Question

The reaction $A\to B$ follows first-order kinetics. The time taken for 0.8 moles of A to produce 0.6 moles of B is 1 hour. What is the time taken for conversion of 0.9 moles of A to produce 0.675 moles of B?

• A. 1 hour
• B. 0.5 hours
• C. 0.25 hours
• D. 2 hours

Answer 1

The correct option is A 1 hour

For first order reaction ,

$k=\frac{2.303}{t}$ log$\frac{a}{a-x}$......(1)

Where k is rate constant

when 0.8 mol of A produces 0.6mol of B then,

$0.8-0.6=0.2$ moles of A is left .

final moles $A=a-x=0.2$

initial moles $a=0.8$

$t=\frac{2.303}{k}$ log$\frac{0.8}{0.2}$

$k=\frac{2.303}{1}$ log$\left[4\right]$........(2)

$k=2.303\times 0.6020$

$k=1.3865$........(3)

In second case , 0.9 moles of A produces 0.675 moles of B so remaining moles of A are $0.9-0.675=0.225$

final moles of $A=a-x=0.225$

initial mole = $0.9$

By using first order equation,

$t=\frac{2.303}{k}$ log$\frac{0.9}{0.225}$

$t=\frac{2.303}{1.3865}$ log$\left(4\right)$.....(4)

$t=1.661\times 0.6020$

$t=0.999=1hr$