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In one kind of chemical reaction, unconverted reactants change into converted reactants.
The fraction 
a of reactants that have been converted increases at a rate proportional to the product of the fraction of converted reactants and the fraction of unconverted reactants.
Which equation describes this relationship?
Choose 1 answer:
(A) 
(da)/(dt)=(ka)/(1-a)
(B) 
(da)/(dt)=ka(1-a)
(c) 
(da)/(dt)=(k)/(a(1-a))
(D) 
(da)/(dt)=ka^(2)

In one kind of chemical reaction, unconverted reactants change into converted reactants.\newlineThe fraction a a of reactants that have been converted increases at a rate proportional to the product of the fraction of converted reactants and the fraction of unconverted reactants.\newlineWhich equation describes this relationship?\newlineChoose 11 answer:\newline(A) dadt=ka1a \frac{d a}{d t}=\frac{k a}{1-a} \newline(B) dadt=ka(1a) \frac{d a}{d t}=k a(1-a) \newline(c) dadt=ka(1a) \frac{d a}{d t}=\frac{k}{a(1-a)} \newline(D) dadt=ka2 \frac{d a}{d t}=k a^{2}

Full solution

Q. In one kind of chemical reaction, unconverted reactants change into converted reactants.\newlineThe fraction a a of reactants that have been converted increases at a rate proportional to the product of the fraction of converted reactants and the fraction of unconverted reactants.\newlineWhich equation describes this relationship?\newlineChoose 11 answer:\newline(A) dadt=ka1a \frac{d a}{d t}=\frac{k a}{1-a} \newline(B) dadt=ka(1a) \frac{d a}{d t}=k a(1-a) \newline(c) dadt=ka(1a) \frac{d a}{d t}=\frac{k}{a(1-a)} \newline(D) dadt=ka2 \frac{d a}{d t}=k a^{2}
  1. Define Fraction Conversion: Let's denote the fraction of reactants that have been converted by a a . According to the problem, the rate of change of a a with respect to time t t , denoted as dadt \frac{da}{dt} , is proportional to the product of the fraction of converted reactants a a and the fraction of unconverted reactants 1a 1 - a . The constant of proportionality is k k .
  2. Rate of Change Equation: The equation that describes this relationship should therefore be dadt=ka(1a) \frac{da}{dt} = k \cdot a \cdot (1 - a) , where k k is the constant of proportionality.
  3. Match with Given Choices: Looking at the given choices, we can see that option (B) dadt=ka(1a) \frac{da}{dt} = ka(1 - a) matches the equation we derived in the previous step.

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