If k= 2.97*10^-2 min^-1 what is the half life of the reactant?
Since k units are min^-1, the reaction is first order. So to find the half-life, ln2/k is used. t(1/2) = ln2/k = 0.693/(2.97*10^-2) = 23.3 minutes.
ln[A] vs time plot yields a linear progression, what is the order of the reaction?
4sqrt(x + 7) = -8 - 2x
Solving the problem above will require a multitude of steps, each simple step will work together to solve the difficult equation: Step 1: To remove the pesky square root, we must raise both sides to the power of 2. (4 sqrt(x + 7))^2 = (-8 - 2x)^2 This leaves us with: 16( x + 7) = 64 + 32x + 4x^2 Step 2: Use the FOIL method to distribute the 16 among (x + 7). This leaves us with: 16x + 112 = 64 + 32x + 4x^2 In order to solve for x, we must now get all the terms to one side. Step 3: Subtract the left side of the equation from the right side. Leaving us with: 0 = -48 + 16x + 4x^2 Rearranging: 0 = 4x^2 + 16x - 48 Each term is divisible by 4, so we will pull the 4 out for simpliciy Step 4: Divide all terms by 4 Leaving us with: 0 = 4(x^2 + 4x - 12) We must now figure out what, when multiplied gives us -12, and when added gives us 4? Step 5: (We could use a substitution method, but guess/check is quicker in this case: 3 and -4 or -3 and 4 can be multiplied to get -12 but not added to get 4 12 and -1 or -12 and 1 can be multiplied to get -12 but not added to get 4 -6 and 2 can be multiplied to get -12 but not added to get 4. 6 and -2 is the only combination that gets us what we need. That leaves us with: 0 = 4(x+6)(x-2) To get 0, (x+6) must equal 0 so the first answer is -6. To get 0, (x-2) must equal 0, so the second answer is 2. x = -6 x=2 These correlate with x-intercepts on a graph.