Consider the reaction X2(g) ⟶2 X(g) . When a vessel initially containing 755 torr of X2 comes to

Consider the reaction X2(g) ⟶2 X(g) . When a vessel...

Consider the reaction $\mathrm{X}_{2}(g) \longrightarrow 2 \mathrm{X}(g) .$ When a vessel initially containing 755 torr of $\mathrm{X}_{2}$ comes to equilibrium at $298 \mathrm{K},$ the equilibrium partial pressure of $\mathrm{X}$ is 103 torr. The same reaction is repeated with an initial partial pressure of 748 torr of $X_{2}$ at 755 $\mathrm{K}$ ; the equilibrium partial pressure of $\mathrm{X}$ is 532 torr. Find $\Delta H^{\circ}$ for the reaction.

Key Concepts

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations or partial pressures of reactants and products remain constant over time. Understanding chemical equilibrium allows one to relate changes in conditions, such as temperature or pressure, to shifts in the equilibrium position.

Equilibrium Constant (Kp)

The equilibrium constant, expressed in terms of partial pressures (Kp) for gaseous reactions, quantifies the ratio of the product pressures to reactant pressures at equilibrium, each raised to the power of their stoichiometric coefficients. It provides a measure of the extent of a reaction at a given temperature, and changes in Kp with temperature can offer insights into the thermodynamic properties of the reaction.

Van't Hoff Equation

The van't Hoff equation describes the temperature dependence of the equilibrium constant. It connects the change in the natural logarithm of the equilibrium constant to the reciprocal of the temperature and the standard enthalpy change of the reaction. This relationship is pivotal in determining the reaction enthalpy (?H°) from experimental equilibrium data at different temperatures.

Standard Reaction Enthalpy (?H°)

The standard reaction enthalpy (?H°) represents the heat absorbed or released during a reaction carried out under standard conditions. It is a key thermodynamic parameter indicating whether a reaction is endothermic or exothermic. ?H° can be derived from the temperature dependence of the equilibrium constant using the van't Hoff equation, linking measurable equilibrium pressures with the heat change of the reaction.

Transcript

00:01 We have been provided in the given question a reaction in which x2 gets converted into 2x.

00:10 Basically, we are breaking the x2 molecule into 2x atoms.

00:14 And for this, we have to answer what will be the delta h.

00:19 Okay, that has been asked in the given question.

00:23 We have been provided first of all, initial pressure of our x2 to be 7 .15.

00:31 Tor okay and we have been provided pressure of x at equilibrium is equal to 103 tor okay these are at 298 kelvin and further we have been provided initial pressure is equals to 748 thor and pressure of x at itlobrium is equal to 532 thor and these are provided at 755 kelvin.

01:18 So to find the delta as we will need to find what is the value of equilibrium constant at both the two temperatures.

01:26 So we know that first of all if we see the reaction x2 get converted into 2x if its initial pressure is p .i.

01:36 And final becomes p .i minus alpha.

01:39 So this will be equals to 2 alpha.

01:41 Okay this will be equal to two alpha and we have been provided the value of two alpha for 298 kelvin okay for 298 kelvin over two alpha is equal to one zero three so alpha will be one zero three by two now with the help of this we can calculate the final pressure of x2 so that will be pi minus a alpha so our pi is 748 minus alpha so our pi is 748 minus alpha that is 1 .3 2 so this will come out to be 703 .5 thor.

02:17 Okay and equilibrium constant for this type of reaction is equals to x to the pressure of x to the power 2 divided by pressure of x2.

02:29 Okay, so over k1 that is the equilibrium constant at 298 kelvin, will come out to 103 whole square.

02:38 Okay, see how px pressure is 103.

02:42 So, 103 whole square divided by px2 final, which over which came out to be 703 .5.

02:49 So our equilibrium constant at 298 kelvin will come out to be 15 .08.

02:56 Okay.

02:57 Now our k2 at 755 kelvin, we can calculate using the same method...