Answer:
[AB] = 0.66M
Explanation:
rate = change in concentration/time
Initial concentration of AB = 1.5M
Let the concentration of AB after 10.3s be y
Therefore, rate = 1.5 - y/10.3
The rate equation is given as
rate = k[AB]^2 = 0.2y^2
0.2y^2 = 1.5 - y/10.3
2.06y^2 = 1.5 - y
2.06y^2 + y - 1.5 = 0
Using the quadratic formula
y = [-1 + or - √(1^2 -4×2.06×-1.5)/2(2.06)]
The value of y must be positive
y = (-1 + √13.36)/4.06 = -1+3.66/4.06 = 2.66/4.06 = 0.66
Concentration of AB after 10.3s is 0.66M
For the simple decomposition reaction, the concentration of reactant i.e. AB after 10.3 sec is 0.66M.
Rate of any reaction is defined as the rate of change of concentration with respect to the time.
Given reaction is:
AB(g) → A(g) + B(g)
Rate for this reaction is 0.20 L/mol·s, which can be calculated as k[AB]².
Initial concentration of AB = 1.50 M (given)
Let, concentration of AB after 10.3 sec = y
So, Rate of the reaction can be expressed as = 1.50 - y/10.3 ...........(i)
Let we calculate the rate on the basis of given equation = 0.20 [y]² ........(ii)
From (i) & (ii) equation,
0.20 [y]² = 1.50 - y/10.3
2.06 [y]² = 1.50 - y
2.06 [y]² + y - 1.50 = 0
We can find the value of y by using the formula of quadratic equation as :
y = [-1 + or - √(1^2 -4×2.06×-1.5)/2(2.06)]
[tex]\[\frac{{{\rm{ - 1 + or - }}\sqrt {{{{\rm{(1)}}}^{\rm{2}}}{\rm{ - 4 \times 2}}{\rm{.06 \times 1}}{\rm{.50}}} }}{{{\rm{2 \times 2}}{\rm{.06}}}}{\rm{ = 0}}\][/tex]
y = + or - 0.66
But value of concentration is never zero.
So, y = 0.66 M
Hence, the concentration of AB after 10.3 sec is 0.66M.
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https://brainly.com/question/517581
