16 neutrons and 18 electrons. State its overall charge and identify which particles are in its nucleus.

The nucleus of an atom has charge $2.08\times10^{-18}\,\mathrm{C}$. Use the proton charge $1.60\times10^{-19}\,\mathrm{C}$ to determine the number of protons. The atom gains two electrons; state the resulting ion charge and its number of electrons.

For the ion $^{81}_{35}\mathrm{Br^-}$, give its proton count, neutron count and electron count.

An element has two isotopes, $^{50}\mathrm{Q}$ with abundance $73.0\%$ and $^{52}\mathrm{Q}$ with abundance $27.0\%$. Calculate the relative atomic mass of Q.

In a TOF mass spectrometer, singly charged $^{64}\mathrm{X^+}$ ions take $1.280\times10^{-5}\,\mathrm{s}$ to reach the detector. Another singly charged isotope of X takes $1.339\times10^{-5}\,\mathrm{s}$. All ions receive the same kinetic energy. Use $t\propto\sqrt{m/z}$ to deduce the mass number of the second isotope.

Write the electron configuration, in sub-shell notation, of $\mathrm{S^{2-}}$. Sulfur has atomic number 16.

Define first ionisation energy and write an equation, including state symbols, for the first ionisation of magnesium.

Element X is in Period 3. Its first five ionisation energies, in $\mathrm{kJ\,mol^{-1}}$, are 780, 1580, 3260, 4380 and 16050. Deduce the group and identity of X, write its outer electron configuration, and write an equation for its fifth ionisation.

Calculate the relative molecular mass of urea, $\mathrm{CO(NH_2)_2}$. Use $A_r$: H $=1.0$, C $=12.0$, N $=14.0$, O $=16.0$.

Calculate the relative formula mass of $\mathrm{MgSO_4\cdot7H_2O}$. Use $A_r$: H $=1.0$, O $=16.0$, Mg $=24.3$, S $=32.1$.

An ionic oxide has formula $\mathrm{X_2O_3}$ and relative formula mass 144.1. Element X contains only isotopes $^{47}\mathrm{X}$ and $^{49}\mathrm{X}$. Calculate $A_r(\mathrm{X})$ and the percentage abundance of $^{47}\mathrm{X}$. Use $A_r(\mathrm{O})=16.0$.

Calculate the amount, in moles, in $5.30\,\mathrm{g}$ of $\mathrm{Na_2CO_3}$. Use $M_r=106.0$.

A sample contains $0.0125\,\mathrm{mol}$ of oxygen molecules. Calculate the number of $\mathrm{O_2}$ molecules. Use $N_A=6.02\times10^{23}\,\mathrm{mol^{-1}}$.

$18.0\,\mathrm{cm^3}$ of $0.250\,\mathrm{mol\,dm^{-3}}$ aluminium sulfate solution contains fully dissociated $\mathrm{Al_2(SO_4)_3}$. Calculate the number of sulfate ions present. Use $N_A=6.02\times10^{23}\,\mathrm{mol^{-1}}$.

$0.100\,\mathrm{mol}$ of gas occupies $2.49\times10^{-3}\,\mathrm{m^3}$ at $300\,\mathrm{K}$. Calculate its pressure. Take $R=8.31$.

Calculate the volume occupied by $0.0350\,\mathrm{mol}$ of an ideal gas at $315\,\mathrm{K}$ and $105\,\mathrm{kPa}$. Give the answer in $\mathrm{dm^3}$. Take $R=8.31$.

A $0.318\,\mathrm{g}$ sample of a volatile liquid forms $85.0\,\mathrm{cm^3}$ of vapour at $98.0\,\mathrm{kPa}$ and $373\,\mathrm{K}$. Calculate its molar mass. Take $R=8.31$.

A compound contains $2.70\,\mathrm{g}$ of aluminium and $2.40\,\mathrm{g}$ of oxygen. Determine its empirical formula. Use $A_r$: Al $=27.0$, O $=16.0$.

A compound is $54.5\%$ carbon, $9.1\%$ hydrogen and $36.4\%$ oxygen by mass. Its $M_r$ is 88. Determine its empirical and molecular formulae. Use $A_r$: H $=1.0$, C $=12.0$, O $=16.0$.

