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Question: A first order reaction has a rate constant \(1.15 \times {10^{ - 3}}{s^{ - 1}}\). How long will 5 g ...

A first order reaction has a rate constant 1.15×10−3s−11.15 \times {10^{ - 3}}{s^{ - 1}}. How long will 5 g of this reactant take to reduce to 3 g?
(A) 444 s
(B) 400 s
(C) 528 s
(D) 669 s

Explanation

Solution

The reaction is called first order reaction when Rate of reaction depends upon concentration of one reactant only.
Example:
2H2O2(g)→2H2O(l)+O22{H_2}{O_{2(g)}} \to 2{H_2}{O_{(l)}} + {O_2}
Rate=k[H2O2] = k[{H_2}{O_2}]
This reaction is first order because Rate of reaction is the first power of H2O2{H_2}{O_2} concentration.

Formula used: t=2.303klog⁡10AoAtt = \dfrac{{2.303}}{k}{\log _{10}}\dfrac{{{A_o}}}{{{A_t}}}

Complete step by step answer:
As the reaction is first order reaction therefore formula used is
t=2.303klog⁡10AoAtt = \dfrac{{2.303}}{k}{\log _{10}}\dfrac{{{A_o}}}{{{A_t}}}______(1)
Where,
t = time
k = Rate constant of first order reaction
Ao{A_o} = Initial concentration
At{A_t} = Final concentration
The values are
k=1.15×10−3s−1k = 1.15 \times {10^{ - 3}}{s^{ - 1}}
Ao=5gm{A_o} = 5gm
At=3gm{A_t} = 3gm
t=?t = ?
Substituting this values in equation number (1) we get
t=2.3031.15×10−3log⁡53t = \dfrac{{2.303}}{{1.15 \times {{10}^{ - 3}}}}\log \dfrac{5}{3}
t=2.3031.15×10−3log⁡1.66t = \dfrac{{2.303}}{{1.15 \times {{10}^{ - 3}}}}\log 1.66
Value of log⁡1.66=0.22\log 1.66 = 0.22
Putting this value we have t=2.3031.15×10−3×0.221t = \dfrac{{2.303}}{{1.15 \times {{10}^{ - 3}}}} \times \dfrac{{0.22}}{1}
t=2.303×0.22×1031.55t = \dfrac{{2.303 \times 0.22 \times {{10}^3}}}{{1.55}}
t=506.661.55t = \dfrac{{506.66}}{{1.55}}
t=440.57sec⁡.t = 440.57\sec .

Therefore, from the above explanation the correct option is (A) 444 s.

Additional information: Overall order of reaction is the sum of the exponent to which concentration terms in the rate law are raised.
Let us consider a reaction.
aA+bB→cA+dDaA + bB \to cA + dD
Here the number of molecules of A reacts with the B molecule.
The order of reaction is not related to the stoichiometric equation of reaction.
It means order of reaction is not equal to = a + b
It is an experimentally determined quantity.

Note: The reaction order is always defined in terms of the concentration of reactant and not of product.
Rate constant for first order depends only on time not concentration reactant.