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Question: For \(xA + yB\) \(\to \) \(zC\), \[-\dfrac{d[A]}{dt}=-\dfrac{d[B]}{dt}=1.5\dfrac{d[C]}{dt}\] t...

For xA+yBxA + yB →\to zCzC,
−d[A]dt=−d[B]dt=1.5d[C]dt-\dfrac{d[A]}{dt}=-\dfrac{d[B]}{dt}=1.5\dfrac{d[C]}{dt}
then x, y and z are.
A. 1, 1, 1
B. 3, 2, 3
C. 3, 3, 2
D. 2, 2, 3

Explanation

Solution

We should know how to write the change in concentration of the reactants versus change in concentration of the product in a chemical reaction.
For xA+yBxA + yB →\to zCzC chemical reaction, the change in concentration of the reactants versus change in concentration of the product is as follows.
−1xd[A]dt=−1yd[B]dt=1zd[C]dt-\dfrac{1}{x}\dfrac{d[A]}{dt}=-\dfrac{1}{y}\dfrac{d[B]}{dt}=\dfrac{1}{z}\dfrac{d[C]}{dt}

Complete step by step solution:
- In the question it is asked to find the x, y and z values for the given chemical reaction.
- For xA + yB →\to zC chemical reaction, the change in concentration of the reactants versus change in the concentration of the products is as follows.
−1xd[A]dt=−1yd[B]dt=1zd[C]dt→(1)-\dfrac{1}{x}\dfrac{d[A]}{dt}=-\dfrac{1}{y}\dfrac{d[B]}{dt}=\dfrac{1}{z}\dfrac{d[C]}{dt}\to (1)
- The given relationship between the reactants and the products in the question is as follows.
−d[A]dt=−d[B]dt=1.5d[C]dt-\dfrac{d[A]}{dt}=-\dfrac{d[B]}{dt}=1.5\dfrac{d[C]}{dt}
- We can simplify the above relationship to get the values of the x, y and z.
−d[A]dt=−d[B]dt=1.5d[C]dt-\dfrac{d[A]}{dt}=-\dfrac{d[B]}{dt}=1.5\dfrac{d[C]}{dt}
- Initially multiply the above equation with 13\dfrac{1}{3}

& -\dfrac{1}{3}\dfrac{d[A]}{dt}=-\dfrac{1}{3}\dfrac{d[B]}{dt}=\dfrac{1}{3}\times \dfrac{3}{2}\dfrac{d[C]}{dt} \\\ & -\dfrac{1}{3}\dfrac{d[A]}{dt}=-\dfrac{1}{3}\dfrac{d[B]}{dt}=\dfrac{1}{2}\dfrac{d[C]}{dt}\to (2) \\\ \end{aligned}$$ \- Now compare the equations (1) and (2) then we will get the x, y and z values. \- The x, y and z values are 3, 3, 2. \- Means 3moles of x reacts with 3 moles of y and forms 2 moles of the z as the product. **So, the correct option is C.** **Note:** We are supposed to multiply the given equation with a proper number to get the values of the x, y and Z. If we choose an improper number then it is very difficult to get the values of x, y and z form the given relationship.