QuestionIn a closed container, $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ dissociates according the following reaction; $\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})$
When 1.00 mol of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ dissociates, the equilibrium mixture contains 0.80 mol of $\mathrm{Cl}_{2}$ at 673 K and a total pressure of 125 atm .
Write an expression for the equilibrium constant, $\mathrm{K}_{\mathrm{p}}$ . Calculate the partial pressure of each gases in the equilibrium mixture. [5 marks]

Studdy Solution

STEP 1

1. The reaction is at equilibrium.
2. The initial amount of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is 1.00 mol.
3. The equilibrium amount of $\mathrm{Cl}_{2}$ is 0.80 mol.
4. The total pressure at equilibrium is 125 atm.
5. The temperature is 673 K.

STEP 2

1. Determine the change in moles for each species.
2. Calculate the equilibrium moles of each species.
3. Calculate the partial pressures of each gas.
4. Write the expression for the equilibrium constant $K_p$ .
5. Calculate $K_p$ using the partial pressures.

STEP 3

Determine the change in moles for each species based on the stoichiometry of the reaction:
- Initial moles of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ = 1.00 mol - Change in moles of $\mathrm{Cl}_{2}$ = +0.80 mol - Since the stoichiometry is 1:1:1, the change in moles for $\mathrm{SO}_{2}$ is also +0.80 mol. - Change in moles of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ = -0.80 mol

STEP 4

Calculate the equilibrium moles of each species:
- Equilibrium moles of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ = $1.00 - 0.80 = 0.20$ mol - Equilibrium moles of $\mathrm{SO}_{2}$ = $0.80$ mol - Equilibrium moles of $\mathrm{Cl}_{2}$ = $0.80$ mol

STEP 5

Calculate the partial pressures of each gas using the total pressure and mole fractions:
- Total moles at equilibrium = $0.20 + 0.80 + 0.80 = 1.80$ mol - Partial pressure of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ : P_{\mathrm{SO}_{2} \mathrm{Cl}_{2}} = \left(\frac{0.20}{1.80}\right) \times 125 \, \text{atm} = 13.89 \, \text{atm} \] - Partial pressure of $\mathrm{SO}_{2}$: P_{\mathrm{SO}_{2}} = \left(\frac{0.80}{1.80}\right) \times 125 \, \text{atm} = 55.56 \, \text{atm} \] - Partial pressure of $\mathrm{Cl}_{2}$ : $ P_{\mathrm{Cl}_{2}} = \left(\frac{0.80}{1.80}\right) \times 125 \, \text{atm} = 55.56 \, \text{atm} \]

STEP 6

Write the expression for the equilibrium constant $K_p$ :
$K_p = \frac{P_{\mathrm{SO}_{2}} \times P_{\mathrm{Cl}_{2}}}{P_{\mathrm{SO}_{2} \mathrm{Cl}_{2}}}$

STEP 7

Calculate $K_p$ using the partial pressures:
$K_p = \frac{55.56 \, \text{atm} \times 55.56 \, \text{atm}}{13.89 \, \text{atm}} = 222.24$
The equilibrium constant $K_p$ is $\boxed{222.24}$ .

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Studdy Solution

STEP 1

1. The reaction is at equilibrium.
2. The initial amount of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is 1.00 mol.
3. The equilibrium amount of $\mathrm{Cl}_{2}$ is 0.80 mol.
4. The total pressure at equilibrium is 125 atm.
5. The temperature is 673 K.

STEP 2

1. Determine the change in moles for each species.
2. Calculate the equilibrium moles of each species.
3. Calculate the partial pressures of each gas.
4. Write the expression for the equilibrium constant $K_p$ .
5. Calculate $K_p$ using the partial pressures.

STEP 3

STEP 4

Calculate the equilibrium moles of each species:
- Equilibrium moles of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ = $1.00 - 0.80 = 0.20$ mol - Equilibrium moles of $\mathrm{SO}_{2}$ = $0.80$ mol - Equilibrium moles of $\mathrm{Cl}_{2}$ = $0.80$ mol

STEP 5

STEP 6

Write the expression for the equilibrium constant $K_p$ :
$K_p = \frac{P_{\mathrm{SO}_{2}} \times P_{\mathrm{Cl}_{2}}}{P_{\mathrm{SO}_{2} \mathrm{Cl}_{2}}}$

STEP 7

Calculate $K_p$ using the partial pressures:
$K_p = \frac{55.56 \, \text{atm} \times 55.56 \, \text{atm}}{13.89 \, \text{atm}} = 222.24$
The equilibrium constant $K_p$ is $\boxed{222.24}$ .

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Studdy Solution

STEP 1

1. The reaction is at equilibrium.2. The initial amount of SO2Cl2\mathrm{SO}_{2} \mathrm{Cl}_{2}SO2​Cl2​ is 1.00 mol.3. The equilibrium amount of Cl2\mathrm{Cl}_{2}Cl2​ is 0.80 mol.4. The total pressure at equilibrium is 125 atm.5. The temperature is 673 K.

STEP 2

1. Determine the change in moles for each species.2. Calculate the equilibrium moles of each species.3. Calculate the partial pressures of each gas.4. Write the expression for the equilibrium constant KpK_pKp​.5. Calculate KpK_pKp​ using the partial pressures.

STEP 3

STEP 4

STEP 5

STEP 6

Write the expression for the equilibrium constant KpK_pKp​:Kp=PSO2×PCl2PSO2Cl2K_p = \frac{P_{\mathrm{SO}_{2}} \times P_{\mathrm{Cl}_{2}}}{P_{\mathrm{SO}_{2} \mathrm{Cl}_{2}}}Kp​=PSO2​Cl2​​PSO2​​×PCl2​​​

STEP 7

Calculate KpK_pKp​ using the partial pressures:Kp=55.56 atm×55.56 atm13.89 atm=222.24K_p = \frac{55.56 \, \text{atm} \times 55.56 \, \text{atm}}{13.89 \, \text{atm}} = 222.24Kp​=13.89atm55.56atm×55.56atm​=222.24 The equilibrium constant KpK_pKp​ is 222.24 \boxed{222.24} 222.24​.

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1. The reaction is at equilibrium.
2. The initial amount of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is 1.00 mol.
3. The equilibrium amount of $\mathrm{Cl}_{2}$ is 0.80 mol.
4. The total pressure at equilibrium is 125 atm.
5. The temperature is 673 K.

1. Determine the change in moles for each species.
2. Calculate the equilibrium moles of each species.
3. Calculate the partial pressures of each gas.
4. Write the expression for the equilibrium constant $K_p$ .
5. Calculate $K_p$ using the partial pressures.

Write the expression for the equilibrium constant $K_p$ :
$K_p = \frac{P_{\mathrm{SO}_{2}} \times P_{\mathrm{Cl}_{2}}}{P_{\mathrm{SO}_{2} \mathrm{Cl}_{2}}}$

Calculate $K_p$ using the partial pressures:
$K_p = \frac{55.56 \, \text{atm} \times 55.56 \, \text{atm}}{13.89 \, \text{atm}} = 222.24$
The equilibrium constant $K_p$ is $\boxed{222.24}$ .