The equilibrium 2 SO2(g) + O2(g) 2 SO3(g) has the value K = 2.5 1010 at 500. K. Find the value of K for each of the following reactions at the same temperature.

(a) SO2(g) + 1/2 O2(g) SO3(g)
K =

(b) SO3(g) SO2(g) + 1/2 O2(g)
K =

(c) 3 SO2(g) + 3/2 O2(g) 3 SO3(g)

I attempted to solve this by first finding Kc using the first equation given...I used Kc=K/ (RT)^delta n where delta n= gas products-gas reactants.

I found Kc to be 1.04E12 and then plugged that in to find K for each of the following reactions..however each of my answers was incorrect so I must not be doing this right.

No, that isn't the way to approach it.

For the reaction
A + B = C + D
Given that K = 25
For 2A + 2B = 2C + 2D
K = 252

For 1/2 A + 1/2B = 1/2 C + 1/2 D
K = 251/2

For C + D ==> A + B
K = 1/25
etc.
This should help.

ok. I was able to get the first two but my last one is incorrect. i keep solving it to equal 2.53E-16 by making that k= 1/(2.5E10)^1.5 Not sure why this is incorrect..I inverted the K since the rxn is reversed and then used the multiplier as the exponent

oop just realized the third one isn't reversed....DOH! Thanks DrBob

Right. It isn't reversed AND it is to the 3/2 power. .

To find the value of K for each of the given reactions at the same temperature, you can use the concept of equilibrium constants. The equilibrium constant (K) is defined as the ratio of the product concentrations to the reactant concentrations, each raised to the power of their respective stoichiometric coefficients.

Let's go through each reaction step-by-step:

(a) SO2(g) + 1/2 O2(g) <-> SO3(g)

In this reaction, the balanced equation shows that the stoichiometric coefficients are already in the ratio of 2:1. Therefore, no need for any adjustments or multiplication. The equilibrium constant, K, for this reaction can be directly obtained from the given equilibrium constant:

K(a) = K = 2.5 × 10^10

(b) SO3(g) <-> SO2(g) + 1/2 O2(g)

In this reaction, the balanced equation shows that the stoichiometric coefficients are in the ratio of 1:1, and 1:0.5, respectively. So, to relate the equilibrium constant of this reaction (K(b)) to the given equilibrium constant (K), we can make use of the fact that the equilibrium constant of a reverse reaction is the reciprocal of the equilibrium constant of the forward reaction.

K(b) = 1 / K = 1 / (2.5 × 10^10) = 4 × 10^(-11)

(c) 3 SO2(g) + 3/2 O2(g) <-> 3 SO3(g)

For this reaction, the balanced equation shows that the stoichiometric coefficients are in the ratio of 2:3, and 3:3, respectively. So to relate the equilibrium constant of this reaction (K(c)) to the given equilibrium constant (K), we can use a power rule. The equilibrium constant (K(c)) for this reaction will be the given equilibrium constant (K) raised to the power of the change in the number of moles of gas particles:

delta n = (3 moles of gas products) - (3 + 3/2 moles of gas reactants) = 3 - (3 + 1.5) = 3 - 4.5 = -1.5

K(c) = K^(-delta n) = (2.5 × 10^10)^(-(-1.5)) = (2.5 × 10^10)^(1.5) = 2.82 × 10^(-11)

So, the values of K for the given reactions at the same temperature (500 K) are:

(a) K(a) = 2.5 × 10^10
(b) K(b) = 4 × 10^(-11)
(c) K(c) = 2.82 × 10^(-11)