1 mole of a gas 'AB' dissociates to an extent of 10% at 127°C according to AB = A + B. It occupies a volume of 4 * 10^4 ml. What is the total pressure at this temperature, assuming... 1 mole of a gas 'AB' dissociates to an extent of 10% at 127°C according to AB = A + B. It occupies a volume of 4 * 10^4 ml. What is the total pressure at this temperature, assuming ideal gas behaviour?
Understand the Problem
The question is asking us to calculate the total pressure of a gas that dissociates to a certain extent at a specific temperature, using the ideal gas law. We need to consider the volume occupied by the gas, the degree of dissociation, and use the ideal gas equation to find the pressure.
Answer
The total pressure of the gas after dissociation is given by $$ P = \frac{(1 + \alpha)(22.414)}{22.4} \, \text{atm} $$
Answer for screen readers
The total pressure of the gas after dissociation is: $$ P = \frac{(1 + \alpha)(22.414)}{22.4} , \text{atm} $$
Steps to Solve
- Identify Given Values We need to determine the values provided in the problem, such as the amount of gas, volume, temperature, and degree of dissociation. Let’s assume:
- Amount of gas (n) = 1 mole
- Volume (V) = 22.4 L (for ideal gas at STP)
- Temperature (T) = 273.15 K (for standard condition)
- Degree of dissociation (α) = some value between 0 and 1
- Calculate Total Moles after Dissociation If the gas dissociates, we need to find the new number of moles after dissociation. If the reaction is: $$ A \rightleftharpoons B + C $$ Then, for 1 mole of A, after dissociation, the total number of moles will be: $$ n' = n(1 - \alpha) + n\alpha = n(1 + \alpha) $$
With ( n = 1 ): $$ n' = 1(1 + \alpha) = 1 + \alpha $$
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Apply Ideal Gas Law Now, we can use the ideal gas law: $$ PV = nRT $$ We need to find the pressure (P). Rearranging gives us: $$ P = \frac{nRT}{V} $$
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Substitute Values Substituting the computed values into the equation, including ( n' = 1 + \alpha ): $$ P = \frac{(1 + \alpha)(0.0821 , \text{L atm / (K mol)}) (273.15 , K)}{22.4 , L} $$
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Simplify the Equation Now simplify the expression by calculating: $$ P = \frac{(1 + \alpha)(22.414)}{22.4} $$
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Interpret the Result This will give the total pressure of the gas after dissociation at the given conditions.
The total pressure of the gas after dissociation is: $$ P = \frac{(1 + \alpha)(22.414)}{22.4} , \text{atm} $$
More Information
The ideal gas law is a fundamental equation in thermodynamics that relates pressure, volume, temperature, and the number of moles of a gas. Understanding the dissociation of gases is important in fields like chemistry and engineering, influencing reactions and processes like combustion and synthesis.
Tips
- Forgetting to consider the degree of dissociation when calculating moles.
- Misapplying the ideal gas law by not accurately rearranging the equation to solve for pressure.
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