Use Hess's law and the reactions
1) CH 4(g)+ Cl 2 (g)--->CH 3 CL(g) + HCl (g)
2) CH 3 Cl (g) + Cl 2 (g)---> CH 2 Cl 2 (g) + HCl (g)
to determine the enthalpy for the reaction
CH4 (g) + 2CH 2 (g)---> CH2 Cl 2 (g) + 2HCl (g)?
I believe you have made a typo in the final equation. I don't think you can obtain equation 3 from 1 and 2. If you intended to write
CH4 + 2Cl2 ==> CH2Cl2 + 2HCl, then just add equation 1 to equation 2.
To determine the enthalpy for the reaction CH4(g) + 2CH2(g) ---> CH2Cl2(g) + 2HCl(g) using Hess's law, you need to use the given reactions and manipulate them in a way that allows you to cancel out certain species and combine the rest to obtain the desired reaction.
First, let's analyze the given reactions:
1) CH4(g) + Cl2(g) ---> CH3Cl(g) + HCl(g)
2) CH3Cl(g) + Cl2(g) ---> CH2Cl2(g) + HCl(g)
Now, we want to combine these reactions in a way that can cancel out CH3Cl and HCl to get the desired reaction. To do this, we can reverse reaction 1 and multiply it by 2 to cancel out CH3Cl:
-2(CH4(g) + Cl2(g) ---> CH3Cl(g) + HCl(g))
Then, we need to multiply reaction 2 by 1 to have the same number of moles for Cl2:
1(CH3Cl(g) + Cl2(g) ---> CH2Cl2(g) + HCl(g))
Now, let's add these two manipulated reactions together:
-2(CH4(g) + Cl2(g)) + 1(CH3Cl(g) + Cl2(g)) ---> CH2Cl2(g) + 2HCl(g)
Simplifying this equation, we get:
-2CH4(g) - 2Cl2(g) + CH3Cl(g) + Cl2(g) ---> CH2Cl2(g) + 2HCl(g)
Finally, we can cancel out the common species on both sides of the equation:
-2CH4(g) - 2Cl2(g) + CH3Cl(g) + Cl2(g) ---> CH2Cl2(g) + 2HCl(g)
-2CH4(g) - Cl2(g) + CH2Cl2(g) + 2HCl(g) ---> CH2Cl2(g) + 2HCl(g)
As a result, we are left with:
-2CH4(g) - Cl2(g) ---> CH2Cl2(g)
Now, we have successfully manipulated the given reactions to obtain the desired reaction. The coefficients in front of each species represent the stoichiometric coefficients, which also apply to the enthalpy change. Therefore, the enthalpy for the reaction CH4(g) + 2CH2(g) ---> CH2Cl2(g) + 2HCl(g) can be determined by summing up the enthalpy changes of the manipulated reactions:
Enthalpy = -2ΔH1 + ΔH2
Where ΔH1 is the enthalpy change for reaction 1 and ΔH2 is the enthalpy change for reaction 2.