4x^2/[(1.5-x)(2.0-2x)^2] =
= 2.72 x 10^11
solve for x
Rewrite it as
4x^2 = (10.88 x 10^11)(1.5-x)(1-x)^2
I graphicsl or iterative solution may be necessary, since this is a cubic equation. I suspect that the roots are very close to 1.5 and 1.0
you helped me with this chem ques and you got close to 1 how did u get it please help me?You end up with a cubic equation for x. You may have to solve it graphically. Take the root that is between 0 and 1.
As x -> 1, the term on the left approaches
4/[(0.5)(2-2x)^2 ] = 2.27*10^11
2/(1-x)^2 = 2.27*10^11
(1-x) = 3*10^-6
x = 0.999997
You are left with 0.500003 moles O2 and
10^-5 moles CO (the limiting reactant). 1.99999 moles of CO2 are formed
This reaction will, however, be very slow at room temperature. The reaction does not proceed kinetically as written, and requires some O or OH as a chain carrier.
To solve the equation 4x^2/[(1.5-x)(2.0-2x)^2] = 2.72 x 10^11 for x, we need to eliminate the denominator and rearrange the equation. Here's the step-by-step process:
Step 1: Multiplying both sides of the equation by the denominator [(1.5-x)(2.0-2x)^2]:
4x^2 = 2.72 x 10^11 * [(1.5-x)(2.0-2x)^2]
Step 2: Expanding the denominator and simplifying:
4x^2 = 2.72 x 10^11 * (3 - 3x - x + x^2) * (2.0-2x)^2
4x^2 = 2.72 x 10^11 * (3 - 4x + x^2) * (4 - 8x + 4x^2)
Step 3: Expanding and simplifying further:
4x^2 = 2.72 x 10^11 * (12 - 24x + 12x^2 - 16x + 32x^2 - 16x^3 + 4x^3 - 8x^2 + 4x^3)
Step 4: Collecting like terms:
4x^2 = 2.72 x 10^11 * (12 - 40x + 40x^2 - 12x^3)
Step 5: Now, divide both sides of the equation by 4:
x^2 = 0.68 x 10^11 * (12 - 40x + 40x^2 - 12x^3)
Step 6: Rearrange the equation to bring all terms to one side, resulting in a cubic equation:
12x^3 - 40x^2 + 40x - (0.68 x 10^11 * (12 - 40x + 40x^2)) = 0
Step 7: Now, we can solve this cubic equation numerically using methods like Newton-Raphson, numerical approximation techniques, or computer algebra systems.