QuestionFor the vaporization of one mole of bromine at $59^{\circ} \mathrm{C}, \Delta H=29.6 \mathrm{~kJ}$ . Calculate (a) $\triangle P V$ (b) $\Delta E$

Studdy Solution

STEP 1

1. We are dealing with the vaporization of bromine, which implies a phase change from liquid to gas.
2. The temperature given is $59^{\circ} \mathrm{C}$ , which we may need to convert to Kelvin for some calculations.
3. $\Delta H$ represents the enthalpy change, which is given as $29.6 \mathrm{~kJ}$ .
4. The ideal gas law may be applied for calculations involving gases.
5. $\Delta P V$ refers to the change in pressure-volume work during the phase change.
6. $\Delta E$ represents the change in internal energy, which is related to $\Delta H$ and $\Delta P V$ .

STEP 2

1. Calculate $\Delta P V$ using the ideal gas law.
2. Calculate $\Delta E$ using the relationship between enthalpy change and internal energy change.

STEP 3

Convert the temperature from Celsius to Kelvin.
$T = 59^{\circ} \mathrm{C} + 273.15 = 332.15 \, \mathrm{K}$

STEP 4

Use the ideal gas law to find the change in volume ( $\Delta V$ ) when one mole of bromine vaporizes. Assuming 1 mole of gas at ideal conditions:
$PV = nRT$
For 1 mole of gas ( $n = 1$ ),
$P \Delta V = RT$

STEP 5

Insert the values into the equation. The gas constant $R = 8.314 \, \mathrm{J/(mol \cdot K)}$ :
$\Delta P V = (1 \, \mathrm{mol}) \times (8.314 \, \mathrm{J/(mol \cdot K)}) \times (332.15 \, \mathrm{K})$

STEP 6

Calculate the product to obtain $\Delta P V$ :
$\Delta P V = 8.314 \times 332.15 = 2761.81 \, \mathrm{J} = 2.76181 \, \mathrm{kJ}$

STEP 7

Use the relationship between enthalpy change ( $\Delta H$ ) and internal energy change ( $\Delta E$ ). For phase changes at constant pressure:
$\Delta H = \Delta E + \Delta P V$

STEP 8

Rearrange the equation to solve for $\Delta E$ :
$\Delta E = \Delta H - \Delta P V$

STEP 9

Insert the values of $\Delta H$ and $\Delta P V$ :
$\Delta E = 29.6 \, \mathrm{kJ} - 2.76181 \, \mathrm{kJ}$

STEP 10

Calculate the difference to find $\Delta E$ :
$\Delta E = 29.6 - 2.76181 = 26.83819 \, \mathrm{kJ}$
Solution: (a) $\Delta P V = 2.76181 \, \mathrm{kJ}$
(b) $\Delta E = 26.83819 \, \mathrm{kJ}$

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