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For a given water sample, the ratio between BOD5-day, 20°C and the ultimate BOD is 0.68. The value of the reaction rate constant k (on base e)( in day-1, up to two decimal places) is ______
Correct answer is '0.23'. Can you explain this answer?
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Calculation of reaction rate constant k
Given data:
Ratio of BOD5-day, 20C to ultimate BOD = 0.68
Formula:
BOD = BODultimate - (BODultimate - BOD5) * e^(-kt)
Where,
BODultimate = ultimate BOD
BOD5 = BOD5-day, 20C
k = reaction rate constant
t = time (in days)
Using the given ratio, we can write:
0.68 = BOD5 / BODultimate
Rearranging the equation, we get:
BODultimate = BOD5 / 0.68
Substituting the values in the formula for BOD, we get:
BOD5 / 0.68 = BODultimate - (BODultimate - BOD5) * e^(-kt)
Simplifying the equation, we get:
0.68 = 1 - (1 - 0.68) * e^(-kt)
0.32 = 0.32 * e^(-kt)
Taking natural logarithm on both sides, we get:
ln(0.32) = -kt
Solving for k, we get:
k = -ln(0.32) / t
Assuming t = 5 days (as BOD5-day, 20C is given), we get:
k = -ln(0.32) / 5
k = 0.23 day^-1 (rounded off to two decimal places)
Therefore, the value of the reaction rate constant k is 0.23 day^-1.
Given data:
Ratio of BOD5-day, 20C to ultimate BOD = 0.68
Formula:
BOD = BODultimate - (BODultimate - BOD5) * e^(-kt)
Where,
BODultimate = ultimate BOD
BOD5 = BOD5-day, 20C
k = reaction rate constant
t = time (in days)
Using the given ratio, we can write:
0.68 = BOD5 / BODultimate
Rearranging the equation, we get:
BODultimate = BOD5 / 0.68
Substituting the values in the formula for BOD, we get:
BOD5 / 0.68 = BODultimate - (BODultimate - BOD5) * e^(-kt)
Simplifying the equation, we get:
0.68 = 1 - (1 - 0.68) * e^(-kt)
0.32 = 0.32 * e^(-kt)
Taking natural logarithm on both sides, we get:
ln(0.32) = -kt
Solving for k, we get:
k = -ln(0.32) / t
Assuming t = 5 days (as BOD5-day, 20C is given), we get:
k = -ln(0.32) / 5
k = 0.23 day^-1 (rounded off to two decimal places)
Therefore, the value of the reaction rate constant k is 0.23 day^-1.
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For a given water sample, the ratio between BOD5-day, 20°C and the ultimate BOD is 0.68. The value of the reaction rate constant k (on base e)( in day-1, up to two decimal places) is ______Correct answer is '0.23'. Can you explain this answer?
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