Respuesta :
if we tabulate the data given, we obtain the following table;
Exp [a](m) [b] (m) Initial rate (m/s)
1 0.273 0.763 2.83
2 0.273 1.526 2.83
3 0.819 0.763 25.47
the rate equation
rate = k [a]ˣ[b]ⁿ
where k = rate constant
x and n are order of reaction with respect to a and b respectively
lets take experiment 1 and 2 where [a] is constant so we can find the order of reaction with respect to b
2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)
2.83 m/s = k [0.273 m]ˣ[1.526 m]ⁿ ----> 2)
2)/1)
1 = [1.526/0.763]ⁿ
1 = 2ⁿ
n = 0
next we have to find out x, we have to take experiment 1 and 3 where [b] remains constant
25.47 m/s =k [0.819]ˣ[0.763]ⁿ --3)
2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)
3)/1)
25.47/2.83 = [0.819/0.273 m]ˣ
9 = 3ˣ
x = 2
therefore order with respect to a = 2 and order with respect to b = 0
rate = k[a]²[b]⁰
to find k lets substitute 1st experiment values
2.83 m/s = k [0.273 m]² [0.763]⁰
k = 2.83/0.0745
k = 37.98 m⁻¹s⁻¹
Exp [a](m) [b] (m) Initial rate (m/s)
1 0.273 0.763 2.83
2 0.273 1.526 2.83
3 0.819 0.763 25.47
the rate equation
rate = k [a]ˣ[b]ⁿ
where k = rate constant
x and n are order of reaction with respect to a and b respectively
lets take experiment 1 and 2 where [a] is constant so we can find the order of reaction with respect to b
2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)
2.83 m/s = k [0.273 m]ˣ[1.526 m]ⁿ ----> 2)
2)/1)
1 = [1.526/0.763]ⁿ
1 = 2ⁿ
n = 0
next we have to find out x, we have to take experiment 1 and 3 where [b] remains constant
25.47 m/s =k [0.819]ˣ[0.763]ⁿ --3)
2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)
3)/1)
25.47/2.83 = [0.819/0.273 m]ˣ
9 = 3ˣ
x = 2
therefore order with respect to a = 2 and order with respect to b = 0
rate = k[a]²[b]⁰
to find k lets substitute 1st experiment values
2.83 m/s = k [0.273 m]² [0.763]⁰
k = 2.83/0.0745
k = 37.98 m⁻¹s⁻¹
In this exercise we will use the knowledge of statistics to calculate the value of the constant, so we have to:
[tex]k = 37.98 m^{-1}s^{-1}[/tex]
Recalling how the form of the rate equation is written, we have:
[tex]rate = k [a]^x[b]^n[/tex]
where:
- k = rate constant
- x and n are order of reaction with respect to a and b respectively
Putting the already known values into the given equation:
[tex]2.83 = k[0.273 m]*[0.763 m]^n \\2.83 = k [0.273 m]*[1.526 m]^n \\1 = [1.526/0.763]^n\\1 = 2^n\\n = 0[/tex]
Now trying to find the value of X in the given equation:
[tex]25.47 =k [0.819]*[0.763]^n\\2.83 = k[0.273]*[0.763]^n\\25.47/2.83 = [0.819/0.273 m]^x\\9 = 3^x\\x = 2[/tex]
Now it will be possible to find the value of the constant as:
[tex]2.83 = k [0.273 m]^2 [0.763]^0\\k = 2.83/0.0745\\k = 37.98 m^{-1}s^{-1}[/tex]
See more about statistics at brainly.com/question/10951564
