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Using this data,

2 NO(g) + Cl2(g) == 2 NOCl(g) Kc = 3.20 X 10-3

NO2(g) == NO(g) + ½ O2(g) Kc = 3.93

calculate a value for Kc for the reaction,

NOCl (g) + ½ O2 (g) == NO2 (g) + ½ Cl2 (g)

I do not understnad how I am suppose to use the Kc values given if they give you a new reaction??

NOCl+1/2 O2 is the same as
2NO+Cl2+1/2O2>>NO2+1/2 Cl2 if you work out the coefficents. Thus, you have a new K which is the product of the Kc's

So am I suppose to use the Kc values that are given??

yes.

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