For a chemical reaction A - B, it was found that concentration of B is increased by 0.2 mol L^-1 in

Q: Why do we use a positive sign for the rate of appearance of B?

Since B is a product, its concentration increases over time. The change in concentration ($\Delta[B]$) is positive, so the rate is naturally positive.

Q: What if the question asked for the rate of disappearance of A?

Because the stoichiometry of the reaction is 1:1 ($A \rightarrow B$), the rate of disappearance of A is exactly equal to the rate of appearance of B.

Q: Why did we convert 30 minutes to 0.5 hours?

The question specifically asks for the rate in $\text{mol L}^{-1} \text{ h}^{-1}$. If we used minutes, our rate would be in $\text{mol L}^{-1} \text{ min}^{-1}$, which would lead to an incorrect final integer.

Q: Can the average rate be different from the instantaneous rate?

Yes! The average rate is measured over a macroscopic time interval (like 30 minutes), while the instantaneous rate is the rate at a specific, exact moment in time.

Q: How do we know the initial concentration of B is 0?

In standard chemical kinetics problems, unless stated otherwise, we assume that at $t=0$, no product has been formed yet.

Question

For a chemical reaction $A \longrightarrow B$, it was found that concentration of $B$ is increased by $0.2 	ext{ mol L}^{-1}$ in $30 	ext{ min}$. The average rate of the reaction is $\dots 	imes 10^{-1} 	ext{ mol L}^{-1} 	ext{ h}^{-1}$. (Nearest integer)

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Imagine you are observing a chemical reaction in a beaker. We have a simple process where reactant $A$ transforms into product $B$.

Initially, at time $t = 0$, there is no product $B$ present. Its concentration is exactly $0 	ext{ M}$.

However, after $30 	ext{ minutes}$, we measure the concentration of $B$ and find it has increased to $0.2 	ext{ mol L}^{-1}$. Our goal is to find the **average rate of the reaction** over this time interval.

### The Master Equation

To find how fast the reaction is proceeding, we need the formula for the average rate.

The average rate of a reaction with respect to a product is defined as the change in its concentration divided by the time interval.

Mathematically, this is expressed as $r_{	ext{avg}} = \frac{\Delta[B]}{\Delta t}$. Since $B$ is being formed, its concentration increases, making the rate a positive value.

### The Unit Conversion Trap

Here is where many students make a **silly mistake**. The time given in the problem is $30 	ext{ minutes}$, but if you look closely at the requested units for the final answer, it asks for the rate in $	ext{mol L}^{-1} 	ext{ h}^{-1}$.

We must convert our time from minutes to hours before doing any calculations!

Since there are $60 	ext{ minutes}$ in an hour, $30 	ext{ minutes}$ is exactly $\frac{30}{60} 	ext{ h}$, which simplifies to $0.5 	ext{ h}$.

### Final Calculation

Now, we are ready to substitute our values into the master equation.

The change in concentration, $\Delta[B]$, is $0.2 	ext{ mol L}^{-1} - 0 	ext{ mol L}^{-1} = 0.2 	ext{ mol L}^{-1}$. The time interval, $\Delta t$, is $0.5 	ext{ h}$.

Plugging these in, we get $r_{	ext{avg}} = \frac{0.2}{0.5}$.

Dividing $0.2$ by $0.5$ gives us $0.4 	ext{ mol L}^{-1} 	ext{ h}^{-1}$.

The question asks for the answer in the specific format of $x 	imes 10^{-1}$. We can rewrite $0.4$ as $4 	imes 10^{-1}$.

Therefore, comparing this to the required format, our final integer value for $x$ is **$4$**.

Animated Solution for Chemistry - Chemical Kinetics: For a chemical reaction $A ⟶ B$ , it was found that concentration of $B$ is increased by $0.2 mol L^{- 1}$ in $30 min$ . The average rate of the reaction is $\dots \times 1 0^{- 1} mol L^{- 1} h^{- 1}$ . (Nearest integer)

Enter Numerical Value:

Visualized Solution

$A ⟶ B$

$r_{avg} = \frac{Δ [ B ]}{Δ t}$

$Unit Conversion$

$Calculation$

$Final Answer$

$The Way Forward$

The Sigma Insight: Rate of Chemical Reaction

Analyzing the Setup

The Master Equation

The Unit Conversion Trap

Final Calculation

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Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A⟶B

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } ravg​=ΔtΔ[B]​

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Unit Conversion

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

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Final Answer

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The Way Forward