Question

In: Chemistry

You proceed to measure the equilibrium constant at three more temperatures, and now have the following...

You proceed to measure the equilibrium constant at three more temperatures, and now have the following results:

Temperature (K)

Equilibrium constant

100.0 ± 0.01

(1.6±0.1) ×104

150.0±0.01

(3.3±0.1) ×104

200.0 ± 0.01

(5.7±0.1) ×104

250.0±0.01

(6.2±0.1) ×104

300.0±0.01

(7.8±0.1) ×104

(a) Linearize your date and perform a linear regression, using Excel or another computer program. Use the program to find the slope, intercept, and uncertainties in the slope and intercept.

(b) Make a figure of the linearized data in 7(a); be sure to include the best-fit line.

(c) Calculate the ΔH and ΔS for this reaction.

(d) Estimate the uncertainties for ΔH and ΔS in part (c).

Solutions

Expert Solution

(a) Linear data points,

Temperature (K) (1/T))            Equilibrium constant (K) (lnK)

100  (0.01)                                  1.6x10^4 (9.68)

150  (0.007)                                3.3x10^4 (10.40)

200  (0.005)                                5.7x10^4 (10.95)

250  (0.004)                                6.2x10^4 (11.035)

300  (0.003)                                7.8x10^4 (11.26)

To calculate maximum slope we will use the values, (100.01,1.5x10^4) and (299.99,7.9x10^4)

maximum slope = y2-y1/x2-x1 = 7.9x10^4-1.5x10^4/299.99-100.01 = 320.032

To calculate minimum slope values, (99.99,1.6x10^4) and (300.01,7.7x10^4)

Minimum slope = 7.7x10^4-1.6x10^4/300.01-99.99) = 304.9695

uncertainty in the slope = max slope-min slope/2 = 320.032-304.9695/2 = 7.53

So the actual slope of this line becomes = 320 +/- 7.53

The uncertainty in the intercept

Intercept of line is 0.33x10^4

the uncertainty is approximately 0.1

(b) Using the relation,

lnKeq = -deltaH/RT + delta S/R

Plot lnKeq vs 1/T [data given above]

(c) Find delta H and delta S from slope and intercept of the line

slope = -240 = -deltaH/R

deltaH = 240 x 8.314 = 1995.36 J/mol

intercept = deltaS/R = 9.5265

delta S = 9.5265 x 8.314 = 79.203 J/K.mol

(d) Uncertainty for delta H +/-0.01

For delta S = +/-0.01


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