The equilibrium constant, Keq, for the reaction:
SO3(g) + NO (g) ⇋ NO2 (g) + SO2 (g)
was found to be 0.500 at a certain temperature. If 0.300 mol of SO3 and 0.300 mol NO were placed in a 2.00 L container and allowed to react, what would be the equilibrium concentration of each gas?
(SO2) = 0.300 mol/2.00 L = 0.150 = (NO)
....................SO3(g) + NO (g) ⇋ NO2 (g) + SO2 (g)
I..................0.150 ......0.150............0..............0
C...................-x..............-x...............x..............x
E...............0.150-x.....0.150-x...........x...............x
Keq = 0.500 = (NO2)(SO2)/(SO3)(NO)
Substitute the E line into the Keq expression and solve for x, then evaluate each material. Post your work if you get stuck.
Well, well, well, it looks like we have a fun equilibrium problem here! Alright, let's dive in and see what's cooking.
So, based on the equation given, we have SO3, NO, NO2, and SO2 doing a little dance inside the container. And the equilibrium constant, Keq, tells us about the ratio of the concentrations at equilibrium.
Now, let's do some math magic! Since we have the initial amounts of SO3 and NO, we can first figure out how much of the reactants will react.
Let's call the change in concentration of SO3 "x." That means the concentration of SO3 at equilibrium will be 0.300 - x. Similarly, the concentration of NO at equilibrium will be 0.300 - x.
According to the balanced equation, the concentrations of NO2 and SO2 formed will be x each (since the stoichiometry is 1:1).
Now, we have the equilibrium concentrations. Hooray! But wait, there's more. Since we know the equilibrium constant (Keq = 0.500), we can write an expression for it.
Keq = [NO2] * [SO2] / [SO3] * [NO]
Plugging in the equilibrium concentrations, we get:
0.500 = x * x / (0.300 - x) * (0.300 - x)
And now, my friend, it's time to solve this equation and find the value of x. Once we have that, we can substitute it back into our equilibrium concentrations equation and voila! The equilibrium concentrations of each gas will be revealed, bringing us one step closer to equilibrium bliss.
I hope that puts a smile on your chemical equations! Let me know if there's anything else I can assist you with!
To find the equilibrium concentrations of each gas, we'll need to use the given equilibrium constant (Keq) and the initial moles of each reactant.
Step 1: Write the balanced chemical equation for the reaction:
SO3(g) + NO(g) ⇋ NO2(g) + SO2(g)
Step 2: Write the expression for the equilibrium constant (Keq) using the concentrations of the reactants and products:
Keq = [NO2] * [SO2] / [SO3] * [NO]
Step 3: Given the equilibrium constant (Keq) = 0.500, set up the equation:
0.500 = [NO2] * [SO2] / [SO3] * [NO]
Step 4: Determine the initial concentrations of each reactant:
Initial concentration of SO3 = 0.300 mol / 2.00 L = 0.150 M
Initial concentration of NO = 0.300 mol / 2.00 L = 0.150 M
Step 5: Let's assume the equilibrium concentration of NO2 is x and the equilibrium concentration of SO2 is also x.
Step 6: Substitute the initial concentrations and assumed equilibrium concentrations into the Keq expression:
0.500 = (x) * (x) / (0.150 - x) * (0.150 - x)
Step 7: Solve the equation for x. Rearrange the equation to solve for x:
0.500(0.150 - x)^2 = x^2
Step 8: Simplify the equation:
0.075 - 0.15x + 0.500x^2 = x^2
0.500x^2 - x^2 + 0.15x - 0.075 = 0
Step 9: Combine like terms:
0.500x^2 - x^2 + 0.15x - 0.075 = 0.400x^2 + 0.15x - 0.075 = 0
Step 10: Solve the quadratic equation using factorization, completing the square, or using the quadratic formula to find the value of x.
Step 11: Once you have found the value of x, substitute it back into the expressions for [NO2] and [SO2] to find their equilibrium concentrations.
Note: The equilibrium concentrations of SO3 and NO can be calculated by subtracting the equilibrium concentrations of NO2 and SO2 from their initial concentrations respectively.
Please work out the calculations based on the steps mentioned.
To determine the equilibrium concentrations of each gas, you'll need to perform some calculations using the given information and the equilibrium constant (Keq) equation.
First, write down the balanced equation for the reaction:
SO3(g) + NO(g) ⇋ NO2(g) + SO2(g)
Next, you're given the initial amounts of SO3 and NO, which are 0.300 mol each, and the volume of the container, which is 2.00 L. From this information, you can determine the initial concentrations of SO3 and NO:
Initial concentration of SO3 = (Amount of SO3) / (Volume of container)
= 0.300 mol / 2.00 L
= 0.150 M
Initial concentration of NO = (Amount of NO) / (Volume of container)
= 0.300 mol / 2.00 L
= 0.150 M
Now, we can use the equilibrium constant equation to find the equilibrium concentrations:
Keq = [NO2] / ([SO3] * [NO])
Given Keq = 0.500, and assuming the equilibrium concentrations of SO3, NO, NO2, and SO2 are represented as [SO3], [NO], [NO2], and [SO2] respectively, we can substitute the values into the equation:
0.500 = [NO2] / ([SO3] * [NO])
Since we're looking for equilibrium concentrations, let's assume x is the concentration of NO2 at equilibrium. At equilibrium, the concentration of SO3 will be [SO3] - x and the concentration of NO will be [NO] - x.
0.500 = x / ((0.150 - x) * (0.150 - x))
Now, we solve the equation to find the value of x, which represents the equilibrium concentration of NO2:
0.500 * (0.150 - x) * (0.150 - x) = x
Expand and rearrange the equation:
0.075 - 0.650x + x^2 = x
Rearranging and combining like terms:
x^2 - 1.650x + 0.075 = 0
Now, you can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -1.650, and c = 0.075. Plug in these values to find the two possible values for x (equilibrium concentration of NO2). From the two values, choose the one that makes sense in the context of the problem.
Once you have the value of x, substitute it back into [NO2] = x to find the equilibrium concentration of NO2. Then, you can calculate the equilibrium concentrations of SO3 and NO using the expressions [SO3] = 0.150 - x and [NO] = 0.150 - x, respectively.
Keep in mind that this problem assumes the reaction has reached equilibrium. However, it is always good to check if the calculated concentrations are reasonable and satisfy the equilibrium condition.