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At particular concentration, the half life of the reaction is 100 minutes. When the concentration of the reactant doubled half life becomes 25 minutes, then what will be the order of the reaction A) 1 B) 2 C) 0 D) 3?
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At particular concentration, the half life of the reaction is 100 minu...
Solution


Given

Concentration = C

Half-life = 100 min

Concentration doubled = 2C

New half-life = 25 min

Formula

The formula for calculating the half-life of a reaction is as follows:

t1/2 = (0.693/k)

where,

t1/2 = Half-life of the reaction

k = Rate constant of the reaction

Explanation

Let's assume that the order of the reaction is 'n'. Therefore, the rate equation for the reaction can be written as:

Rate = k[C]n

Substituting the given values, we get the following equations:

For the first case,

t1/2 = 100 min

Rate = k[C]n

Substituting t1/2 in the formula, we get:

100 = (0.693/k)[C]-n

Taking the natural logarithm on both sides, we get:

ln(100) = ln(0.693/k) - nln[C]

ln(100) - ln(0.693/k) = -nln[C]

ln(100/0.693) = nln[C]

n = ln(100/0.693)/ln[C] - - - - (1)

For the second case,

t1/2 = 25 min

Rate = k[2C]n

Substituting t1/2 in the formula, we get:

25 = (0.693/k)[2C]-n

Simplifying the equation, we get:

ln(2) + ln(25) = ln(0.693/k) - nln[2C]

ln(50/0.693) = nln[2C] - ln(0.693/k)

n = ln(50/0.693)/(ln[2C]) - - - - (2)

Dividing equation (2) by equation (1), we get:

n/n = ln(50/0.693)ln[C]/ln(100/0.693)ln[2C]

Simplifying the equation, we get:

ln(2) = ln[C]/ln[2C]

2ln(2) = ln[C] - ln[2C]

ln[C] = 2ln(2) + ln[2C]

ln[C] = ln(22) + ln(21C)

ln[C] = ln(4) + ln(C)

ln[C] - ln(C) = ln(4)
Community Answer
At particular concentration, the half life of the reaction is 100 minu...
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Read the passage given below and answer the following questions:The rate of a reaction, which may also be called its velocity or speed, can be defined with relation to the concentration of any of the reacting substances, or to that of any product of the reaction. If the species chosen is a reactant which has a concentration c at time t the rate is - dc/dt, while the rate with reference to a product having a concentration x at time t is dx/dt. Any concentration units may be used for expressing the rate; thus, if moles per liter are employed for concentration and seconds for the time, the units for the rate are moles litre–1sec–1. For gas reactions pressure units are sometimes used in place of concentrations, so that legitimate units for the rate would be (mm. Hg) sec–1 and atm. sec–1 The order of a reaction concerns the dependence of the rate upon the concentrations of reacting substances; thus, if the rate is found experimentally to be proportional to the ath power of the concentration of one of the reactants A, to the both power of the concentration of a second reactant B, and so forth, via., rate = k CAα CAβ the over-all order of the reaction is simply n = α + β + ----- (2) Such a reaction is said to be of the αth order with respect to the substance A, the βth order with respect to B.In the following questions, a statement of Assertion followed by a statement of Reason is given. Choose the correct answer out of the following choices on the basis of the above passage.Assertion: Rate of reaction is a measure of change in concentration of reactant with respect to time.Reason: Rate of reaction is a measure of change in concentration of product with respect to time.

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At particular concentration, the half life of the reaction is 100 minutes. When the concentration of the reactant doubled half life becomes 25 minutes, then what will be the order of the reaction A) 1 B) 2 C) 0 D) 3?
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At particular concentration, the half life of the reaction is 100 minutes. When the concentration of the reactant doubled half life becomes 25 minutes, then what will be the order of the reaction A) 1 B) 2 C) 0 D) 3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about At particular concentration, the half life of the reaction is 100 minutes. When the concentration of the reactant doubled half life becomes 25 minutes, then what will be the order of the reaction A) 1 B) 2 C) 0 D) 3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At particular concentration, the half life of the reaction is 100 minutes. When the concentration of the reactant doubled half life becomes 25 minutes, then what will be the order of the reaction A) 1 B) 2 C) 0 D) 3?.
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