Question

Borax, sodium tetraboratedecahydrate, is an important mineral found in dry lakebeds in California. It is used to make soap and glass and used as a preservative. You can use the values of Ksp (solubility-product constant) of borax at different temperatures to determine ΔH∘, ΔS∘, and ΔG∘ for the dissolution of borax:

Na2B4O5(OH)4⋅8H2O(s)(borax)→2Na+(aq)+B4O5(OH)42−(aq)(tetraborate)+8H2O(l)

The relationship

ln(Ksp)=−ΔH∘RT+ΔS∘R

has the form of a linear equation, y=mx+b, where y is lnKsp and x is 1/T. The slope (m) is equal to −ΔH∘/R, and the y intercept (b) is ΔS∘/R, where R is the gas constant, 8.314 J/(mol⋅K) . If you measure Ksp at several temperatures, you can plot lnK versus 1/T (where T is temperature in kelvins) as shown in Figure 1 (Figure 1).

Knowing the values of ΔH∘ and ΔS∘ at a specific temperature allows the calculation of the change in Gibbs free energy for the reaction ΔG∘=ΔH∘−TΔS∘.

The table below lists Ksp values for the dissolution of borax at several temperatures (∘C).

Temperature (∘C) Ksp  
40.0      0.041
45.0 0.083
50.0 0.264
55.0 0.486
60.0 0.552

Temperature C	KSP
40.0	0.041
45.0	0.083
50.0	0.264
55.0	0.486
60.0	0.552

On your own, plot a graph of lnKsp versus 1/T (in kelvins). Then, determine the slope (m ) and y intercept (b ) of the best-fitting line that results from the data points of that plot and report them below.

Express the slope and y intercept to three significant figures separated by a comma.

Answer 1

Slope = -1.46 x 10⁴

y-intercept = 43.5

Explanation

The equation of the best fit line obtained from graph is : y = -14589x + 43.502

This is in the form : y = mx + b

Slope = m = -14589

y-intercept = b = 43.502

Chart Tools Home er Page Layout Formulas Data Revie V Design Layout Format Chart 1 1 Temperature (oC) sp T (K) InKsp 0.041 313.15 0.00319336-3.1941832 Inksp vs. 1/T 45 0.083 318.15 0.00314317 -2.4889147 0.264323.15 0.003094541.3318062 0.486 328.15 0.00304739 -0.7215467 0.003 0.00305 0.0031 0.00315 0.0032 0.00325 0.552 333.15 0.00300165 -0.5942072 0.5 10 13 y -14589x 43.502 15 16 17 -2.5 18 19 3.5 25 26 27 28 Ready :1凾ELI (- .83 151 7784 Count: 12 Sum:-8.3151 77842 110% Average: