Calculate ΔHrxn for the reaction: CH4(g)+4 Cl2(g) ⟶CCl4(g)+4 HCl(g) Use the following reactions

Calculate ΔHrxn for the reaction: CH4(g)+4 Cl2(g) ⟶CCl4(g)+4...

Calculate $\Delta H_{\mathrm{rxn}}$ for the reaction: $$ \mathrm{CH}_{4}(g)+4 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+4 \mathrm{HCl}(g) $$ Use the following reactions and given $\Delta H^{\prime} s :$ $$ \begin{array}{ll}{\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{4}(g)} & {\Delta H=-74.6 \mathrm{kJ}} \\ {\mathrm{C}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)} & {\Delta H=-95.7 \mathrm{kJ}} \\ {\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g)} & {\Delta H=-92.3 \mathrm{kJ}}\end{array} $$

Calculate $\Delta H_{\mathrm{rxn}}$ for the reaction:
$$
\mathrm{CH}_{4}(g)+4 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+4 \mathrm{HCl}(g)
$$
Use the following reactions and given $\Delta H^{\prime} s :$
$$
\begin{array}{ll}{\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{4}(g)} & {\Delta H=-74.6 \mathrm{kJ}} \\ {\mathrm{C}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)} & {\Delta H=-95.7 \mathrm{kJ}} \\ {\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g)} & {\Delta H=-92.3 \mathrm{kJ}}\end{array}
$$

Key Concepts

State Function

Enthalpy is a state function, meaning its change depends only on the initial and final states of the system, not on the specific pathway taken. This property underlies the validity of Hess's Law and justifies combining different thermochemical equations to calculate overall reaction enthalpy.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same no matter how the reaction occurs in steps. This principle allows the use of known enthalpy changes from multiple reactions to determine the enthalpy change of an overall reaction by algebraically adding, reversing, or scaling the provided reaction equations.

Thermochemical Equation Manipulation

Manipulating thermochemical equations involves processes such as reversing reactions, multiplying entire reactions by coefficients, and adding or subtracting reactions to form a target reaction. When a reaction is reversed, the sign of its enthalpy change is also reversed; when scaled, the enthalpy change is multiplied by the same factor. These techniques are essential for applying Hess's Law.

Transcript

0:00 Right.

00:01 So for this problem, we got to form one reaction out of a combination of three others.

00:06 So this is a classic has -as -law problem.

00:10 The eventual, what we want to get to eventually, well, let's go ahead and run through the problem first, but we want to eventually get to ch4 of methane plus four molecules of chlorine gas, going to carbon tetrachloride plus four molecules.

00:31 Of hydrogen chloride.

00:33 So that's what we eventually want to go to.

00:36 So let's start piecing together our equations here.

00:41 So we know we want the methane or ch4 on the left.

00:48 So the first thing we should probably let's go ahead and start there.

00:51 One equation that involves ch4 is the one that looks like carbon plus hydrogen yielding ch4, but the ch4 is on the product side in that one.

01:03 So let's flip it so that it's on the reactant side.

01:06 So after we flip it, we get ch4 yields carbon plus two molecules of hydrogen gas.

01:16 And because we flipped the products and reactants, the change of enthalpy of this reaction is now equal to, let me just emphasize this, positive 74 .4.

01:30 0 .6 kilojoules.

01:34 Lovely.

01:37 Where the ch4 on the left is something that we wanted.

01:40 So now let's look at the next piece of our puzzle.

01:44 We've got the ch4.

01:46 What about the 4 cl2s? well, this one's a little bit tougher because two of our possible chemical equations involve chlorine gas.

01:54 And so should we use one of them and multiply it by four? should we use both of them? it's a little unclear how to go from this point.

02:01 So let's skip this one and go on to ccl4, carbon tetrachloride.

02:09 That only appears in one of our equations, so that's a good place to start.

02:14 Anytime you have something like the chlorine gas and it has multiple different options, skip it, come back to it later, it'll all work out in the end.

02:23 But i know the carbon tetrachloride only has one equation.

02:26 So carbon tetrachloride, a nice thing is it's already sort of set up for us.

02:31 So the equation is c plus 2cl2 yields c, cl4.

02:41 And it's already on the right hand side.

02:43 It's already on the product side.

02:44 Already has the correct stoichiometric number, right number of molecules.

02:48 And so it's just the exact same.

02:51 Negative 95 .7.

02:55 Kill the jewels.

02:56 Lovely.

02:58 Now, let's look at the four units of hydrogen chloride.

03:03 Again, we've only got one option here.