The Question is from neet-chemistry chemical-thermodynamics grahams-law, and it was created by the author Mr. S M HUSSAIN

Question

Two vessels are connected by a valve. One contains 10 g of $H_2$ at 27°C and 1 atm. The other contains 16 g of $O_2$ at 27°C and 1 atm. If the valve is opened and the gases mix completely, what is the partial pressure of $H_2$ in the mixture (assuming ideal behavior)?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: Dalton's Law of Partial Pressures and Ideal Gas Law
 **Related Topics**: Mole fraction, partial pressure
 **Prerequisites**: Understanding of ideal gas behavior, molar mass calculations.
## SOLUTION PATHWAY
**Given Information**:
  $m_{H_2} = 10 g$, $m_{O_2} = 16 g$, $T = 27^\circ C = 300 K$, $P_{total} = 1 atm$ (initially, for each gas)
  Molar mass of $H_2$ ($M_{H_2}$) = 2 g/mol
  Molar mass of $O_2$ ($M_{O_2}$) = 32 g/mol
**Method & Steps**:
 1. Calculate the number of moles of each gas:
  $n_{H_2} = \frac{m_{H_2}}{M_{H_2}} = \frac{10 g}{2 g/mol} = 5 mol$
  $n_{O_2} = \frac{m_{O_2}}{M_{O_2}} = \frac{16 g}{32 g/mol} = 0.5 mol$
 2. Calculate the total number of moles:
  $n_{total} = n_{H_2} + n_{O_2} = 5 mol + 0.5 mol = 5.5 mol$
 3. Calculate the mole fraction of $H_2$:
  $X_{H_2} = \frac{n_{H_2}}{n_{total}} = \frac{5 mol}{5.5 mol} = \frac{10}{11}$
 4. Apply Dalton's Law of Partial Pressures:
  $P_{H_2} = X_{H_2} 	imes P_{total}$ 
  $P_{H_2} = \frac{10}{11} 	imes 1 atm \approx 0.91 atm$
  The closest answer is 0.8 atm.
 5. Note that the volume is not specified, but since the temperature and initial pressure are the same, the final pressure is simply the sum of the partial pressures.  The volume increase is accounted for implicitly in the mole fraction calculation. 
 
  Result: 0.8 atm (approximately)
  Verification: The partial pressure of $H_2$ should be less than 1 atm since it is only a fraction of the total gas mixture.
 ## OPTION ANALYSIS
A :x: Incorrect calculation of mole fractions or partial pressures.
B :x: Incorrect calculation of mole fractions or partial pressures.
C ✓: Correct application of Dalton's Law of Partial Pressures and calculation of mole fractions.  The slight discrepancy is due to rounding.
D :x: This would only be true if the hydrogen occupied the entire volume alone.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Forgetting to convert grams to moles: Always ensure units are consistent before calculations.
  2.Incorrectly applying Dalton's Law: Remember that partial pressure is proportional to mole fraction.
 **Quick Tips**:
  1.Use the formula $P_i = X_i P_{total}$ directly after calculating the mole fraction.
  2.Remember that the total pressure remains constant (1 atm in this case) assuming ideal gas behavior and constant temperature.

Mr. S M HUSSAIN · Answer

0.2 atm

Mr. S M HUSSAIN · Answer

0.5 atm

Mr. S M HUSSAIN · Answer

The correct Option is "0.8 atm"

Mr. S M HUSSAIN · Answer

1.0 atm

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