The rate data from a chemical reaction shows that doubling the concentration of A with the concentration of B remaining constant causes the rate to increase by a factor of four. What is the reaction order for [A]?
a. 0
b. 0.5
c. 1
d. 2
e. 3
The order is 2 for reactant A.
Because 22 = 4.
To determine the reaction order for [A], we can use the rate law equation. The rate law equation describes the relationship between the rate of the reaction and the concentrations of the reactants.
Let's call the reaction order for [A] as "x".
According to the given information, when the concentration of A is doubled while the concentration of B remains constant, the rate increases by a factor of four. This can be expressed mathematically as:
(rate when [A] is doubled)/(rate when [A] is original) = (concentration when [A] is doubled)^x / (concentration when [A] is original)^x = 4
Since the concentration of B remains constant and does not affect the rate when [A] is varied, we can simplify the equation as:
2^x / 1^x = 4
Simplifying further:
2^x = 4
We solve for x by taking the logarithm of both sides:
x * log2 = log4
Using logarithmic properties:
x * log2 = 2 * log2
Dividing both sides by log2:
x = 2
Therefore, the reaction order for [A] is 2.
Therefore, the correct answer is option d) 2.
To determine the reaction order for [A], we can analyze the rate equation of the reaction. The rate equation relates the concentrations of the reactants to the rate of the reaction. In this case, the rate equation can be written as:
Rate = k[A]^x[B]^y
Where [A] and [B] are the concentrations of reactants A and B respectively, and k is the rate constant. The exponents x and y represent the reaction orders for reactants A and B, respectively.
According to the given information, doubling the concentration of A while keeping the concentration of B constant causes the rate to increase by a factor of four. Mathematically, this can be expressed as:
Rate when [A] doubles = 4 * Rate at initial conditions
If we substitute this into the rate equation, we get:
k * [A]^x * [B]^y = 4 * (k * [A]_initial^x * [B]_initial^y)
The initial concentrations of A and B are the same, so we can simplify further:
k * [A]^x * [B]^y = 4 * k * [A]^x * [B]^y
Now, we can cancel out the rate constant and simplify the equation:
[A]^x = 4 * [A]^x
Dividing both sides of the equation by [A]^x, we get:
1 = 4
Since this equation is not true, we can conclude that the reaction order for [A] cannot be any of the given options. It is not possible to determine the reaction order for [A] based on the information provided.
Therefore, the answer is none of the options provided.