A chemist studying the equilibrium N2O4(g)<----->2NO2(g) controls the temperature so that keq ( equilibrium constant)= 0.028. At one equilibrium position, the concentration of N2O4 is 1.5 times greater than the concentration of NO2. Find the concentrations of the two gases in mol/L. (Hint: Let x=[NO2] and 1.5x=[N2O4] in the equilibrium constant expression.)
My answer:
[NO2]= 0.042M
[N2O4]= 0.063M
I agree.
To solve this problem, we can start by representing the equilibrium concentrations of N2O4 and NO2 as x and 1.5x, respectively, based on the given information.
The equilibrium constant expression for the reaction is Keq = [NO2]^2 / [N2O4]. Given that Keq = 0.028, we can substitute the concentrations into the expression:
0.028 = (x^2) / (1.5x)
To solve this equation for x, we can multiply both sides by 1.5x:
0.028 * 1.5x = x^2
0.042x = x^2
Dividing both sides by x and rearranging, we have:
x = 0.042
Therefore, the concentration of NO2 ([NO2]) is 0.042 mol/L.
Using the given information that [N2O4] is 1.5 times greater than [NO2], we can calculate its concentration:
[N2O4] = 1.5 * 0.042 = 0.063 mol/L
So, the concentration of N2O4 is 0.063 mol/L.
Therefore, the concentrations of the two gases are as follows:
[NO2] = 0.042 mol/L
[N2O4] = 0.063 mol/L
To find the concentrations of the two gases N2O4 and NO2, we need to use the equilibrium constant expression and the given information.
The equilibrium constant expression for the reaction is Keq = ([NO2]^2) / [N2O4].
According to the given information, the concentration of N2O4 is 1.5 times greater than the concentration of NO2. Therefore, we can say that [N2O4] = 1.5 * [NO2], or [N2O4] = 1.5x and [NO2] = x.
Substituting these values into the equilibrium constant expression, we get:
Keq = ([NO2]^2) / [N2O4]
0.028 = (x^2) / (1.5x)
Now, cross-multiply and simplify the equation:
0.028 * 1.5x = x^2
0.042x = x^2
Rearrange the equation to set it equal to zero:
x^2 - 0.042x = 0
Next, solve this quadratic equation by factoring it or using the quadratic formula. In this case, let's use factoring:
x(x - 0.042) = 0
Equating each factor to zero, we get two possible solutions:
x = 0 (This corresponds to no concentration of the gases, which doesn't make sense in this context.)
x - 0.042 = 0
x = 0.042
Since we're dealing with concentrations, we discard the solution x = 0.
Therefore, the concentration of NO2 is 0.042 M.
To find the concentration of N2O4, we can substitute this value back into the equation [N2O4] = 1.5x:
[N2O4] = 1.5 * 0.042
[N2O4] = 0.063 M
So, the concentrations of NO2 and N2O4 are [NO2] = 0.042 M and [N2O4] = 0.063 M, respectively.