You measure Ksp for borax to be 7.8 x 10-3 and 2.9 x 10-3 at 23.6°C and 1.8°C, respectively. Calculate the standard enthalpy change, ΔH°, (in kJ) for the dissolution of borax.
To calculate the standard enthalpy change ΔH° for the dissolution of borax, we can use the van 't Hoff equation:
ln(Ksp2/Ksp1) = (-ΔH°/R) * (1/T2 - 1/T1)
Where:
- Ksp1 and Ksp2 are the solubility product constants at the corresponding temperatures,
- ΔH° is the standard enthalpy change,
- R is the gas constant (8.314 J/(mol*K)),
- T1 and T2 are the temperatures in Kelvin.
First, let's convert the given temperatures from Celsius to Kelvin:
T1 = 23.6°C + 273.15 = 296.75 K
T2 = 1.8°C + 273.15 = 275.95 K
Now, we can substitute the given values into the van 't Hoff equation:
ln(2.9 × 10^(-3) / 7.8 × 10^(-3)) = (-ΔH°/8.314) * (1/275.95 - 1/296.75)
Simplifying the equation:
ln(2.9 × 10^(-3) / 7.8 × 10^(-3)) = (-ΔH°/8.314) * (-0.00360)
Taking the natural logarithm:
-1.28155 = (-ΔH°/8.314) * (-0.00360)
Now, let's solve for ΔH°:
ΔH° = (-1.28155 * 8.314) / (-0.00360)
Calculating the result:
ΔH° ≈ 296.359 kJ
Therefore, the standard enthalpy change ΔH° for the dissolution of borax is approximately 296.359 kJ.
To calculate the standard enthalpy change (ΔH°) for the dissolution of borax, we will use the van 't Hoff equation:
ln(Ksp2/Ksp1) = ΔH°/R * (1/T1 - 1/T2)
Where:
- ln represents the natural logarithm.
- Ksp1 and Ksp2 are the solubility product constants of borax at temperatures T1 and T2, respectively.
- ΔH° is the standard enthalpy change.
- R is the ideal gas constant (8.314 J/(mol·K)).
- T1 and T2 are the temperatures in Kelvin.
First, we need to convert the temperatures from Celsius to Kelvin:
T1 = 23.6 + 273.15 = 296.75 K
T2 = 1.8 + 273.15 = 275.95 K
Now, we can substitute the given values into the equation:
ln(2.9 x 10^(-3)/7.8 x 10^(-3)) = ΔH°/(8.314 J/(mol·K)) * (1/296.75 K - 1/275.95 K)
Next, we can solve for ΔH° by rearranging the equation:
ΔH° = ln(2.9 x 10^(-3)/7.8 x 10^(-3)) * (8.314 J/(mol·K)) * (1/296.75 K - 1/275.95 K)
Calculating this expression should give you the value for ΔH° in joules. To convert it to kilojoules, simply divide the result by 1000.
Note: The value of ln(2.9 x 10^(-3)/7.8 x 10^(-3)) should be taken with the natural logarithm (ln) function on your calculator or by using logarithmic tables.