I don’t understand how to write this equation.
Write an equation relating the concentration for a reactant A at t=0 to that at t=t for a first-order reaction. Define all the terms, and give their units. Do the same for a second- order reaction.
-Would it be the rate law equation?? Please help.
Yes, I think so. For first order,
ln(Ao/A) = akt; therefore, for t = 0, we have ln(Ao/A) = 0
(Ao/A) = 1
and A = Ao = 1
Then I believe you are to use the original with t for t, and solve for (A).
Same thing with second order but more challenging mathematically.
To write an equation relating the concentration for a reactant A at different times for a first-order or second-order reaction, you need to understand the rate law equations for these reactions.
For a first-order reaction, the rate law equation is generally written as:
Rate = k[A]
In this equation:
- Rate represents the rate of the reaction
- k is the rate constant, which is specific for each reaction and is determined experimentally.
- [A] represents the concentration of reactant A.
Now, to relate the concentration of A at t=0 to that at t=t for a first-order reaction, you can use the integrated rate law equation. For a first-order reaction, the integrated rate law equation is:
ln([A]t/[A]0) = -kt
In this equation:
- [A]t represents the concentration of A at time t
- [A]0 represents the concentration of A at t=0.
- k is the rate constant obtained from the rate law equation.
- t represents the time elapsed.
The units for concentration are typically expressed in moles per liter (mol/L), while the unit for time is usually in seconds (s).
Now, let's consider the same for a second-order reaction. The rate law equation for a second-order reaction can be written as:
Rate = k[A]^2
In this equation:
- Rate represents the rate of the reaction.
- k is the rate constant.
- [A] represents the concentration of reactant A.
To relate the concentration of A at t=0 to that at t=t for a second-order reaction, you need to use the integrated rate law equation for a second-order reaction, which is:
1/[A]t - 1/[A]0 = kt
Here:
- [A]t represents the concentration of A at time t.
- [A]0 represents the concentration of A at t=0.
- k is the rate constant obtained from the rate law equation.
- t represents the time elapsed.
Again, the units for concentration are usually expressed in mol/L, and the unit for time is typically in seconds (s).
Remember, the rate law equations and integrated rate law equations differ for different reaction orders. The rate law equations indicate how the rate of the reaction depends on the concentration of reactants, while the integrated rate law equations help in relating the concentrations at different times.