At a particular temperature, K = 3.75 for the following reaction.
SO2(g) + NO2(g) SO3(g) + NO(g)
If all four gases had initial concentrations of 0.870 M, calculate the equilibrium concentrations of the gases.
First you must determine Q in order to know which way the reaction will move.
Qrxn = (NO)(SO3)/(SO2)(NO2) = 1.00 so the reaction will move to the right.
............SO2 + NO2 ==> SO3 + NO
initial....0.870.0.870..0.870..0.870
change.....-x.....-x.....x.....x
equil.....0.870-x etc.
Substitute from the ICE chart above into K expression and solve for x, then evaluate the concns of each gas.
To calculate the equilibrium concentrations of the gases, we need to use the equilibrium constant expression and the given equilibrium constant value.
The equilibrium constant expression for the reaction is given by:
K = [SO3][NO] / [SO2][NO2]
Given that K = 3.75, and the initial concentration of all four gases is 0.870 M, we can assume that at equilibrium, the change in concentration of each of the gases will be x M.
Therefore, the equilibrium concentrations for the gases can be represented as follows:
[SO2] = 0.870 - x
[NO2] = 0.870 - x
[SO3] = x
[NO] = x
Substituting these equilibrium concentrations into the equilibrium constant expression, we have:
3.75 = ([SO3][NO]) / ([SO2][NO2])
3.75 = (x * x) / ((0.870 - x) * (0.870 - x))
Now, we can solve this equation to find the value of x, which represents the change in concentration of the gases at equilibrium.
Multiply both sides of the equation by (0.870 - x)^2:
3.75 * (0.870 - x)^2 = x^2
Expand:
3.25275 - 7.5x + 3.75x^2 = x^2
Rearrange the equation:
2.75x^2 - 7.5x + 3.25275 = 0
Now, we can solve this quadratic equation for x to find the change in concentration of the gases at equilibrium. This can be done using the quadratic formula or by factoring.
Once the value of x is determined, you can substitute it back into the equilibrium concentration expressions to find the equilibrium concentrations of the gases [SO2], [NO2], [SO3], and [NO].