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Thermodynamics from Equilibrium Essay Assignment

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InstructionsQUESTIONS NEED TO BE ANSWER

Thermodynamics from Equilibrium: Determination of DG°, DH°, and DS°

Purpose

Determine a variety of thermodynamic quantities from the solubility information of a sparingly soluble salt at various temperatures.

Introduction

The system you will be studying involves a relatively simple solubility equilibrium of borax (Na2B4O7•10H2O) in water:

Na2B4O7 • 10H2O(s) ⇌ 2Na+(aq) + B4O5(OH)42-(aq) + 8H2O(l)

Which has an solubility product equilibrium expression as follows, once you remove the solid and liquid terms:

Ksp = [Na+]2 [B4O5(OH)42-]

Since the concentration of sodium ion is two times the concentration of borate, we can plug the borate concentration value in for both the sodium and borate terms. This simplifies what we have to measure so that we can solve the problem by finding only the concentration of borate.

K = [ (2 [B4O5(OH)42-] ) ]2 [B4O5(OH)42-]

Ksp = 4 [B4O5(OH)42-]3

We find the borate concentration by titrating with HCl. The titration reaction is:

B4O5(OH)42-(aq) + 2HCl(aq) + 3H2O(l) ———-> 4 B(OH)3(aq) + 2 Cl- (aq)

Remember that K is dependent upon temperature, so if we record the amount of HCl needed to complete the titration at different temperatures, we can find Ksp at different temperatures. This will allow us to calculate enthalpy and entropy for the reaction.

Simplified lab procedure: Make a saturated solution of borax at 60 °C. You will know it is saturated if there is solid that won’t dissolve. A saturated solution is at equilibrium, so any concentrations we measure will be the equilibrium concentrations. Take 5 mL of the saturated solution and titrate with HCl. Cool the solution 10 degrees then take another portion and titrate it. Repeat until you are at room temperature.

Calculations for titration:

Multiple the concentration of HCl times the volume used in the titration (found by subtracting the initial buret reading from the final reading). This is the moles of HCl used. Using the titration equation shown above, calculate the moles of borate from the moles of HCl. Divide by the 5 mL portion of borate solution to get concentration of borate in molarity. Use the borate concentration is the bold Ksp equation above to solve for Ksp. You will do this for each temperature.

How to make a graph:

Now that you have equilibrium constant values at different temperatures, we can solve for free energy.

DG = -RT ln Ksp

The free energy change at a given temperature is itself related to both the change in enthalpy, and the change in entropy, by the following equation:

DG = DH – TDS

Which means that you can combine the two equations for DG into:

-RT ln Ksp = DH – TDS

In order to solve for DH and DS, we need to make this equation into something we can easily graph as a straight line. You divide both sides of the equation by –RT, simplify, and define the x axis to be 1/T and the y axis to be ln K:

That will make -DH/R and DS/R the slope and Y-intercept, respectively. Thus, by generating one graph, two values can be arrived at simultaneously, H and S.

Convert your temperatures into Kelvin and calculate the natural log of your Ksp values. Calculate the inverse of each temperature value. Collect those numbers in the following table:

ln K Inverse temperature Copy this table into Excel (or a similar program). Create a scatterplot and add a trendline.

Calculations of thermodynamic values:

Use the slope of the trendline to determine DH and the y-intercept to determine DS.

Calculate the value for DG = DH – TDS using the values for DH and DS from your graph.

Read the lab activity.

- Plot your values of ln(Ksp) vs. 1/T and find the slope and y-intercept of the best fit line. Use the equation for the best fit line and the following equation
ln K = -∆H°/RT + ∆S°/R

Enter your graph trendline below.

- What is the slope from your graph?
- What is the value of ΔΔH?
- What is the y-intercept?
- What is the ΔΔS?
ln K

sp

=

–

D

H

RT

T

D

S

RT

+

ln K

sp

=

–

D

H

R

D

S

R

+

1

T

y = m x + b

November 27, 2021

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