Complete combustion of $0.900\,\mathrm{g}$ of a compound containing only carbon, hydrogen and oxygen produces $1.320\,\mathrm{g}$ of $\mathrm{CO_2}$ and $0.540\,\mathrm{g}$ of $\mathrm{H_2O}$. The compound has $M_r=150$. Determine its molecular formula. Use $A_r$: H $=1.0$, C $=12.0$, O $=16.0$.

Balance the equation $\mathrm{C_3H_8+O_2\rightarrow CO_2+H_2O}$ using the smallest whole-number coefficients.

$25.0\,\mathrm{cm^3}$ of $0.150\,\mathrm{mol\,dm^{-3}}$ hydrochloric acid reacts with excess calcium carbonate: $\mathrm{CaCO_3+2HCl\rightarrow CaCl_2+CO_2+H_2O}$. Calculate the maximum mass of calcium carbonate that can react. Use $M_r(\mathrm{CaCO_3})=100.1$.

Urea is made by $\mathrm{2NH_3+CO_2\rightarrow CO(NH_2)_2+H_2O}$. A process uses $85.0\,\mathrm{kg}$ of ammonia and $132\,\mathrm{kg}$ of carbon dioxide. Determine the limiting reactant, the maximum mass of urea, the percentage atom economy for urea and the percentage yield if $126\,\mathrm{kg}$ is obtained. Use molar masses in $\mathrm{kg\,kmol^{-1}}$: $\mathrm{NH_3}=17.0$, $\mathrm{CO_2}=44.0$, urea $=60.0$, $\mathrm{H_2O}=18.0$.

Write the formula of aluminium sulfate from $\mathrm{Al^{3+}}$ and $\mathrm{SO_4^{2-}}$ ions.

Explain the nature of ionic bonding in magnesium oxide.

An element X forms the ionic compound $\mathrm{X_2(CO_3)_3}$. Deduce the charge on the X ion, then write the formulae of its nitrate and hydroxide. Nitrate is $\mathrm{NO_3^-}$ and hydroxide is $\mathrm{OH^-}$.

State what is meant by a single covalent bond.

$\mathrm{BCl_3}$ accepts a lone pair from $\mathrm{NH_3}$. Represent the dative covalent bond in the product and state which atom donates the electron pair.

Ammonia reacts with a proton to form ammonium. Write an equation for the reaction, show the direction of dative-bond formation, and explain why all four N-H bonds in the ammonium ion are equivalent after formation.

Complete the definition of metallic bonding.

Explain why a metal conducts electricity when solid and remains conductive when molten.

Magnesium has a higher melting point than sodium. Explain this difference using metallic bonding and the electron configurations $\mathrm{Na:[Ne]3s^1}$ and $\mathrm{Mg:[Ne]3s^2}$.

Iodine forms crystals containing discrete $\mathrm{I_2}$ molecules. State the type of crystal structure and the attractions overcome when iodine melts.

Graphite has a high melting point and conducts electricity parallel to its layers. Explain both properties in terms of its structure and bonding.

Three crystalline solids have these properties. A: high melting point, does not conduct when solid, conducts when molten. B: low melting point, never conducts. C: conducts when solid and is malleable. Deduce the structure type of A, B and C and justify each choice.

State the shape and bond angle of $\mathrm{BF_3}$ around the boron atom.

Use electron-pair repulsion theory to explain the shape of $\mathrm{NH_3}$ and its H-N-H bond angle of $107^{\circ}$.

The ion $\mathrm{BrF_4^-}$ has four Br-F bonding pairs. Deduce the number of lone pairs on Br, the arrangement of all electron pairs, the molecular shape and the F-Br-F bond angles.

The electronegativities of hydrogen and chlorine are $2.2$ and $3.2$, respectively. Add the correct partial charge to each atom in an $\mathrm{H-Cl}$ bond.

Both $\mathrm{CO_2}$ and $\mathrm{SO_2}$ contain polar bonds. Explain why only one of these molecules has a permanent dipole.

Fluorine is more electronegative than carbon. Compare the polarity of tetrahedral $\mathrm{CF_4}$ and tetrahedral $\mathrm{CH_3F}$, referring to bond dipoles and molecular shape.

State the strongest type of intermolecular force between $\mathrm{CH_3Cl}$ molecules.

Explain why ethane, $\mathrm{C_2H_6}$, has a higher boiling point than methane, $\mathrm{CH_4}$.

Explain why water has a much higher boiling point than $\mathrm{H_2S}$ and why solid water is less dense than liquid water.

