Question

for: rate=k[A]^x determine the value of x if the rate doubles when [A] is doubled; and if the rate quadruples when [A] is doubled.,

Answer 1

1. The value of x if the rate doubles when [A] is doubled is that x = 1 

2. Then if the rate quadruples when [A] is doubled is that x= 2
Since x=1 when the rate doubles, so if it quadruples, it will be times 2.
So the solution to this is 1 times 2= 2
x=2

Answer 2

Answer:

• If the rate doubles when [A] is doubled,  x = 1
• If the rate quadruples when  [A] is doubled, x=2

Explanation:

We have the equation for the rate:

$r=k[A]^{x}$  equation 1

• For the first case, we  can rewrite the equation 1, as follows:

$2r=k[2A]^{x}=2^{x}k[A]^{x}$  equation 2

Replacing  equation 1 in 2, we get:

$2r=2^{x}r$

Then x must be equal to 1, in order to satisfy equality

• For the second case, we  can rewrite the equation 1, as follows:

$4r=k[2A]^{x}=2^{x}k[A]^{x}$  equation 3

Replacing equation 1 in 3, we get:

$4r=2^{x}r$

Then x must be equal to 2, in order to satisfy equality