
A first-order reaction has a specific reaction rate of $\text{1}{{\text{0}}^{-3}}\text{ }{{\text{s}}^{1-}}$. How much time will it take for 10gm of this to reduce to 2.5 gm?
Answer
483.9k+ views
Hint: The first-order reaction depends only on one reactant whereas Zero order reaction does not depend on any reacting species. The formula of the first-order reaction is $\text{k = }\dfrac{2.303}{\text{t}}\log \dfrac{{{\text{A}}_{\text{O}}}}{\text{A}}$.
Complete answer:
-To find the time that will reduce the concentration from 10 g to 2.5 g it is given that specific reaction rate or k = ${{10}^{-3}}$, initial concentration is $({{\text{A}}_{\text{O}}}\text{) = 10g}$ and the final concentration is $(\text{A) = 2}\text{.5g}$.
-So, we can apply the formula of the first order that is:
$\text{k = }\dfrac{2.303}{\text{t}}\log \dfrac{{{\text{A}}_{\text{O}}}}{\text{A}}$
-It can also be written as:
$\text{t = }\dfrac{2.303}{\text{k}}\log \dfrac{{{\text{A}}_{\text{O}}}}{\text{A}}$
$\text{t = }\dfrac{2.303}{{{10}^{-3}}}\log \dfrac{10}{2.5}$
$\text{t = 2030 }\cdot \text{ log4}$
-Now, the value of log4 from the log table is 0.6021, so by applying it in the above equation, we will get:
$\text{t = 2303 }\cdot \text{ 0}\text{.6021}$
$\text{t = 1386}\text{.6 sec}$
-Therefore, a total of 1386.6 sec time will be taken by the reactant to reduce up to 2.5g.
Additional Information:
-The physical significance of k is: It represents the fraction of the reactant decomposed per unit time of the constant concentration.
-The common formula of rate equation for all the orders except for n=1 will be: ${{\text{k}}_{\text{n}}}\text{ = }\dfrac{1}{t\left( n-1 \right)}\left( \dfrac{1}{{{\left( a-x \right)}^{n-1}}}-\dfrac{1}{{{a}^{n-1}}} \right)$
-Zero-order reactions occur under special conditions and are very uncommon.
They generally occur in the heterogeneous system.
Note: Students should not get confused between specific reaction rate and rate constant. The specific reaction rate is also a rate constant but it is a rate of reaction in which the specific conditions are applied.
Complete answer:
-To find the time that will reduce the concentration from 10 g to 2.5 g it is given that specific reaction rate or k = ${{10}^{-3}}$, initial concentration is $({{\text{A}}_{\text{O}}}\text{) = 10g}$ and the final concentration is $(\text{A) = 2}\text{.5g}$.
-So, we can apply the formula of the first order that is:
$\text{k = }\dfrac{2.303}{\text{t}}\log \dfrac{{{\text{A}}_{\text{O}}}}{\text{A}}$
-It can also be written as:
$\text{t = }\dfrac{2.303}{\text{k}}\log \dfrac{{{\text{A}}_{\text{O}}}}{\text{A}}$
$\text{t = }\dfrac{2.303}{{{10}^{-3}}}\log \dfrac{10}{2.5}$
$\text{t = 2030 }\cdot \text{ log4}$
-Now, the value of log4 from the log table is 0.6021, so by applying it in the above equation, we will get:
$\text{t = 2303 }\cdot \text{ 0}\text{.6021}$
$\text{t = 1386}\text{.6 sec}$
-Therefore, a total of 1386.6 sec time will be taken by the reactant to reduce up to 2.5g.
Additional Information:
-The physical significance of k is: It represents the fraction of the reactant decomposed per unit time of the constant concentration.
-The common formula of rate equation for all the orders except for n=1 will be: ${{\text{k}}_{\text{n}}}\text{ = }\dfrac{1}{t\left( n-1 \right)}\left( \dfrac{1}{{{\left( a-x \right)}^{n-1}}}-\dfrac{1}{{{a}^{n-1}}} \right)$
-Zero-order reactions occur under special conditions and are very uncommon.
They generally occur in the heterogeneous system.
Note: Students should not get confused between specific reaction rate and rate constant. The specific reaction rate is also a rate constant but it is a rate of reaction in which the specific conditions are applied.
Recently Updated Pages
Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Statement I Reactivity of aluminium decreases when class 11 chemistry CBSE

Trending doubts
10 examples of friction in our daily life

Difference Between Prokaryotic Cells and Eukaryotic Cells

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Define least count of vernier callipers How do you class 11 physics CBSE