A reaction transfers $38\,\text{kJ}$ of heat from the reacting chemicals to the surroundings. State whether the reaction is exothermic or endothermic and give the sign of $\Delta H$.

Define standard enthalpy of formation and standard enthalpy of combustion. Include the amount of substance and the required conditions in each definition.

Complete combustion of $0.250\,\text{mol}$ of a liquid releases $222\,\text{kJ}$ under standard conditions. Calculate its standard enthalpy of combustion.

A $100\,\text{g}$ sample of water warms by $6.5\,\text{K}$. Use $c=4.18\,\text{J g}^{-1}\text{K}^{-1}$ to calculate the heat gained by the water.

Equal $50.0\,\text{cm}^3$ portions of hydrochloric acid and sodium hydroxide are combined. Each solution has concentration $1.00\,\text{mol dm}^{-3}$, and the temperature rises by $6.80\,\text{K}$. Assume density $=1.00\,\text{g cm}^{-3}$ and $c=4.18\,\text{J g}^{-1}\text{K}^{-1}$. Calculate the enthalpy change per mole of water formed.

Burning $0.720\,\text{g}$ of propan-1-ol, $\mathrm{C_3H_8O}$, heats $250\,\text{g}$ of water by $18.4\,\text{K}$. Use $c=4.18\,\text{J g}^{-1}\text{K}^{-1}$ and $M_r(\mathrm{C_3H_8O})=60.0$. Calculate the experimental enthalpy of combustion and suggest one reason its magnitude is lower than the accepted value.

For the changes $\mathrm{A\rightarrow B}$ and $\mathrm{B\rightarrow C}$, the enthalpy changes are $+25\,\text{kJ mol}^{-1}$ and $-80\,\text{kJ mol}^{-1}$. Calculate the enthalpy change for $\mathrm{A\rightarrow C}$.

Use $\Delta_\mathrm{f}H^\circ[\mathrm{SO_2(g)}]=-297\,\text{kJ mol}^{-1}$ and $\Delta_\mathrm{f}H^\circ[\mathrm{SO_3(g)}]=-396\,\text{kJ mol}^{-1}$ to calculate $\Delta_\mathrm{r}H^\circ$ for $\mathrm{SO_2(g)+\tfrac12O_2(g)\rightarrow SO_3(g)}$.

The standard enthalpies of combustion of $\mathrm{C_3H_6(g)}$, $\mathrm{H_2(g)}$ and $\mathrm{C_3H_8(g)}$ are $-2058$, $-286$ and $-2220\,\text{kJ mol}^{-1}$, respectively. Use Hess's law to calculate the enthalpy change for $\mathrm{C_3H_6(g)+H_2(g)\rightarrow C_3H_8(g)}$.

Define the term mean bond enthalpy.

Use the mean bond enthalpies $E(\mathrm{H-H})=436$, $E(\mathrm{Cl-Cl})=243$ and $E(\mathrm{H-Cl})=431\,\text{kJ mol}^{-1}$ to estimate $\Delta H$ for $\mathrm{H_2(g)+Cl_2(g)\rightarrow2HCl(g)}$.

Estimate the enthalpy change for $\mathrm{C_2H_4(g)+H_2(g)\rightarrow C_2H_6(g)}$ using $E(\mathrm{C{=}C})=612$, $E(\mathrm{H-H})=436$, $E(\mathrm{C-C})=348$ and $E(\mathrm{C-H})=413\,\text{kJ mol}^{-1}$. Explain why a value obtained from standard formation enthalpies may differ.

Define activation energy.

Explain why most collisions between reactant particles do not produce a reaction.

A reacting mixture undergoes $2.0\times10^{10}$ molecular collisions each second. A fraction $4.0\times10^{-6}$ have at least the activation energy, and one quarter of these have a suitable orientation. Calculate the number of successful collisions per second and explain the role of the activation energy.

State the quantity represented on each axis of a Maxwell–Boltzmann distribution for a gas.

Describe how to add a higher-temperature curve to a Maxwell–Boltzmann distribution while keeping the number of gas molecules constant.

Two equal samples of the same gas are at temperatures $T_1$ and $T_2$, where $T_2>T_1$. A fixed energy $E^*$ lies in the high-energy tail, beyond the point where the two Maxwell–Boltzmann curves cross. Explain why the curves must cross and compare the fractions of molecules with energy greater than $E^*$.

State the effect of increasing temperature on the rate of a reaction, with all other conditions unchanged.

