2X(g) + Y(g) → Z(g): In the equation above, The rate of formation of Z is found to be independent of the concentration of Y and to quadruple when the concentration of X is doubled. The correct equation for the reaction is?
The problem states that the rate of formation of Z is independent of the concentration of Y. In chemical kinetics, if the rate does not change when the concentration of a reactant changes, the reaction is zero-order with respect to that reactant.
Order with respect to Y = 0. Mathematically, R ∝ [Y]\(^0\)
The problem also states that the rate quadruples (increases by a factor of 4) when the concentration of X is doubled. We can use the general rate proportion
Rate ∝ [Y]\(^n\)
When concentration is 2 [X], the rate is 4 R\(_1\),
This confirms the reaction is second-order with respect to X.
By combining the orders for both reactants, we get the overall rate equation: R = K [X]\(^2\)[Y]\(^0\)
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