A reaction was found to be second order with respect to the concentration of carbon monoxide. If the

Q: Why do we square the 2 when the concentration is doubled?

Because the reaction is second order, the entire concentration term is squared in the rate law. So, when concentration becomes $2c$, you must square the entire $(2c)$, which gives $4c^2$.

Q: What would happen if the reaction was first order instead?

If it were a first-order reaction, the rate law would be $r = k[\text{CO}]^1$. Doubling the concentration would simply double the rate, not quadruple it.

Q: Does the rate constant '$k$' change when we change the concentration?

No, the rate constant $k$ is independent of the concentration of reactants. It only changes if you change the temperature or add a catalyst.

Q: What does the phrase 'with everything else kept the same' imply?

It means that variables like temperature, volume of the container, and the concentration of any other reactants (if present) are held constant, so they don't affect our rate calculation.

Q: Can the order of a reaction be a fraction or negative?

Yes, reaction orders can be fractions or even negative numbers, which indicates complex reaction mechanisms. However, in this specific problem, it is explicitly given as a positive integer (second order).

Question

A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will

Options:

(A) remain unchanged

(B) triple

(C) increase by a factor of 4

(D) double

Sigma Percentile · Accepted Answer

### The Power of Second-Order Kinetics

Imagine you are driving a car, and the speed of your car doesn't just increase linearly with how hard you press the pedal, but it increases with the **square** of the pressure. That is exactly what a second-order reaction feels like!

In chemical kinetics, the order of a reaction tells us how sensitive the reaction rate is to changes in the concentration of the reactants. For a reaction that is second order with respect to a reactant, the relationship is quadratic.

### The Master Equation

Let's translate the problem statement into a mathematical equation. The problem states that the reaction is second order with respect to carbon monoxide ($	ext{CO}$). We can write the rate law as:
$$r = k[	ext{CO}]^2$$

Here, $r$ is the rate of the reaction, $k$ is the rate constant, and $[	ext{CO}]$ is the concentration of carbon monoxide.

### The Mathematical Substitution

Now, the question poses a scenario: what happens if we double the concentration of carbon monoxide? Let's set up our initial state. Let the initial concentration be $c$. 
$$r_{	ext{initial}} = kc^2$$

If we double the concentration, our new concentration becomes $2c$. Let's substitute this new value into our rate law to find the new rate, $r_{	ext{final}}$:
$$r_{	ext{final}} = k(2c)^2$$

**Don't make a silly mistake here!** Remember that the square applies to the entire term inside the parenthesis, including the $2$. 
$$r_{	ext{final}} = k(4c^2) = 4kc^2$$

### The Final Revelation

We know from our initial setup that $kc^2$ is exactly equal to our initial rate, $r_{	ext{initial}}$. Substituting this back in, we get:
$$r_{	ext{final}} = 4 	imes r_{	ext{initial}}$$

This beautifully demonstrates the power of a quadratic relationship. By merely doubling the input, the output has quadrupled! Therefore, the rate of the reaction **increases by a factor of 4**.

Animated Solution for Chemistry - Chemical Kinetics: A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will

Select Answer:

Visualized Solution

$r \propto [CO]^{2}$

$r_{1} = k c^{2}$

$[CO]^{'} = 2 c$

$r_{2} = k (2 c)^{2}$

$r_{2} = 4 r_{1}$

\text{Conclusion}

The Sigma Insight: Order and Molecularity

The Power of Second-Order Kinetics

The Master Equation

The Mathematical Substitution

The Final Revelation

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Animated Solution for Chemistry - Chemical Kinetics: A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will

Select Answer:

Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } r∝[CO]2

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } r1​=kc2

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } [CO]′=2c

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } r2​=k(2c)2

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } r2​=4r1​