The initial concentration of NH3 in the zero order reaction NH3→3H2+N2 is 0.0312 M. After 30.0 seconds, the concentration of NH3 is 0.0302 M. What is the rate constant k for the reaction?
Well, isn't this a chemical mystery? Let me put on my lab coat and calculate that rate constant for you.
In a zero-order reaction like this, the rate of the reaction is independent of the concentration of the reactant. So, we have the equation:
rate = k
Now, we can find the value of k using the given information. We know that the initial concentration of NH3 is 0.0312 M, and after 30.0 seconds, it decreases to 0.0302 M.
To find the rate, we need to calculate the change in NH3 concentration:
Change in [NH3] = [NH3]final - [NH3]initial
= 0.0302 M - 0.0312 M
= -0.001 M
Since the reaction is zero-order, the rate is equal to k. So, the rate of the reaction is -0.001 M/s.
Now we can use the rate equation to solve for k:
k = rate / [NH3]initial
= -0.001 M/s / 0.0312 M
≈ -0.032 M/s
So, the rate constant for this reaction is approximately -0.032 M/s. Now, aren't you glad I brought my lab coat to the party?
To determine the rate constant (k) for the reaction, you can use the integrated rate law for a zero-order reaction:
[A] = [A]₀ - kt
Where:
[A] is the concentration of NH3 at time t,
[A]₀ is the initial concentration of NH3,
k is the rate constant of the reaction, and
t is the time.
Based on the given information, we can substitute the values:
0.0302 M = 0.0312 M - k(30.0 s)
Now we can solve for k. Rearranging the equation:
k(30.0 s) = 0.0312 M - 0.0302 M
k(30.0 s) = 0.001 M
Dividing both sides by 30.0 s:
k = 0.001 M / 30.0 s
k ≈ 0.0333 M/s
To find the rate constant (k) for the reaction, we need to use the integrated rate law for a zero-order reaction. The integrated rate law equation for a zero-order reaction is:
[Reactant] = [Reactant]₀ - kt
Where:
- [Reactant] is the concentration of the reactant at a given time
- [Reactant]₀ is the initial concentration of the reactant
- k is the rate constant
- t is the time
We are given:
- [Reactant] at t = 0 seconds ([NH3]₀) = 0.0312 M
- [Reactant] at t = 30.0 seconds ([NH3]) = 0.0302 M
Using the given data, we can rearrange the integrated rate law equation to solve for k:
[Reactant] - [Reactant]₀ = -kt
Substituting the given values:
0.0302 M - 0.0312 M = -k * 30.0 seconds
Simplifying this equation:
-0.001 M = -30k
Dividing both sides by -30:
0.001 M / 30 = k
Therefore, the rate constant (k) for the reaction is 0.0000333 s⁻¹.