The value of K in the Equilibrium constant question?

Question

Ok the question is 2 mole of ethane and 4 mole of oxygen are mixed together in a 4 liter sealed container. At equilibrium it is found that 44 grams of carbon dioxide is present. What is the value of K?

The equation is 2 C2H6(g) + 7 O2(g) <==> 4 CO2(g) + 6 H2O(g)

I need to see where I need to go now or if i messed up or what?

I took them and got the moles of each and divide by 4

1.0 mole CO2 /4L = 0.25 M CO2 at equilibrium

1.5 mole H2O/4L= 0.375 M H2O at equilibrium

1.5 moles C2H6/4L = 0.375 M C2H6 at equilibrium

2.25 moles O2/4L = 0.563 at equilibrium

I know i need to divide CO2 4(exponent 4) times H2O 6 (exponent) divided by O2 7(exponent) C2H6 2(exponent) but i cant figure out the right answer. I hope it can be figured out how i have it, if not tell me. If its possible to help me out I would greatly appreciate it!

Thanks!

Answer 1

work in moles, then divide by 4 litres later to get molarity.

ratios: 2 C2H6 + 7 O2 &lt;==&gt; 4 CO2 + 6 H2O

it was: 2 moles &amp; 4 moles

but then the reaction shifted to the right using up some of the C2H6 &amp; O2 in order to make the 1 mole of CO2

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so lets find the number of moles of C2H6 lost:

making 1 mol CO2 @ 2 mol C2H6 / 4 mol CO2 = 0.5 mol C2H6 was lost,...

wich means that out of the 2 moles of C2H6, you have 1.5 moles left

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so lets find the number of moles of O2 lost:

making 1 mol CO2 @ 7 mol O2 / 4 mol CO2 = 1.75 mol O2 was lost,...

wich means that out of the 4 moles of O2, you have 2.25 moles left

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so lets find the number of moles of H2O made :

making 1 mol CO2 @ 6 mol H2O / 4 mol CO2 = 1.5 mol H2O was made,...

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next we find molarities

1.0 mole CO2 /4L =   0.25 M CO2 at equilibrium

1.5 mole H2O/4L  =   0.375 M H2O at equilibrium

1.5 moles C2H6/4L = 0.375 M C2H6 at equilibrium

2.25 moles O2/4L  =   0.563 M O2 at equilibrium

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K = [CO2]^4 [H2O]^6 / [C2H6]^2 [O2]^7

K = [0.25]^4 [0.375]^6 / [0.375]^2 [0.563]^7

so ,,,, to answer your question:

you do good work!!

K = [0.003906] [0.002781] / [0.1406] [0.01793]

K = [0.000010863] / [0.0025208]

K = 4.3092 e-3

now comes the real problem, how many significant digits were in the &quot;2&quot; moles, &quot;4&quot; moles, &amp; &quot;4&quot; litres

right now , I only see a 1 sig fig problem, so unless you have moe sig figs inthose numbers....

your answer is : 4e-3