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Help me solve this If half-­life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams is

If half-­life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams is

  • Option 1)

    16 grams

  • Option 2)

    2 grams

  • Option 3)

    32 grams

  • Option 4)

    8 grams

 
Answers (1)
197 Views

As learnt in concept

First Order Reaction -

The rate of the reaction is proportional to the first power of the concentration of the reaction

- wherein

Formula:

R    \rightarrow        P

a                 0

a-x             x

rate[r]=K[R]^{1}

\frac{-d(a-x)}{dt}=K(a-x)

\frac{-dx}{dt}=K(a-x)  [differentiate rate law]

ln \:[\frac{a}{a-x}]=kt \:(Integrated rate law)

Unit of k=sec^{-1}

t_\frac{1}{2}=\frac{0.693}{k}

 

 

 T1/2 = 5 years

K = \frac{0.693}{5}= \frac{2.303}{15} log \frac{64}{x}\\ \log \frac{64}{x} = \frac{15 X 0.693}{5 X 2.303} = 3 X 0.3010

log \frac{64}{x}= log{2}^{3} = log 8

X = 8 gm


Option 1)

16 grams

This option is incorrect. 

Option 2)

2 grams

This option is incorrect. 

Option 3)

32 grams

This option is incorrect. 

Option 4)

8 grams

This option is correct. 

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