How do I solve this for c?
Ka = (0.02c)(0.02c)/(c-0.02)
1.7x10^-5=(0.02c)(0.02c)/(c-0.02)
Thanks.
Use algebra to solve the quadratic equation
1.7*10^-5 *(c - 0.02) = 4*10^-4 c^2
which can be rewritten
4*10^-4 c^2- 1.7*10^-5 c +3.4*10^-7 = 0
c^2 -4.25*10-2 c + 8.5*10^-4 = 0
It appears there is no real-number solution to this equation, because B^2 - 4AC is negative. (A, B and C refer to the polynomical coefficients: 1, -4.25*10-2, and 8.5*10^-4.
I made a typo: it should be 1.8 x10^-5.
So in the quadratic it should be: 0=4.0x10^-4-1.8x10^-5c + 3.6x10^-8.
When I solve I get 2 positive answers, so I am not sure how to figure out which one is inadmissible. Thanks.
The quadratic should then be:
0 = 4.0x10^-4 c^2 -1.8x10^-5 c + 3.6x10^-7. (The last term is not 3.6*10^-8)
c^2 - 4.5*10^-2 c + 9.00*10^-4 = 0
B^2 - 4AC is still negative.
hmhm that is odd. The question is supposed to have an answer of 0.044M, so that is weird. Thanks very much for trying to help me with this.
-Sadie
If 0.044 is supposed to be what c is,
(0.02c)(0.02c)/(c-0.02) = 3.2*10^-5
That does not agree with your starting equation.
Are you sure you are starting with the correct equation? If you are dealing with a reaction A -> B + C, 2% of A dissociates, and the starting concentration is c, then at equilibrium
(.02 c)(0.02c)/0.98 c = Kc = 1.8*10^-5
(0.02)^2 c = 4*10^-4 c = = 1.8*10^-5
c = 0.045
That is close to the book's answer.
You apparently started with the wrong equation, with the wrong term in the denominator
To solve the given equation for c, you can follow the steps below:
Step 1: Start with the given equation:
Ka = (0.02c)(0.02c)/(c-0.02)
Step 2: Simplify the expression by expanding the numerator:
Ka = (0.02c)^2 / (c-0.02)
Step 3: Multiply through by the denominator:
Ka(c-0.02) = (0.02c)^2
Step 4: Expand and rearrange the equation:
Kac - 0.02Ka = (0.02c)(0.02c)
Kac - 0.02Ka = 0.0004c^2
Step 5: Move all the terms to one side of the equation, so it becomes a quadratic equation:
0.0004c^2 - Kac + 0.02Ka = 0
Step 6: The equation is now in the form of ax^2 + bx + c = 0, where a = 0.0004, b = -Ka, and c = 0.02Ka.
Step 7: Apply the quadratic formula to solve for c:
c = (-b ± √(b^2 - 4ac)) / (2a)
c = (-(-Ka) ± √((-Ka)^2 - 4(0.0004)(0.02Ka))) / (2(0.0004))
c = (Ka ± √(K^2a^2 - 0.00032Ka^2)) / 0.0008
c = (Ka ± √(Ka^2(K^2 - 0.00032))) / 0.0008
Now you have the general formula for c, where you can substitute the provided values of Ka to find its value.