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Suppose 50 bacteria are placed in a flas...

Suppose 50 bacteria are placed in a flask contining nutrients for the bacteria so that they can multiply.
A study at `35^(@)C` gave the following results.:
`{:("Time (minute)",0,15,30,45,60),("Number of bacteria" ,50,100,200,400,800):}`
Show that the rate of productin of bacteria is of first order. How many bacteria wil be there after 3 hours?

Text Solution

Verified by Experts

For bacteril growth,
`k=-(2.303)/(t)log_(10).((a)/(a+x))`
At 15 minutes : `k=-(2.303)/(15)log_(10).((50)/(100))`
`=0.0462 "min"^(-1)`
At 30 minutes : `k=-(2.303)/(30)log_(10).((50)/(200))`
`=0.0462 "min"^(-1)`
At 45 minutes :
`k=-(2.303)/(45)log_(10).((50)/(400))=0.0462 "min"^(-1)`
Same values of rate constans show that the process corresponds to first order.
Let there be 'n' bacteria after 3 hrs.
`k=-(2.303)/(t)log_(10).((a)/(a+x))`
`0.0462=-(2.303)/(180)log_(10).(50)/(n)`
`n=2.04xx10^(5)`
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