Urbium (Ur) is an upscale element found in big cities. Its oxide (UrO2) is not very stable and decomposes readily at temperatures exceeding 66∘ C. The figure below shows how the rate of reaction varies with the concentration of UrO2 at 75∘ C.
The rate r is in units of M⋅s−1 and the concentration c of UrO2 is in units of M (mole⋅L−1). The slope has a value of 1.34 and the intercept has a value of 1.51. What is the order of reaction for the decomposition of urbium oxide?
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To determine the order of reaction for the decomposition of urbium oxide (UrO2), we need to analyze the data given in the figure.
The rate of reaction is given in units of M⋅s^−1, and the concentration of UrO2 is given in units of M (mole⋅L^−1). The figure shows how the rate of reaction varies with the concentration of UrO2 at 75∘C.
First, let's analyze the slope of the graph, which is given as 1.34. In a rate equation, the exponent of the concentration represents the order of reaction with respect to that reactant. Therefore, the slope of the graph represents the order of reaction with respect to UrO2.
Since the slope is 1.34, we can conclude that the order of reaction with respect to UrO2 is approximately 1.
Now, let's analyze the intercept of the graph, which is given as 1.51. The intercept represents the rate constant, k, of the reaction when the concentration of UrO2 is zero.
Since the decomposition of UrO2 is a first-order reaction (order of reaction = 1), the rate equation for this reaction can be written as:
rate = k * [UrO2]^1
From the given intercept, we can calculate the rate constant, k:
1.51 = k * 0
Since anything multiplied by zero is zero, we can conclude that the intercept of 1.51 is not meaningful in this case. It is likely an experimental measurement error or an indication that the reaction rate cannot be determined at zero concentration.
In conclusion, the order of reaction for the decomposition of urbium oxide (UrO2) is approximately 1, based on the slope of the graph.