The Question is from neet-zoology microbes-in-human-welfare , and it was created by the author K SUNKANNA

Question

A mixture of gases containing 0.2 moles of O2, 0.3 moles of N2, and 0.5 moles of H2 is collected at STP. If 20% of the H2 escapes due to a leak, what is the final volume occupied by the remaining gas mixture?

K SUNKANNA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Ideal Gas Law and Mole Concept
	**Related Topics**: Stoichiometry, Gas Laws
	**Prerequisites**: Understanding of STP conditions, mole calculations, and the ideal gas law.
## SOLUTION PATHWAY
**Given Information**:
	- 0.2 moles of $O_2$
	- 0.3 moles of $N_2$
	- 0.5 moles of $H_2$
	- 20% of $H_2$ escapes
	- STP conditions (Standard Temperature and Pressure: T = 273.15 K, P = 1 atm)
**Method & Steps**:
	1. Calculate the initial total moles of gas:
		Reasoning:  The total number of moles initially present is the sum of the moles of each gas.
		Working: Total moles = moles of $O_2$ + moles of $N_2$ + moles of $H_2$ = 0.2 + 0.3 + 0.5 = 1.0 mole
	2. Calculate the moles of $H_2$ that escaped:
		Working: Moles of $H_2$ escaped = 20% of 0.5 moles = 0.20 * 0.5 = 0.1 moles
	3. Calculate the remaining moles of $H_2$:
		Working: Remaining moles of $H_2$ = Initial moles of $H_2$ - Escaped moles of $H_2$ = 0.5 - 0.1 = 0.4 moles
	4. Calculate the final total moles of gas:
		Working: Final total moles = moles of $O_2$ + moles of $N_2$ + remaining moles of $H_2$ = 0.2 + 0.3 + 0.4 = 0.9 moles
	5. Calculate the final volume using the ideal gas law at STP:
		Reasoning: At STP, 1 mole of any ideal gas occupies 22.4 L.
		Formula/Rule: $V = n 	imes 22.4$ L/mol (at STP)
		Working: $V = 0.9 	ext{ moles} 	imes 22.4 	ext{ L/mol} = 20.16$ L
		Result: Final volume = 20.16 L
## OPTION ANALYSIS
[A] :x: Incorrect. This represents the volume if no hydrogen escaped.
[B] ✓: Correct. This is the volume calculated based on the remaining 0.9 moles of gas.
[C] :x: Incorrect. This value is too low.
[D] :x: Incorrect. This value is too high and would represent more gas than initially present.
## LEARNING AIDS
	**Common Mistakes**:
		1. Forgetting to subtract the escaped $H_2$: Ensure you account for the change in moles due to the leak.
		2. Not using STP conditions: Remember that 1 mole of an ideal gas occupies 22.4 L at STP.
	**Quick Tips**:
		1. At STP, the molar volume of any ideal gas is 22.4 L. This simplifies calculations.
		2. Remember to account for all changes in the number of moles when gases are added or removed.

K SUNKANNA · Answer

22.4 L

K SUNKANNA · Answer

The correct Option is "20.16 L"

K SUNKANNA · Answer

17.92 L

K SUNKANNA · Answer

24.64 L

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