H2 reacts with the halogens (X2) according to the reaction: H2(g)+X2(g) ⇌2 HX(g) where X2 can be

H2 reacts with the halogens (X2) according to the reaction:...

$\mathrm{H}_{2}$ reacts with the halogens $\left(\mathrm{X}_{2}\right)$ according to the reaction: $$\mathrm{H}_{2}(g)+\mathrm{X}_{2}(g) \rightleftharpoons 2 \mathrm{HX}(g)$$ where $\mathrm{X}_{2}$ can be $\mathrm{Cl}_{2}, \mathrm{Br}_{2}$, or $\mathrm{I}_{2}$. Use the thermodynamic data in Appendix IIB to calculate $\Delta H^{\circ}, \Delta S^{\circ}, \Delta G^{\circ}$, and $K_{\mathrm{p}}$ for the reaction between hydrogen and each of the three halogens. Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions more spontaneous or less spontaneous?

$\mathrm{H}_{2}$ reacts with the halogens $\left(\mathrm{X}_{2}\right)$ according to the reaction:
$$\mathrm{H}_{2}(g)+\mathrm{X}_{2}(g) \rightleftharpoons 2 \mathrm{HX}(g)$$
where $\mathrm{X}_{2}$ can be $\mathrm{Cl}_{2}, \mathrm{Br}_{2}$, or $\mathrm{I}_{2}$. Use the thermodynamic data in Appendix IIB to calculate $\Delta H^{\circ}, \Delta S^{\circ}, \Delta G^{\circ}$, and $K_{\mathrm{p}}$ for the reaction between hydrogen and each of the three halogens. Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions more spontaneous or less spontaneous?

Key Concepts

Enthalpy Change (?H)

This concept refers to the heat absorbed or released during a chemical reaction. It involves the energy required to break bonds in the reactants and the energy released upon forming bonds in the products. In exothermic reactions, energy is released (negative ?H), making the process potentially more favorable.

Entropy Change (?S)

Entropy measures the degree of disorder or randomness in a system. A change in entropy reflects how the reaction alters the microstates available to the system, particularly when the number of gas molecules changes. An increase in entropy (positive ?S) can help drive a reaction forward by favoring disorder.

Gibbs Free Energy (?G)

Gibbs free energy is a thermodynamic function defined by the equation ?G = ?H - T?S, which combines the effects of enthalpy and entropy at a given temperature. It is the key determinant of reaction spontaneity; a negative ?G indicates that the reaction proceeds spontaneously under standard conditions.

Equilibrium Constant (Kp)

The equilibrium constant quantifies the ratio of the concentrations or partial pressures of products to reactants at equilibrium and is directly related to the Gibbs free energy through the equation Kp = exp(–?G/RT). A larger Kp value generally indicates a more product-favored, or spontaneous, reaction under the given conditions.

Temperature Effects on Reaction Spontaneity

Temperature influences reaction spontaneity through its impact on the T?S term in the Gibbs free energy equation. Depending on the sign of ?S, an increase in temperature can either increase or decrease the spontaneity of a reaction. This relationship explains how thermal energy contributes to shifting the reaction equilibrium.

Bond Energy Differences

Differences in bond energies, particularly between different bonds formed and broken during a reaction, play a crucial role in determining the overall enthalpy change. Variations in bond strengths, such as those of hydrogen–halogen versus halogen–halogen bonds, largely account for differences in the reaction’s enthalpic favorability and directly affect the overall spontaneity of the process.

Transcript

00:01 Here we're going to calculate delta h, delta has delta g and k for this equation.

00:08 Replacing x with cl i in br.

00:11 I've already given the delta h and s values here.

00:15 So let's start with cl, which makes our equation h2 plus cl2 gives 2h cl.

00:28 So let's begin with calculating delta h with this equation.

00:37 Using the formula delta h is equal to summation in delta h of the products, minus summation and delta h of the reactors.

00:46 Beginning with a product, we have two moles of hcl, which is minus 92 .3, minus both our reactants have zero and ptl, so this is just zero, which gives us a the final value of minus 184 .6 kilojou.

01:12 Next calculating delta s, you have delta s is equal to summation and delta the products minus summation and delta s of the reactants.

01:23 Putting in our values, two moles of delta s is 186 .9 chou per kelvin mole, 9s are reactants, r130 points, 7 plus 2 to 3 .0 .0.

01:52 Kelvin and jail for kelvin because they only each have one more.

01:59 That gives us 20 choles for kelvin.

02:05 Next we're going to calculate the delta g using the delta h delta h and delta s values minus 184 .6 kilojoules minus 298 kelvin times 20 joules to kelvin, but we have a kilojole here and a joel here, so let's connect this into kilojole.

02:46 So our delta g value is minus 190 .6 kilojoule.

02:54 And finally, calculating for k, we know our delta g value could be minus 190 .6 kilojol, but r is in joules.

03:07 So i'm going to convert this by multiplying it by thousand.

03:13 We know that our value to be minus 8 .34.

03:17 Temperature was given to be 298 kelvin and we don't know what k is.

03:26 So calculating for k, it goes as a final value of 2 .57 into 10 to the power to be 3.

03:37 So we calculated at delta h, delta s, delta g and k values with c l2 now we're going to use the same method and equations to calculate for br and i so let's start with br h2 plus br gives to h br br starting with delta h same equation to br to br to each br starting with delta h same equation so 2 moles into minus 36 .3 per mole minus h20 .0 with br is br2 is 30 .9.

04:56 That gives us minus 103 .5.

05:03 Next we have delta s.

05:18 Delta s for hbr...

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