Use a Maxwell–Boltzmann distribution to explain why a small temperature increase can cause a large increase in reaction rate.

In the first $10.0\,\text{s}$ of a reaction, $8.4\,\text{cm}^3$ of gas forms at $25\,^{\circ}\text{C}$ and $14.1\,\text{cm}^3$ forms at $35\,^{\circ}\text{C}$. Calculate the factor by which the average rate over this interval increases, then explain the change using molecular energies.

State why increasing the concentration of a dissolved reactant usually increases reaction rate.

A gaseous reacting mixture is compressed to half its original volume at constant temperature. Explain why its reaction rate increases.

The concentration of one aqueous reactant is increased while temperature and all other concentrations are fixed. Explain why the rate changes, distinguishing the effect on collision frequency from any effect on activation energy or particle energy.

Define a catalyst.

Use a Maxwell–Boltzmann distribution to explain how a catalyst increases the rate of a gas-phase reaction at constant temperature.

An exothermic reaction has $\Delta H=-35\,\text{kJ mol}^{-1}$ and an uncatalysed forward activation energy of $145\,\text{kJ mol}^{-1}$. A catalyst lowers the forward activation energy to $82\,\text{kJ mol}^{-1}$. Calculate the reverse activation energy for each route and state why $\Delta H$ is unchanged.

State two features of a reversible reaction at dynamic equilibrium.

For $\mathrm{N_2(g)+3H_2(g)\rightleftharpoons2NH_3(g)}$, the forward reaction is exothermic. Predict the effect on the equilibrium yield of ammonia of increasing pressure, increasing temperature and adding a catalyst.

Sulfur trioxide is made by the exothermic equilibrium $\mathrm{2SO_2(g)+O_2(g)\rightleftharpoons2SO_3(g)}$. Explain why an industrial process may use a moderate temperature, a pressure that is not extremely high, and a catalyst.

Write the expression for $K_\mathrm{c}$ for $\mathrm{H_2(g)+I_2(g)\rightleftharpoons2HI(g)}$.

At equilibrium, $[\mathrm{H_2}]=0.200\,\text{mol dm}^{-3}$, $[\mathrm{I_2}]=0.300\,\text{mol dm}^{-3}$ and $[\mathrm{HI}]=1.20\,\text{mol dm}^{-3}$ for $\mathrm{H_2(g)+I_2(g)\rightleftharpoons2HI(g)}$. Calculate $K_\mathrm{c}$ and state its units.

For the exothermic equilibrium $\mathrm{A(g)+B(g)\rightleftharpoons2C(g)}$, a $2.00\,\text{dm}^3$ vessel initially contains $0.800\,\text{mol}$ of A, $0.600\,\text{mol}$ of B and no C. At equilibrium it contains $0.500\,\text{mol}$ of C. Calculate $K_\mathrm{c}$ and predict the effect of increasing temperature on its value.

Determine the oxidation state of manganese in $\mathrm{MnO_4^-}$.

Combine the half-equations $\mathrm{Fe^{2+}\rightarrow Fe^{3+}+e^-}$ and $\mathrm{Cl_2+2e^-\rightarrow2Cl^-}$ to give the overall redox equation.

In acidic solution, dichromate(VI) ions oxidise $\mathrm{Sn^{2+}}$ ions to $\mathrm{Sn^{4+}}$. Construct the overall ionic equation.

Define the lattice enthalpy of formation of $\mathrm{MgCl_2}$.

For $\mathrm{NaCl(s)}$, $\Delta_fH^\circ=-411\,\mathrm{kJ\,mol^{-1}}$. The atomisation enthalpy of sodium is $+108\,\mathrm{kJ\,mol^{-1}}$, half the chlorine bond enthalpy is $+121\,\mathrm{kJ\,mol^{-1}}$, the first ionisation energy of sodium is $+496\,\mathrm{kJ\,mol^{-1}}$ and the first electron affinity of chlorine is $-349\,\mathrm{kJ\,mol^{-1}}$. Calculate the lattice enthalpy of formation of $\mathrm{NaCl}$.

The lattice enthalpy of formation of $\mathrm{MgCl_2}$ is $-2526\,\mathrm{kJ\,mol^{-1}}$. The hydration enthalpies of $\mathrm{Mg^{2+}}$ and $\mathrm{Cl^-}$ are $-1920$ and $-364\,\mathrm{kJ\,mol^{-1}}$ respectively. Calculate the enthalpy of solution of $\mathrm{MgCl_2}$.

