Question

For a given reaction of the type \( \frac{3}{5}X(aq) \rightarrow \frac{1}{2}Y(aq) + Z(g) \), the correct expression for the rate of disappearance of \(X\) with reference to \(Y\) is}

• A. \( -\frac{d[X]}{dt} = \frac{6}{5}\frac{d[Y]}{dt} \)
• B. \( -\frac{d[X]}{dt} = \frac{5}{6}\frac{d[Y]}{dt} \)
• C. \( -\frac{d[X]}{dt} = \frac{3}{10}\frac{d[Y]}{dt} \)
• D. \( -\frac{d[X]}{dt} = \frac{d[Y]^{1/2}}{dt} \)

Hint:

Always use stoichiometric coefficients: divide rate by coefficients to relate reactant and product rates.

Answer 1

The Correct Option is A

Step 1: Write general rate expression.
For a reaction:
\[ aA \rightarrow bB \]
Rate is given by:
\[ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = \frac{1}{b}\frac{d[B]}{dt} \]

Step 2: Apply to given reaction.
\[ \frac{3}{5}X \rightarrow \frac{1}{2}Y + Z \]
So,
\[ \text{Rate} = -\frac{1}{\frac{3}{5}}\frac{d[X]}{dt} = \frac{1}{\frac{1}{2}}\frac{d[Y]}{dt} \]

Step 3: Simplify coefficients.
\[ \text{Rate} = -\frac{5}{3}\frac{d[X]}{dt} = 2\frac{d[Y]}{dt} \]

Step 4: Equate both expressions.
\[ -\frac{5}{3}\frac{d[X]}{dt} = 2\frac{d[Y]}{dt} \]

Step 5: Rearrange for \( -\frac{d[X]}{dt} \).
\[ -\frac{d[X]}{dt} = \frac{3}{5} \times 2 \frac{d[Y]}{dt} \]
\[ -\frac{d[X]}{dt} = \frac{6}{5}\frac{d[Y]}{dt} \]

Step 6: Interpret result.
Rate of disappearance of \(X\) is proportional to rate of formation of \(Y\).

Step 7: Final conclusion.
\[ \boxed{-\frac{d[X]}{dt} = \frac{6}{5}\frac{d[Y]}{dt}} \]