A graph of experimental data is a straight line when ln[H2] is plotted versus time. Which rate law fits the data?
1 Rate = k(ln[H2])
2 Rate = k/[H2]
3 Rate = k[H2]
4 Rate = k[H2]2
The rate law that fits the data is rate = k(ln[H2]). This is because when the natural logarithm of the concentration of H2 is plotted against time and results in a straight line, it suggests that the reaction follows a first-order kinetic behavior with respect to the concentration of H2. Hence, the rate of the reaction is directly proportional to the natural logarithm of [H2].
To determine which rate law fits the given experimental data, we need to analyze the graph of ln[H2] versus time.
First, let's understand the different rate laws:
1. Rate = k(ln[H2])
In this rate law, the rate is directly proportional to the natural logarithm of [H2].
2. Rate = k/[H2]
This rate law shows that the rate is inversely proportional to [H2].
3. Rate = k[H2]
Here, the rate is directly proportional to [H2] without any exponent.
4. Rate = k[H2]^2
This rate law indicates that the rate is directly proportional to the square of [H2].
Now, observe the given graph: if it is a straight line when ln[H2] is plotted against time, it means that ln[H2] changes linearly as time progresses.
From the rate laws mentioned above, only option 1 (Rate = k(ln[H2])) shows a linear relationship with ln[H2]. Therefore, the rate law that fits the data is 1.
straight lines have a constant slope. That is often written
y = kx
In this case, the quantities have different names, but it should be clear which choice is correct if you just use your names instead.