<u>Answer:</u> The value of
is 0.044
<u>Explanation:</u>
We are given:
Initial moles of methane = ![4.10\times 10^{-2}mol=0.0410moles](https://tex.z-dn.net/?f=4.10%5Ctimes%2010%5E%7B-2%7Dmol%3D0.0410moles)
Initial moles of carbon tetrachloride = ![6.51\times 10^{-2}mol=0.0651moles](https://tex.z-dn.net/?f=6.51%5Ctimes%2010%5E%7B-2%7Dmol%3D0.0651moles)
Volume of the container = 1.00 L
Concentration of a substance is calculated by:
![\text{Concentration}=\frac{\text{Number of moles}}{\text{Volume}}](https://tex.z-dn.net/?f=%5Ctext%7BConcentration%7D%3D%5Cfrac%7B%5Ctext%7BNumber%20of%20moles%7D%7D%7B%5Ctext%7BVolume%7D%7D)
So, concentration of methane = ![\frac{0.0410}{1.00}=0.0410M](https://tex.z-dn.net/?f=%5Cfrac%7B0.0410%7D%7B1.00%7D%3D0.0410M)
Concentration of carbon tetrachloride = ![\frac{0.0651}{1.00}=0.0651M](https://tex.z-dn.net/?f=%5Cfrac%7B0.0651%7D%7B1.00%7D%3D0.0651M)
The given chemical equation follows:
![CH_4(g)+CCl_4(g)\rightleftharpoons 2CH_2Cl_2(g)](https://tex.z-dn.net/?f=CH_4%28g%29%2BCCl_4%28g%29%5Crightleftharpoons%202CH_2Cl_2%28g%29)
<u>Initial:</u> 0.0410 0.0651
<u>At eqllm:</u> 0.0410-x 0.0651-x 2x
We are given:
Equilibrium concentration of carbon tetrachloride = ![6.02\times 10^{-2}M=0.0602M](https://tex.z-dn.net/?f=6.02%5Ctimes%2010%5E%7B-2%7DM%3D0.0602M)
Evaluating the value of 'x', we get:
![\Rightarrow (0.0651-x)=0.0602\\\\\Rightarrow x=0.0049M](https://tex.z-dn.net/?f=%5CRightarrow%20%280.0651-x%29%3D0.0602%5C%5C%5C%5C%5CRightarrow%20x%3D0.0049M)
Now, equilibrium concentration of methane = ![0.0410-x=[0.0410-0.0049]=0.0361M](https://tex.z-dn.net/?f=0.0410-x%3D%5B0.0410-0.0049%5D%3D0.0361M)
Equilibrium concentration of ![CH_2Cl_2=2x=[2\times 0.0049]=0.0098M](https://tex.z-dn.net/?f=CH_2Cl_2%3D2x%3D%5B2%5Ctimes%200.0049%5D%3D0.0098M)
The expression of
for the above reaction follows:
![K_{eq}=\frac{[CH_2Cl_2]^2}{[CH_4]\times [CCl_4]}](https://tex.z-dn.net/?f=K_%7Beq%7D%3D%5Cfrac%7B%5BCH_2Cl_2%5D%5E2%7D%7B%5BCH_4%5D%5Ctimes%20%5BCCl_4%5D%7D)
Putting values in above expression, we get:
![K_{eq}=\frac{(0.0098)^2}{0.0361\times 0.0603}\\\\K_{eq}=0.044](https://tex.z-dn.net/?f=K_%7Beq%7D%3D%5Cfrac%7B%280.0098%29%5E2%7D%7B0.0361%5Ctimes%200.0603%7D%5C%5C%5C%5CK_%7Beq%7D%3D0.044)
Hence, the value of
is 0.044