Convert temperatures to Kelvin: T1 = 27 + 273 = 300 K, T2 = 127 + 273 = 400 K. By Charles's law V1/T1 = V2/T2, so V2 = V1 x T2/T1 = 300 x 400/300 = 400 mL.

V1/T1 = V2/T2

The ideal gas equation is PV = nRT, where P = pressure, V = volume, n = number of moles, T = absolute temperature and R = universal gas constant. R = 0.0821 L atm K^-1 mol^-1 = 8.314 J K^-1 mol^-1.

PV = nRT

Using PV = nRT, V = nRT/P = (2 x 0.0821 x 300) / 2 = 49.26/2 = 24.63 L.

V = nRT / P

1) A gas consists of a large number of tiny particles (molecules) whose actual volume is negligible compared with the volume of the container. 2) There are no forces of attraction or repulsion between the molecules. 3) The molecules are in constant, rapid, random motion and collide with one another and with the walls of the container. 4) The collisions are perfectly elastic (no loss of kinetic energy). 5) The average kinetic energy of the molecules is directly proportional to the absolute temperature.

KE(avg) proportional to T

The van der Waals equation is (P + a n^2/V^2)(V - nb) = nRT. The constant 'a' corrects for the intermolecular forces of attraction (it accounts for the pressure being lower than ideal), and the constant 'b' corrects for the finite volume actually occupied by the gas molecules (excluded volume). Real gases deviate from ideal behaviour at high pressure and low temperature.

(P + a n^2/V^2)(V - nb) = nRT

A system is the specified part of the universe under study; the surroundings are the rest of the universe outside the system that can interact with it. The three types are: open system (exchanges both matter and energy with surroundings), closed system (exchanges only energy, not matter) and isolated system (exchanges neither matter nor energy).

The first law of thermodynamics states that energy can neither be created nor destroyed, only transformed from one form to another; the total energy of an isolated system remains constant. Mathematically, delta U = q + w, where delta U is the change in internal energy, q is the heat added to the system (positive when absorbed) and w is the work done on the system (positive when done on the system).

delta U = q + w

Heat supplied to the system q = +1 kJ = +1000 J. Work is done BY the gas, so work done on the system w = -200 J. By the first law, delta U = q + w = 1000 + (-200) = 800 J. The internal energy increases by 800 J.

delta U = q + w

Enthalpy (H) is the total heat content of a system at constant pressure, defined as H = U + PV. For a reaction at constant pressure and temperature, delta H = delta U + P delta V. For ideal gases, P delta V = delta ng RT, where delta ng is the change in the number of moles of gaseous species. Hence delta H = delta U + delta ng RT.

delta H = delta U + delta ng RT

We want C(s) + 1/2 O2(g) -> CO(g). By Hess's law, subtract the second equation from the first: delta H(reqd) = delta H1 - delta H2 = (-393.5) - (-283.0) = -110.5 kJ. So the enthalpy of formation of CO is -110.5 kJ/mol.

delta H(reqd) = delta H1 - delta H2

Hess's law states that the total enthalpy change of a reaction is the same whether the reaction takes place in one step or in several steps, provided the initial and final conditions are the same. It follows from the fact that enthalpy is a state function. Applications: it is used to calculate enthalpies of formation, bond enthalpies and reaction enthalpies that cannot be measured directly.

Entropy (S) is a thermodynamic state function that measures the degree of randomness or disorder of a system. When ice (a highly ordered solid) melts into water (a more disordered liquid), disorder increases, so the entropy increases and delta S is positive.

delta S = q(rev) / T

The Gibbs energy change is given by delta G = delta H - T delta S. Criteria of spontaneity: if delta G < 0 (negative), the process is spontaneous; if delta G = 0, the system is at equilibrium; if delta G > 0 (positive), the process is non-spontaneous (the reverse is spontaneous). A reaction is always spontaneous when delta H is negative and delta S is positive.

delta G = delta H - T delta S

Convert delta S to kJ: -198 J/K = -0.198 kJ/K. delta G = delta H - T delta S = -92.4 - (298 x -0.198) = -92.4 - (-59.0) = -92.4 + 59.0 = -33.4 kJ. Since delta G is negative, the reaction is spontaneous at 298 K.

delta G = delta H - T delta S

Standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states (at 298 K and 1 bar); e.g. for CO2 it is -393.5 kJ/mol. Standard enthalpy of combustion is the enthalpy change when one mole of a substance is completely burnt in excess oxygen under standard conditions; it is always negative (exothermic).

A reversible reaction is one that proceeds in both forward and backward directions under the same conditions. Characteristics of chemical equilibrium: (1) it is dynamic in nature, i.e. the forward and backward reactions continue at equal rates; (2) the observable properties (concentration, pressure, colour) remain constant with time; (3) it can be attained from either direction and is disturbed by changing conditions.

rate(forward) = rate(backward)

Kc = [NH3]^2 / ([N2][H2]^3). The relation between Kp and Kc is Kp = Kc (RT)^(delta ng), where delta ng = (moles of gaseous products) - (moles of gaseous reactants). Here delta ng = 2 - (1 + 3) = -2, so Kp = Kc (RT)^-2.

Kp = Kc (RT)^(delta ng)

Kc = [NO2]^2 / [N2O4] = (0.04)^2 / 0.02 = 0.0016 / 0.02 = 0.08 mol/L. The units are mol/L because delta ng = 1 for this reaction.

Kc = [products]^coeff / [reactants]^coeff

Le Chatelier's principle states that if a system at equilibrium is subjected to a change in concentration, pressure or temperature, the equilibrium shifts in the direction that tends to counteract (reduce) the effect of that change. Increasing the pressure shifts this equilibrium in the forward direction (towards NH3), because the forward reaction reduces the number of gas moles from 4 (1 + 3) to 2, thereby lowering the pressure.

Temperature: increasing temperature favours the endothermic direction and decreasing temperature favours the exothermic direction (as per Le Chatelier's principle); temperature also changes the value of the equilibrium constant K. Catalyst: a catalyst speeds up both the forward and backward reactions equally, so it helps the system reach equilibrium faster but does not shift the position of equilibrium or change the value of K.