A decomposition reaction is found to be first order with respect to the reactant. What is the relationship between the rate and concentration of the reactant?
A) The rate is inversely proportional to the square of the concentration
B) The rate is inversely proportional to the common logarithm of the concentration
C) The rate is directly proportional to the concentration
D) The rate is directly proportional to the common logarithm of the concentration
I think it is A, just want to clarify.
Hey, the answer to your question would be
C) The rate is directly proportional to the concentration
That's because the "exponent" or, superscript, of the reactant is 1. Thus, whatever value the concentration multiplies by, the same goes for the rate.
Well, well, well, it seems we have a decomposition reaction in the house! And it's first order, how exciting! Now, let me put on my thinking nose... I mean, hat, and get to the bottom of this.
In a first-order decomposition reaction, the rate of the reaction is directly proportional to the concentration of the reactant. So, the correct answer is... *drumroll*... C) The rate is directly proportional to the concentration!
It's a pure and simple relationship, just like peanut butter and jelly. The higher the concentration of the reactant, the faster the reaction goes. So, keep those reactant concentration levels up, my friend!
The correct answer is C) The rate is directly proportional to the concentration.
In a first-order decomposition reaction, the rate of the reaction is directly proportional to the concentration of the reactant. This means that as the concentration of the reactant increases, the rate of the reaction also increases, and as the concentration of the reactant decreases, the rate of the reaction decreases.
Option A is incorrect because it suggests that the rate is inversely proportional to the square of the concentration, which is not the case for a first-order reaction. Option B is incorrect because it suggests that the rate is inversely proportional to the common logarithm of the concentration, which is not true for a first-order reaction either. Option D is also incorrect for the same reason.
To determine the relationship between the rate and concentration of a reactant in a first-order decomposition reaction, you can use the integrated rate law for a first-order reaction.
The integrated rate law for a first-order reaction is written as follows:
ln[A]t = -kt + ln[A]0
Where [A]t represents the concentration of the reactant at time "t", [A]0 represents the initial concentration of the reactant, "k" represents the rate constant, and ln represents the natural logarithm.
From this equation, we can observe that the concentration of the reactant decreases exponentially with time. However, we are interested in the instantaneous rate of the reaction, which is measured at a specific time. To determine the relationship between the rate and concentration, we need to differentiate the integrated rate law with respect to time.
Differentiating both sides of the equation gives:
d[A]/dt = -k
From this equation, we see that the rate of a first-order reaction is independent of the concentration of the reactant. It is solely determined by the rate constant "k" of the reaction.
Therefore, the correct option would be C) The rate is directly proportional to the concentration.