If the time elapsed is 4.26 min, what is the value of the rate constant, k?
ln[R]t / [R]o = -0.0237
I am not sure how to slove this.
Would I do ln 4.26 minutes times -0.0237???
How are you defining k?
Are you taking the ln of [R] or of [R(t)]/R(0)] ?
Is [R] the concentration of a reactant?
This looks like an equation for first-order chemical decomposition or radioactive decay.
If [R(t)] = [Ro]e^-kt, then
ln{[R(t)]/R(0)]} = -kt
If -kt = -0.0237 when t = 4.26 min, then
k = 5.56*10^-3 min^-1
Ok how did you get 5.56e-3???
To determine the value of the rate constant, k, given the equation ln[R]t / [R]o = -0.0237, you need to rearrange the equation to solve for k. Here's how you can do it:
1. Start with the equation: ln[R]t / [R]o = -0.0237
2. Multiply both sides by [R]o to get rid of the denominator:
ln[R]t = -0.0237 * [R]o
3. Since ln[R]t is the natural logarithm of some value, you can rewrite it as:
[R]t = e^(-0.0237 * [R]o)
4. Now, let's substitute the given time elapsed of 4.26 minutes into the equation:
[R]t = e^(-0.0237 * [R]o)
5. Plug in 4.26 for [R]t:
4.26 = e^(-0.0237 * [R]o)
6. To isolate [R]o, take the natural logarithm of both sides:
ln(4.26) = ln(e^(-0.0237 * [R]o))
7. By applying the logarithmic property ln(e^x) = x, simplify the equation:
ln(4.26) = -0.0237 * [R]o
8. Finally, divide both sides by -0.0237 to solve for [R]o:
[R]o = ln(4.26) / -0.0237
The value obtained for [R]o will represent the rate constant, k.