Q. 22

# The rate constant

Answer :

To convert the temperature in °C to °K we add 273 K.  The graph is given as:

The Arrhenius equation is given by k = Ae-Ea/RT

Where, k- Rate constant

A- Constant

Ea-Activation Energy

R- Gas constant

T-Temperature

Taking natural log on both sides,

ln k = ln A-(Ea/RT)

→ equation 1

By plotting a graph, ln K Vs 1/T, we get y-intercept as ln A and Slope is –Ea/R.

Slope = (y2-y1)/(x2-x1)

By substituting the values, slope = -12.301

⇒ –Ea/R = -12.301

But, R = 8.314 JK-1mol-1

⇒ Ea = 8.314 JK-1mol-1 × 12.301 K

⇒ Ea = 102.27 kJ mol-1

Substituting the values in equation 1 for data at T = 273K  (∵ At T = 273K, ln k = -7.147)

On solving, we get ln A = 37.911

∴ A = 2.91×106

When T = 300C, hence T = 30 + 273 = 303K  ⇒ ln k = -2.8

⇒ k = 6.08x10-2s-1.

When T = 500C, hence T = 50 + 273 = 323K

Substituting in equation 1,

A = 2.91 × 106, Ea = 102.27 kJ mol-1

Ln K = ln(2.91 × 106)- 102.27/(8.314 × 323)

Thus, ln k = -0.5 and k = 0.607s-1.

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