For a reaction, the total standard entropy of the products is $465\,\mathrm{J\,K^{-1}\,mol^{-1}}$ and that of the reactants is $392\,\mathrm{J\,K^{-1}\,mol^{-1}}$. Calculate $\Delta S^\circ$.

A reaction has $\Delta H=+42.0\,\mathrm{kJ\,mol^{-1}}$ and $\Delta S=+135\,\mathrm{J\,K^{-1}\,mol^{-1}}$. Calculate $\Delta G$ at $350\,\mathrm{K}$ and state whether the reaction is feasible at this temperature.

For a reaction, $\Delta G=+18.0\,\mathrm{kJ\,mol^{-1}}$ at $300\,\mathrm{K}$ and $\Delta G=-12.0\,\mathrm{kJ\,mol^{-1}}$ at $500\,\mathrm{K}$. Assume $\Delta H$ and $\Delta S$ are constant. Determine $\Delta H$, $\Delta S$ and the temperature at which the reaction first becomes feasible.

A reaction has rate equation $\text{rate}=k[A]^2[B]$. State the factor by which the rate changes when $[A]$ is halved and $[B]$ is doubled at constant temperature.

For $\text{rate}=k[A][B]^2$, the rate is $4.80\times10^{-4}\,\mathrm{mol\,dm^{-3}\,s^{-1}}$ when $[A]=0.200\,\mathrm{mol\,dm^{-3}}$ and $[B]=0.0500\,\mathrm{mol\,dm^{-3}}$. Calculate $k$ and give its units.

For this calculation use $R=8.31$. A reaction has rate constants $1.80\times10^{-3}\,\mathrm{s^{-1}}$ at $298\,\mathrm{K}$ and $7.20\times10^{-3}\,\mathrm{s^{-1}}$ at $318\,\mathrm{K}$. Calculate $E_a$ in $\mathrm{kJ\,mol^{-1}}$ from $\ln(k_2/k_1)=-(E_a/R)(1/T_2-1/T_1)$.

At constant temperature, doubling $[X]$ while all other concentrations remain unchanged doubles the initial rate. Deduce the order with respect to $X$.

Three invented kinetic trials gave these values. Trial 1: $[A]=0.100$, $[B]=0.200$, rate $=1.50\times10^{-4}$; trial 2: $[A]=0.200$, $[B]=0.200$, rate $=6.00\times10^{-4}$; trial 3: $[A]=0.200$, $[B]=0.400$, rate $=6.00\times10^{-4}$. Concentrations are in $\mathrm{mol\,dm^{-3}}$ and rates in $\mathrm{mol\,dm^{-3}\,s^{-1}}$. Deduce the rate equation and calculate $k$ with units.

The experimental rate equation for a reaction is $\text{rate}=k[X][Y]^2$. Mechanism I has a single slow step $\mathrm{X+Y\rightarrow products}$. Mechanism II has a fast equilibrium $\mathrm{X+Y\rightleftharpoons I}$ followed by the slow step $\mathrm{I+Y\rightarrow products}$. Determine which mechanism is consistent with the rate equation and explain your choice.

A gas mixture contains $2.00\,\mathrm{mol}$ of $A$ and $3.00\,\mathrm{mol}$ of $B$ at a total pressure of $500\,\mathrm{kPa}$. Calculate the partial pressure of each gas.

At equilibrium for $\mathrm{N_2O_4(g)\rightleftharpoons2NO_2(g)}$, there are $0.300\,\mathrm{mol}$ of $\mathrm{N_2O_4}$ and $0.400\,\mathrm{mol}$ of $\mathrm{NO_2}$ at a total pressure of $2.00\times10^2\,\mathrm{kPa}$. Calculate $K_p$, including units.

Initially, a vessel contains $1.00\,\mathrm{mol}$ of $\mathrm{H_2}$ and $1.00\,\mathrm{mol}$ of $\mathrm{I_2}$ for $\mathrm{H_2(g)+I_2(g)\rightleftharpoons2HI(g)}$. At equilibrium there are $1.20\,\mathrm{mol}$ of $\mathrm{HI}$ and the total pressure is $250\,\mathrm{kPa}$. Calculate $K_p$. State the effect of increasing the total pressure at constant temperature on the equilibrium position and on $K_p$.