Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with \(t_{\frac 12} = 3.00\ hours\). What fraction of sample of sucrose remains after \(8 \ hours\)?
Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with \(t_{\frac 12} = 3.00\ hours\). What fraction of sample of sucrose remains after \(8 \ hours\)?
Solution and Explanation
For a first order reaction,
\(k = \frac {2.303}{t} log \ \frac {[R]_o}{[R]}\)
It is given that, \(t_{\frac 12} = 3.00\ hours\)
\(k = \frac {0.693}{t_{1/2}}\)
Therefore, \(k = \frac {0.693}{3} h^{-1}\)
\(k = 0.231\ h^{-1}\)
Then, \(0.231 \ h^{-1} = \frac {2.303}{t} log \ \frac {[R]_o}{[R]}\)
⇒ \(log\ \frac { [R]_o}{[R]} =\frac { 0.231 h^{-1} \times 8 h}{2.303}\)
⇒ \(\frac {[R]_o}{[R]}\) = \(antilog \ (0.8024)\)
⇒ \(\frac {[R]_o}{[R]}\) = \(6.3445\)
⇒ \(\frac {[R]_o}{[R]}\) = \(0.1576 \ (approx)\)
⇒ \(\frac {[R]_o}{[R]}\) = \(0.158\)
Hence, the fraction of sample of sucrose that remains after 8 hours is \(0.158\).
Top Questions on Chemical Kinetics
- For a reaction : \( N_2 + 3H_2 \rightarrow 2NH_3 \), the rate of reaction with respect to \( NH_3 \) is
- CBSE CLASS XII - 2026
- Chemistry
- Chemical Kinetics
- Following reaction takes place in one step :
\( 2A + B \rightarrow 2C \)
How will the rate of above reaction change if the volume of the reaction vessel is decreased to one third of its original volume? Will there be any change in the order of reaction with the reduced volume?
- CBSE CLASS XII - 2026
- Chemistry
- Chemical Kinetics
- The half-life of a first-order reaction depends on:
- KBPE - 2026
- Chemistry
- Chemical Kinetics
- The initial concentration of the first order reaction:
N2O5 (g) → 2NO2 (g) + 1/2 O2 (g)
was 1.24 × 10⁻² mol L⁻¹ at 300 K. The concentration of N2O5 after 60 minutes was 0.20 × 10⁻² mol L⁻¹.
Calculate the rate constant of the reaction at 300 K.- KBPE - 2026
- Chemistry
- Chemical Kinetics
(i) Write any two differences between order and molecularity.
(ii) What do you mean by pseudo order reaction?- KBPE - 2026
- Chemistry
- Chemical Kinetics
Questions Asked in CBSE CLASS XII exam
- Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]
- CBSE CLASS XII - 2026
- Differential Equations
- A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:
- CBSE CLASS XII - 2026
- Electromagnetic induction
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).
- CBSE CLASS XII - 2026
- Integration
- Consider a cylindrical conductor of length \( l \) and area of cross-section \( A \). Current \( I \) is maintained in the conductor and electrons drift with velocity \( \vec{v}_d \, (|\vec{v}_d| = \frac{eE}{m} \tau) \), where symbols have their usual meanings. Show that the conductivity of the material of the conductor is given by \[ \sigma = \frac{n e^2 \tau}{m}. \]
- CBSE CLASS XII - 2026
- Current Density
- The painting Hazrat Nizamuddin Auliya and Amir Khusro belongs to which sub-school of Deccan Miniature?
- CBSE CLASS XII - 2026
- Indian Miniature Paintings and Museums
Concepts Used:
Order of Reaction
The Order of reaction refers to the relationship between the rate of a chemical reaction and the concentration of the species taking part in it. In order to obtain the reaction order, the rate equation of the reaction will given in the question.
Characteristics of the reaction order
- Reaction order represents the number of species whose concentration directly affects the rate of reaction.
- It can be obtained by adding all the exponents of the concentration terms in the rate expression.
- The order of reaction does not depend on the stoichiometric coefficients corresponding to each species in the balanced reaction.
- The reaction order of a chemical reaction is always defined with the help of reactant concentrations and not with product concentrations.
- Integer or a fraction form the value of the order of reaction will be there and it can be zero.