Question

During a chemical treatment of wastewater the reaction rate found to be 20.8 /minutes when the temperature of wastewater was 29.4°C. What will be the reaction rate when the same reaction is performed in the evening when temperature reduced to Y °C. The value of temperature coefficient is 1.130

NaOH + FeCl_{3 >}    Fe(OH)₃ + NaCl

Answer 1

The temperature coefficient (Q) can be obtained from the equation :

Q = (R₂/R₁)^(10/T₂ - T₁)

R = rate of reaction

T = Temperature at which the reaction takes place in degree Celsius

given:

R₁ = 20.8 /minutes

T₁ = 29.4⁰C

Q = 1.13

T₂ = Y⁰C

substituting in the equation

Q = (R₂/R₁)^(10/T₂ - T₁)

1.13 = (R₂ /20.8)^(10/Y - 29.4)

On taking log on both sides, we get,

ln(1.13) = (10/Y - 29.4)ln(R₂/20.8)

0.1222(Y - 29.4/10) = ln(R₂/20.8)

0.01222Y - 0.3593 =ln(R₂/20.8)

e^(0.01222Y - 0.3593) = R₂/20.8

R₂ = 20.8e^(0.01222Y - 0.3593)

R₂ =[20.8e^(0.01222Y)]/e^(0.3593)

R₂ = [20.8e^(0.01222Y)] / 1.432

R₂ = 14.52e^(0.01222Y)

For temperature Y⁰C the reaction rate will be:

R₂ = 14.52e^(0.01222Y)