At 518 degress celsius that rate of decomposition of a sample of acetaldehyde, initially at a pressure of 363 torr, was 1.07 Torr/sec when 5% had reacted, and 0.760 torr/sec when 20% had reacted. What is the order of the reaction?
To determine the order of the reaction, we need to analyze the relationship between the rate of decomposition and the extent of reaction. The order of the reaction can be identified from the reaction rate expression.
Given that the reaction is the decomposition of acetaldehyde, the reaction rate expression can be written as:
Rate = k[A]^m[B]^n
Where:
- Rate is the rate of decomposition
- [A] and [B] are the concentrations of the reactants (in this case, acetaldehyde)
- k is the rate constant
- m and n are the respective orders of the reaction with respect to [A] and [B]
In this case, since acetaldehyde is the only reactant mentioned, we can simplify the rate expression to:
Rate = k[A]^m
Since we are given that the rate of decomposition is dependent on the extent of reaction, we can equate the rate to a fraction of the initial concentration of acetaldehyde, [A]:
Rate = (d[A]/dt) = - (1/x)(d[A]/dt)
Where:
- d[A]/dt represents the rate of change of concentration of acetaldehyde over time.
- x represents the extent of reaction (the fraction of acetaldehyde that has reacted).
The negative sign in front indicates that the concentration of acetaldehyde is decreasing with time (as it is decomposing).
Using the given information:
At 5% reacted:
Rate = 1.07 Torr/sec
x = 5% = 0.05
At 20% reacted:
Rate = 0.760 Torr/sec
x = 20% = 0.20
Now, let's calculate the orders of reaction (m) for the two data points:
For the first data point:
(1.07 Torr/sec) = (- (1/0.05))(d[A]/dt)
- (1.07 Torr/sec) * (-0.05) = (d[A]/dt)
For the second data point:
(0.760 Torr/sec) = (- (1/0.20))(d[A]/dt)
- (0.760 Torr/sec) * (-0.20) = (d[A]/dt)
Now, we have two expressions for the rate of change of concentration with respect to time. By comparing these expressions, we can determine the order of the reaction.
((d[A]/dt)(x=0.05)) / ((d[A]/dt)(x=0.20)) = (((1.07 Torr/sec) * (-0.05)) / ((0.760 Torr/sec) * (-0.20)))
By simplifying and solving this equation, we can find the order of the reaction.