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At 30oC the amounts of acetone adsorbed at partial pressure of 10 and 100 mmHg are 0.1 and 0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes the adsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kg
of activated carbon) at a partial pressure of 50 mmHg and 30oC?
of activated carbon) at a partial pressure of 50 mmHg and 30oC?
- a)0.23
- b)0.25
- c)0.30
- d)0.35
Correct answer is option 'C'. Can you explain this answer?
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Given data:
- Adsorption of acetone on activated carbon follows Langmuir isotherm.
- At 30oC, the amounts of acetone adsorbed at partial pressure of 10 and 100 mmHg are 0.1 and 0.4 kg acetone/kg activated carbon, respectively.
To find:
- The amount of acetone adsorbed (in kg per kg of activated carbon) at a partial pressure of 50 mmHg and 30oC.
Solution:
The Langmuir isotherm is given as:
π = ππππ₯π/(1 + πΎπ)
where,
- q is the amount of adsorbate adsorbed per unit mass of the adsorbent (kg/kg)
- qmax is the maximum amount of adsorbate that can be adsorbed per unit mass of the adsorbent (kg/kg)
- K is the Langmuir constant (mmHg^-1)
- P is the partial pressure of the adsorbate (mmHg)
We can use the Langmuir isotherm equation to find the value of K and qmax:
At a partial pressure of 10 mmHg:
0.1 = qmax x 10/(1 + K x 10)
At a partial pressure of 100 mmHg:
0.4 = qmax x 100/(1 + K x 100)
Dividing the two equations above, we get:
0.4/0.1 = (qmax x 100/(1 + K x 100))/(qmax x 10/(1 + K x 10))
4 = (1 + K x 10)/(1 + K x 100)
Solving for K, we get:
K = 0.0333 mmHg^-1
Substituting the value of K and the given partial pressure of 50 mmHg in the Langmuir isotherm equation, we get:
q = qmax x 50/(1 + 0.0333 x 50)
q = 0.299 kg acetone/kg activated carbon
Therefore, the amount of acetone adsorbed at a partial pressure of 50 mmHg and 30oC is 0.30 kg acetone/kg activated carbon. Hence, option (c) is the correct answer.
- Adsorption of acetone on activated carbon follows Langmuir isotherm.
- At 30oC, the amounts of acetone adsorbed at partial pressure of 10 and 100 mmHg are 0.1 and 0.4 kg acetone/kg activated carbon, respectively.
To find:
- The amount of acetone adsorbed (in kg per kg of activated carbon) at a partial pressure of 50 mmHg and 30oC.
Solution:
The Langmuir isotherm is given as:
π = ππππ₯π/(1 + πΎπ)
where,
- q is the amount of adsorbate adsorbed per unit mass of the adsorbent (kg/kg)
- qmax is the maximum amount of adsorbate that can be adsorbed per unit mass of the adsorbent (kg/kg)
- K is the Langmuir constant (mmHg^-1)
- P is the partial pressure of the adsorbate (mmHg)
We can use the Langmuir isotherm equation to find the value of K and qmax:
At a partial pressure of 10 mmHg:
0.1 = qmax x 10/(1 + K x 10)
At a partial pressure of 100 mmHg:
0.4 = qmax x 100/(1 + K x 100)
Dividing the two equations above, we get:
0.4/0.1 = (qmax x 100/(1 + K x 100))/(qmax x 10/(1 + K x 10))
4 = (1 + K x 10)/(1 + K x 100)
Solving for K, we get:
K = 0.0333 mmHg^-1
Substituting the value of K and the given partial pressure of 50 mmHg in the Langmuir isotherm equation, we get:
q = qmax x 50/(1 + 0.0333 x 50)
q = 0.299 kg acetone/kg activated carbon
Therefore, the amount of acetone adsorbed at a partial pressure of 50 mmHg and 30oC is 0.30 kg acetone/kg activated carbon. Hence, option (c) is the correct answer.
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At 30oCthe amounts of acetone adsorbed at partial pressure of 10 and 100 mmHgare 0.1 and0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes theadsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kgof activated carbon) at a partial pressure of 50 mmHg and 30oC?a)0.23b)0.25c)0.30d)0.35Correct answer is option 'C'. Can you explain this answer?
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At 30oCthe amounts of acetone adsorbed at partial pressure of 10 and 100 mmHgare 0.1 and0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes theadsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kgof activated carbon) at a partial pressure of 50 mmHg and 30oC?a)0.23b)0.25c)0.30d)0.35Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about At 30oCthe amounts of acetone adsorbed at partial pressure of 10 and 100 mmHgare 0.1 and0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes theadsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kgof activated carbon) at a partial pressure of 50 mmHg and 30oC?a)0.23b)0.25c)0.30d)0.35Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At 30oCthe amounts of acetone adsorbed at partial pressure of 10 and 100 mmHgare 0.1 and0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes theadsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kgof activated carbon) at a partial pressure of 50 mmHg and 30oC?a)0.23b)0.25c)0.30d)0.35Correct answer is option 'C'. Can you explain this answer?.
At 30oCthe amounts of acetone adsorbed at partial pressure of 10 and 100 mmHgare 0.1 and0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes theadsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kgof activated carbon) at a partial pressure of 50 mmHg and 30oC?a)0.23b)0.25c)0.30d)0.35Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about At 30oCthe amounts of acetone adsorbed at partial pressure of 10 and 100 mmHgare 0.1 and0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes theadsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kgof activated carbon) at a partial pressure of 50 mmHg and 30oC?a)0.23b)0.25c)0.30d)0.35Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At 30oCthe amounts of acetone adsorbed at partial pressure of 10 and 100 mmHgare 0.1 and0.4 kg acetone/kg activated carbon, respectively. Assume Langmuir isotherm describes theadsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in kg per kgof activated carbon) at a partial pressure of 50 mmHg and 30oC?a)0.23b)0.25c)0.30d)0.35Correct answer is option 'C'. Can you explain this answer?.
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